text:
\section{Introduction}

Multiscale modeling techniques that involve quantum-chemical methods\cite{szabo} are important tools widely used in many areas such as solution chemistry, catalysis, or enzymology.\cite{warshel, senn, brunk, tomasi1,tomasi2} Among them, hybrid quantum mechanics/molecular mechanics (QM/MM) approaches are especially important in reactive biochemical systems where the explicit treatment of the electronic structure as well as the handling of the environment, including several tens to hundreds of thousands of atoms, is mandatory.\cite{senn2, friesner, campomanes, campomanes2} Regardless of the progress in linear scaling\cite{zalesny} and parallelization of electronic-structure methods,\cite{skylaris} a fully quantum-mechanical (QM) treatment for such intrinsically large systems is not possible. Fortunately, a proper description of the electronic structure by quantum-chemical methods is only required for smaller regions of the system where, e.g., chemical processes take place. In turn, all the other parts of the system can be described effectively by some simplified approach, typically at the molecular-mechanical (MM) level by a classical force-field.\cite{ponder, oostenbrink, jorgensen}

In additive QM/MM approaches\cite{brunk} the Hamiltonian of the whole system is split into three parts:
\begin{equation}
\hat{H}_{\mathrm{tot}} = \hat{H}_{\mathrm{QM}} + \hat{H}_{\mathrm{MM}} + \hat{H}_{\mathrm{QM/MM}}.
\end{equation}
While $\hat{H}_{\mathrm{QM}}$ and $\hat{H}_{\mathrm{MM}}$ are the Hamiltonians of the QM and MM subsystem, the crucial part of any QM/MM implementation is a proper description of the coupling Hamiltonian $\hat{H}_{\mathrm{QM/MM}}$ of the two subsystems. The QM/MM coupling is usually done at one of three levels of complexity.\cite{senn, brunk} The simplest one is {\em mechanical embedding},\cite{senn3} where the QM/MM interactions are described at the MM level and therefore the electron density of the QM subsystem is not polarised by the MM subsystem. The use of pure QM and MM calculations makes this approach computationally advantageous, but prone to errors whenever the electron density of the QM subsystem is strongly polarised by the MM subsystem. The most popular coupling approach today is {\em electrostatic embedding}\cite{senn3} where the point charges of the MM subsystem are included in the one-electron Hamiltonian of the QM subsystem. This leads to a direct polarisation of the QM subsystem and usually a reasonable accuracy of its description. If electrostatic embedding is not enough to describe the coupling between the QM and MM subsystems, the final step is to use a {\em polarised embedding}\cite{senn3} approach, where the QM part is coupled to a polarisable force field, or to use hierarchical QM/QM layering.

The choice of QM method to be used used in a QM/MM simulation depends on the compromise between the accuracy needed for a given problem/system\cite{senn} and the computational resources available. Currently, methods based on density-functional theory\cite{parr,becke2} (DFT) are the most common choice, because of their favourable cost/accuracy ratio.\cite{senn, brunk, eichinger} Nevertheless, for some specific applications (e.g., involving photo-excited electronic states), the use of more accurate post-Hartree--Fock\cite{szabo} methods, such as M\o{}ller--Plesset perturbation theory,\cite{cremer} coupled-cluster theory,\cite{shavitt} or multiconfigurational methods, like complete active space self-consistent field (CAS-SCF),\cite{werner, shepard} is preferable.\cite{claeyssens, kongsted}

Having access to software offering a wide range of QM methods and different MM force fields would guarantee maximal flexibility in the choice of the most accurate and suitable QM/MM approach, as well as the possibility of consistent benchmarking for the least expensive approaches.
To date, there exist a number of packages that are optimised toward specific QM or MM methods. Therefore, universal, flexible QM/MM could be more effectively achieved by coupling those specialised software than by rewriting a monolithic package dealing with all possible QM and MM implementations. MiMiC\cite{mimic, mimic2} is a recently developed framework for multiscale modeling in computational chemistry showcasing the wanted flexibility for easy yet efficient interfacing among different programs, with only small adaptions in the individual codes. So far MiMiC offers a coupling between the plane-wave DFT\cite{marx} program CPMD\cite{cpmd} and the widely used classical molecular dynamics (MD) program GROMACS.\cite{gromacs1,gromacs2} In that implementation, MiMiC uses CPMD as the main driver for the MD and for the description of the QM subsystem.

In this work, we present a wavefunction-based QM/MM implementation by coupling the CFOUR program package\cite{cfour} to the MiMiC framework. This allows the use of Hartree--Fock (HF), post-HF methods, like second-order M\o{}ller--Plesset (MP2) and truncated coupled-cluster methods (e.g., CCSD and CCSD(T)), and multiconfigurational methods within both ab-initio MD (AIMD) and electrostatic-embedding QM/MM-MD. The use of CPMD as the main MD driver also offers access to a multiple time step (MTS) algorithm\cite{liberatore} in which we can directly combine DFT with wavefunction-based methods. The MTS algorithm together with a long-range electrostatic coupling scheme\cite{laio} reduces the computational cost and makes QM/MM-MD simulations with high-accuracy QM methods feasible.

The paper is organized as follows. In section \ref{theory} the implementation of the electrostatic interactions between the QM and MM subsystems in the quantum-chemical package CFOUR is described, before we discuss the coupling of CFOUR within the MiMiC framework. In section \ref{compdet} we outline the computational details of the test systems and the benchmark simulations. The results of these simulations are shown in section \ref{verification} where we demonstrate the computational stability and functionality of our implementation.

\section{Methods}\label{theory}

\subsection{QM/MM coupling Hamiltonian}

In the present QM/MM implementation, we use a full Hamiltonian electrostatic-coupling scheme, following ref. \citenum{laio}. The interaction Hamiltonian $\hat{H}_{\mathrm{QM/MM}}$ is split into a bonded and a nonbonded part:
\begin{equation}
\hat{H}_{\mathrm{QM/MM}} = \hat{H}_{\mathrm{bonded}} + \hat{H}_{\mathrm{nonbonded}}.
\end{equation}
The bonded part $\hat{H}_{\mathrm{bonded}}$ is only nonzero if the QM/MM boundary cuts through covalent bonds, and treated at the molecular mechanics level. In this case the QM atoms at the boundary are replaced by monovalent pseudopotentials.\cite{lilienfeld,senn,mimic}
The non-bonded interactions consist of van der Waals interactions, which are described by the classical force field, and electrostatic interactions. For the latter, we adapted and implemented the electronic-coupling scheme developed by Laio et al.\cite{laio} in CFOUR. Because of the cost of the explicit treatment of electrostatic interactions, the MM atoms are divided into short- and long-range terms. The short-range contribution takes into account the explicit interactions between the nuclei and electrons of the QM subsystem and the point charges of the MM subsystem. In contrast, the interactions between the MM atoms belonging to the long-range region and the QM subsystem are calculated through a multipole expansion of the electrostatic potential from the QM electrons. This is possible because of the local character of the QM electron density and the distance to the long-range MM atoms:\cite{laio}
\begin{equation}
\hat{H}_{\mathrm{QM/MM}}^{\mathrm{el}} = \hat{H}_{\mathrm{sr}} + \hat{H}_{\mathrm{lr}}.
\end{equation}
The short- and long-range regions are determined by a cut-off radius from the central QM part dividing the MM atoms into either region. This leads to the following short-range interaction Hamiltonian:
\begin{equation}\label{hsr}
\hat{H}_{\mathrm{sr}} =  - \sum_{i}^n \sum_{A}^{M_{\mathrm{sr}}} \frac{q_A}{|\boldsymbol{R}_A - \boldsymbol{r}_i|} +  \sum_{I}^N \sum_{A}^{M_{\mathrm{sr}}} \frac{q_A Z_I}{|\boldsymbol{R}_A - \boldsymbol{R}_I|}
\end{equation}
where the sums run over all short-range MM atoms $M_{\mathrm{sr}}$, all electrons $n$, and all nuclei of the $N$ QM atoms. Thus, $q_A$ and $\boldsymbol{R}_A$ are the point charge and coordinate of an MM atom, $\boldsymbol{r}_i$ is an electron coordinate, and $Z_I$ is the charge of a nucleus. This leads to an external potential that is included in the optimization of the wavefunction of the QM subsystem.

The forces on an MM atom and a QM nucleus due to the interactions between MM point charges and QM nuclei are given by the negative derivative of the second term in eq. \ref{hsr} with respect to the MM and QM coordinates, respectively:
\begin{equation}\label{nnforce1}
\boldsymbol{F}_{IA}(A) = \sum_I^N \frac{q_A Z_I}{| \boldsymbol{R}_A - \boldsymbol{R}_I |^3} (\boldsymbol{R}_A -\boldsymbol{R}_I)
\end{equation}
and
\begin{equation}\label{nnforce2}
\boldsymbol{F}_{IA}(I) = -  \sum_A^{M_{\mathrm{sr}}} \frac{q_A Z_I}{| \boldsymbol{R}_A - \boldsymbol{R}_I |^3} (\boldsymbol{R}_A - \boldsymbol{R}_I).
\end{equation}
The force on an MM atom due to its interaction with the QM electrons is given by the expectation value of the negative derivative of the first term in eq. \ref{hsr} with respect to the MM coordinates:
\begin{equation}\label{mmsrforce}
\boldsymbol{F}_{iA}(A) = \sum_{\mu\nu} D_{\mu \nu} \left\langle \chi_\mu \bigg\vert \frac{q_A}{|\boldsymbol{R}_A - \boldsymbol{r}|^3} (\boldsymbol{R}_A- \boldsymbol{r}) \bigg\vert \chi_\nu \right\rangle
\end{equation}
with the density matrix elements $D_{\mu\nu}$ and basis functions $\chi_\mu$ and $\chi_\nu$. The corresponding force on a QM nucleus is given by
\begin{equation}\label{qmsrforce}
\boldsymbol{F}_{iA}(I) =  \sum_{A}^{M_{\mathrm{sr}}} \sum_{\mu\nu} D_{\mu \nu} \left[ \left\langle \frac{\delta \chi_\mu}{\delta \boldsymbol{R}_I} \bigg\vert \frac{q_A}{|\boldsymbol{R}_A - \boldsymbol{r}|} \bigg\vert \chi_\nu \right\rangle + \left\langle \chi_\mu \bigg\vert \frac{q_A}{|\boldsymbol{R}_A - \boldsymbol{r}|} \bigg\vert \frac{\delta \chi_\nu}{\delta \boldsymbol{R}_I} \right\rangle \right].
\end{equation}
There are also implicit forces on the QM atoms due to the polarisation of the QM subsystem by the MM point charges and the consequent changes in the molecular orbitals.

In our implementation of the long-range interactions, we truncate the multipole expansion after the fourth order and only expand the electronic part of the electrostatic interactions. The interactions between QM nuclei and MM atoms in the long-range region are still calculated explicitly (compare eq. \ref{nnforce1} and \ref{nnforce2}). The multipole expansion (with the origin at zero) is given by
\begin{equation}\label{multe}
\begin{split}
\sum_i \sum_A \frac{q_A}{|\boldsymbol{R}_A - \boldsymbol{r}_i|} & = \sum_A q_A \Biggl[ C \frac{ 1}{|\boldsymbol{R}_A|} + \sum_\alpha \mu^\alpha \frac{ R_A^\alpha}{|\boldsymbol{R}_A|^3} + \frac{1}{2} \sum_{\alpha,\beta} \Theta^{\alpha \beta} \frac{R_A^\alpha R_A^\beta}{|\boldsymbol{R}_A|^5} \\
 & + \frac{1}{6} \sum_{\alpha, \beta, \gamma} \Omega^{\alpha \beta \gamma} \frac{ R_A^\alpha R_A^\beta R_A^\gamma}{|\boldsymbol{R}_A|^7} + \frac{1}{24} \sum_{\alpha, \beta, \gamma, \epsilon} \Phi^{\alpha \beta \gamma \epsilon} \frac{R_A^\alpha R_A^\beta R_A^\gamma R_A^\epsilon}{|\boldsymbol{R}_A|^9}   \Biggr]
\end{split}
\end{equation}
with charge $C$, dipole moment $\mu^\alpha$, quadrupole moment $\Theta^{\alpha \beta}$, octopole moment $\Omega^{\alpha \beta \gamma}$, and hexadecapole moment $\Phi^{\alpha \beta \gamma \epsilon}$ of the QM electron density. Here $\alpha$, $\beta$, etc.\ denote Cartesian components. Because of the use of atom-centered Gaussian-type orbital (GTO) basis functions in the QM part, we express the multipoles in an integral form. For the charge and the dipole moment the expressions have the following form:
\begin{equation}
C = \sum_{\mu, \nu} D_{\mu\nu}\langle \chi_\mu | \chi_\nu \rangle \qquad \mathrm{and} \qquad
\mu^\alpha = \sum_{\mu, \nu} D_{\mu\nu}\langle \chi_\mu | \alpha | \chi_\nu \rangle.
\end{equation}
The forces on the MM atoms and QM nuclei are calculated by differentiation of eq. (\ref{multe}) with respect to the coordinates of the long-range MM atoms $R_A$ and with respect to the coordinates of the QM nuclei $R_I$ at which the basis functions are centered. The expressions for the derivatives are given in the appendix together with the explicit form of the quadrupole moment $\Theta^{\alpha \beta}$, the octopole moment $\Omega^{\alpha \beta \gamma}$, and the hexadecapole moment $\Psi^{\alpha \beta \gamma \epsilon}$.

The calculation of the long-range energy contribution and forces is computationally much cheaper than the explicit calculation for the short-range region. This is the case, because the calculation of the multipoles (and their derivatives) is decoupled from the sum over MM point charges whereas for the short-range region a one-electron integral must be calculated individually for every MM atom (see eq. \ref{hsr} and \ref{mmsrforce}). The resulting reduction in the computational cost is shown in section \ref{sectionlr}.

\subsection{Interface to the MiMiC framework}

The CFOUR quantum-chemistry package was interfaced to the AIMD program CPMD and the classical MD package GROMACS through the MiMiC framework.\cite{mimic,mimic2} The MiMiC communication library is responsible for the exchange of all relevant information, like sending coordinates and charges of the MM atoms to CFOUR, and returning the calculated energy and forces necessary for each MD step via a message passing interface (MPI). The workflow of our QM/MM implementation is shown in figure (\ref{workflow}).
In this implementation CPMD is the MD driver, GROMACS calculates the MM and van der Waals QM/MM energy and forces, and CFOUR calculates the QM energy and forces. In contrast to the MiMiC-based QM/MM implementation in ref. \citenum{mimic}, where the electrostatic QM/MM interactions are calculated by MiMiC (transparent yellow box in figure \ref{workflow}), in the present implementation these contributions are calculated by CFOUR. This is done because of the integral form of these terms, which numerically strongly depends on the functional form of basis functions used in the QM region. All three programs run independently on their own compute nodes while MiMiC manages the communication and data exchange between the programs.

\begin{figure}
\includegraphics[width=0.80\textwidth]{workflow.pdf}\centering
\caption{Scheme of the QM/MM-MD workflow using CFOUR (QM), GROMACS (MM) and CPMD (MD driver) via the MiMiC framework.}
\label{workflow}
\end{figure}

\newpage

\subsection{Computational Details}\label{compdet}

To verify the QM/MM implementation, we used a small system consisting of one QM water molecule solvated by 1011 MM water molecules and a larger one consisting of one QM water molecule solvated by 12000 MM water molecules. The small and large systems are used for the analysis and validation of the short- and long-range coupling, respectively. All simulations were performed using the MiMiC framework coupling locally modified versions of GROMACS (version 2018) and CPMD (version 4.3), and a modified developer version of CFOUR. We also performed AIMD simulations on a single water molecule in vacuum that are used to compare with the solvated systems. For these AIMD simulations of water in vacuum, the starting geometries were obtained by a geometry optimization at the same level as the one used in the simulations, i.e., either HF, MP2, CCSD(T), or CAS-SCF(6,6) together with the cc-pVTZ\cite{dunning} basis set. In our case CAS-SCF(6,6) means an active space of 6 orbitals filled with 6 electrons for the CI calculation.

The liquid water systems for QM/MM-MD simulations were built and preequilibrated by classical MM-MD simulations. We filled boxes of 3.164$^3$ and 7.184$^3$ nm with 1012 and 12001 water molecules, respectively. The structures were minimized with a steepest-descent scheme until the maximum force was lower than $1000$ kJ $\cdot$ (mol $\cdot$ nm)$^{-1}$. After the minimization, a 100 ps (2 fs time step) simulation was run in the NVT ensemble. The initial velocities were assigned from a Maxwell distribution at a temperature of 300 K that was maintained by a modified Berendsen thermostat\cite{berendsen} using one coupling group and a time constant of 0.1 ps. After that, we ran a 100 ps (2 fs time step) simulation in the NPT ensemble at 1.0 bar using a Parrinello--Rahman\cite{parrinello} barostat with a time constant of 2 ps. The temperature was again controlled by a modified Berendsen thermostat at 300 K. Finally, we performed a 1 ns (2 fs time step) simulation run in the NVT ensemble, again at 300 K and with the same parameters as before. For all the preequilibration steps, we used periodic boundary conditions, a cutoff of 1.0 nm for the short-range electrostatic and van der Waals interactions using the Verlet\cite{pall} scheme and all bonds involving H-atoms were constrained using the LINCS algorithm\cite{hesslincs} and the rigidity of the water molecules is ensured by the SETTLE algorithm.\cite{miyamoto} The long-range electrostatic interactions were calculated using the particle-mesh Ewald\cite{essmann} (PME) method. As integrator, we used the leap-frog scheme.\cite{hockney} In this way, we obtained equilibrated liquid water systems with 1012 water molecules in a cubic box with dimensions of 3.116 nm for the extended simple point charge (SPC/E)\cite{berendsen2} water model and one with dimensions of 3.129 nm for the three points (TIP3P)\cite{jorgensen2} water model, as well as a large liquid water system with 12001 SPC/E water molecules in a cubic box with dimensions of 7.119 nm.

The Born--Oppenheimer approach was used for all AIMD and QM/MM-MD simulations.\cite{marx} The simulation times were approximately 12.1 ps (50000 time steps of 10 a.u.). The AIMD simulations were initialized to a temperature of 1 K and the QM/MM-MD simulations on liquid water were initialized to a temperature of 300 K and none of the systems were coupled to a thermostat (NVE ensemble).

The MM subsystem was described by the TIP3P and the SPC/E water models. As in the preequilibration, periodic boundary conditions were applied for the MM subsystem, a cutoff of 1.5 nm was used for the short-range electrostatic, and van der Waals interactions together with a PME scheme for the long-range electrostatic interactions.

The QM subsystem was described by either plane-wave (PW) based DFT (PW-DFT) or a wavefunction-based method. In case of PW-DFT, we used the BLYP exchange--correlation functional\cite{becke,lee} with Troullier--Martins norm-conserving pseudopotentials.\cite{troullier} We used isolated system conditions for the QM subsystem and the Tuckerman \& Martyna\cite{martyna} scheme to solve Poisson's equation. The cell size was 30 a.u.\ and we used a PW cutoff of 100 Ry. For the SCF optimization, a convergence criterion of $10^{-5}$ a.u.\ for the gradient of the orbitals was used.
In case of wavefunction-based methods, the correlation consistent cc-pVTZ basis\cite{dunning} was used in all cases. The SCF convergence criterion was $10^{-9}$ a.u.\ for the density matrix and, in case of the CCSD(T) calculations, convergence criteria of $10^{-7}$ a.u.\ were used for the CC- and lambda equations.

All electrostatic QM/MM interactions on the system with 1012 water molecules were computed without periodic conditions using the short-range coupling for the entire system. For the system with 12001 water molecules, both short- and long-range electrostatic interactions were used with different cutoff distances.
The dipole moment of the QM system was calculated on the fly at every step of the simulations. For the analysis of the systems and evaluation of properties, the last 30000 steps of the simulations were used.

\clearpage

\section{Results}

\subsection{Validation}\label{verification}

\subsubsection{Energy conservation}\label{energycons}

Conservation of the energy during a simulation is an important indicator of a stable AIMD or QM/MM-MD implementation and guarantees that the interface is suitable to sample a thermodynamic ensemble. Therefore, we investigated the profile of the energy as well as the deviation from the average energy per particle during a NVE simulation of one water molecule in the gas phase. The results for the AIMD simulations using HF, MP2, CCSD(T), and CAS-SCF(6,6) are shown in the top part of figure (\ref{nrg_fig}).
\begin{figure}[ht!]\centering
     \includegraphics[width=\textwidth]{nrg_cons.png}
    \caption{Total energy of a single water molecule (top part) and of the QM/MM system with 1012 water molecules (bottom part) simulated within the NVE ensemble using HF, MP2, CCSD(T), and CAS-SCF(6,6) with the cc-pVTZ basis to model the QM water molecule and SPC/E for all MM water molecules. The insets show the fluctuation of the total energy per atom for the respective system.}
    \label{nrg_fig}
\end{figure}
The energy deviation is calculated by $ \Delta E(t) = E(t) - \langle E \rangle $. For all QM methods, the energy fluctuation is very small and there is no visible drift in the energy. For CAS-SCF(6,6) comparatively larger fluctuations for the single water molecule are observed, but with a standard deviation of $2.4 \cdot 10^{-8}$ a.u.\ they anyway remain within negligible values.

We also examined the energy fluctuation for the QM/MM-MD simulations using HF, MP2, CCSD(T), and CAS-SCF(6,6) for the QM water molecule solvated by 1011 classical SPC/E water molecules. The results are shown in the bottom part of figure (\ref{nrg_fig}). Also in this case, the energy fluctuations are very small and no significant drift in the energy is seen. The standard deviation of the energy per particle is $3.7 \cdot 10^{-5}$ a.u.\ for HF, $4.0 \cdot 10^{-5}$ a.u.\ for MP2, $4.9 \cdot 10^{-5}$ a.u.\ for CCSD(T), and $2.7 \cdot 10^{-5}$ a.u.\ for CAS-SCF(6,6). These results show that our AIMD and QM/MM-MD implementation enables stable simulations using various wavefunction-based QM methods.

\subsubsection{Polarisation of the QM region}\label{dipole}

An important aspect in QM/MM approaches is the description of the effect of the MM environment on the structure and polarisation of the QM part.\cite{cascella} To test that, we investigated two properties as indicators of the quality of the QM/MM coupling, namely, the dipole moment of one QM water molecule surrounded by 1011 SPC/E water molecules, and its radial distribution function\cite{soper} (RDF).

In contrast to classical MM-MD simulations, QM/MM-MD (and AIMD) simulations give detailed information about the electronic structure of the solute. Thus we can analyse bonding and electronic properties such as the dipole moment.

\begin{table}[ht]\centering\scriptsize
\begin{threeparttable}
\caption{Dipole Moment of a QM Water Molecule\textsuperscript{\emph{a}}}
\label{tab_dipole}
\begin{tabular}{lllllll}
\toprule \toprule
 method & HF & MP2 & CCSD(T) & CAS(6,6) & BLYP & exp. \\
 \midrule
single-point		 & 	1.988		&	1.936	&	1.916	&	1.935	&	1.814	&	1.847 $\pm$ 0.001 \cite{clough}		\\
AIMD (in vacuo) 		&	1.988 $\pm$ 0.004	&1.936 $\pm$ 0.004	&1.916 $\pm$ 0.004	&	1.909 $\pm$ 0.031	&	1.846 $\pm$ 0.005 &	\\
QM/MM (SPC/E)	&	2.694 $\pm$ 0.160	&2.742 $\pm$ 0.145&2.765 $\pm$ 0.166	&	2.624 $\pm$ 0.177&	2.720 $\pm$ 0.169	&	2.9 $\pm$ 0.6\cite{badyal}	\\
QM/MM (TIP3P) &	2.732  $\pm$ 0.146		&2.692  $\pm$ 0.166	&	2.632  $\pm$ 0.168		&	2.755 $\pm$ 0.157	& 2.699	$\pm$ 0.200	& \\	\bottomrule  \bottomrule
\end{tabular}
\textsuperscript{\emph{a}} The dipole moment (in Debye) is obtained from single-point QM calculations as well as AIMD (at 1~K) and QM/MM-MD simulations (at 300~K) using the cc-pVTZ basis for the wavefunction-based QM methods. Standard deviations are given for the dipoles obtained from MD simulations.
\end{threeparttable}
\end{table}

It is well known that the polarisation of the electronic structure of a water molecule in liquid water leads to an increase of the dipole moment compared to the gas phase.\cite{silvestrelli,grubskaya,liu,scipioni,badyal}
To get a reference for the dipole moment of an unpolarised water molecule, we performed AIMD simulations of a single water molecule as well as single-point calculations on the geometry-optimized structure. For a polarised water molecule, we calculated the average dipole moment of the QM water molecule from the QM/MM-MD trajectories of the small liquid water system. The results are shown in table (\ref{tab_dipole}). The single-point and average dipole moments of gaseous water are the same (minor deviation for CAS-SCF and DFT), as expected, and it is again a good indication that the AIMD implementation works well. All gas-phase values agree well with the experimental value, within the approximation associated to their respective level of theory.

The dipole moment of a water molecule in the liquid phase obtained from the QM/MM-MD simulations are, for every QM method, much larger than the gas-phase dipole moment. This is mainly a result of the polarisation of the electronic structure due to the environment. The dipole moments of the two SPC/E and TIP3P classical water models are only slightly different ($2.351$ D for SPC/E\cite{berendsen2} and $2.344$ D for TIP3P\cite{jorgensen2}), and produce a similar polarisation of the QM water (Table~\ref{tab_dipole}). For both classical models, the standard deviation of the dipole moment of the QM water is quite large. The significant shift in the average value of the water dipole from gas to liquid phase, and the large fluctuations of the dipole moment during the simulation indicate that our implementation correctly captures the very strong coupling between the electronic density and the  surrounding mobile classical charges.
The obtained values are somewhat smaller than the experimental value but still well within the uncertainty and also match well with other theoretical studies of the dipole moment of liquid water.\cite{silvestrelli,grubskaya,liu,scipioni,badyal}
Since our QM/MM implementation only considers the polarisation of the QM subsystem due to the MM subsystem using water models with fixed dipole moments that are in general smaller than the experimental values, it is plausible to find that also the dipole moment of the QM water is smaller than the experimental one. In general, quantitatively better results
 for liquid water require that mutual polarisation and other effects between the central and the surrounding waters are taken into account. These include (among others) charge transfer and better descriptions of Pauli repulsion and dispersion. Therefore, either larger QM regions or a more advanced water model would be needed, for example polarisable variants like the MB-pol\cite{reddy} force-field, which is constructed including many-body terms calculated at the CCSD(T)/CBS level of theory.

\begin{figure}[hbt]
\centering
\includegraphics[width=0.95\textwidth]{new_rdf.png}
\caption{Oxygen--oxygen radial distribution function (RDF) between the QM and MM oxygen atoms at 300~K from QM/MM-MD simulations within the NVE ensemble using the SPC/E water model and from a pure MM-MD simulation with the SPC/E water model. The cc-pVTZ basis was used for the wavefunction-based QM methods.}
\label{rdf_spce}
\end{figure}

The structure of the QM water and its solvation shell was monitored by calculation of the RDF between the QM and MM oxygens.
The results for the different QM methods and for a pure SPC/E MM-MD simulation are shown in figure (\ref{rdf_spce}). For all QM methods, the distances of the first maximum is in very good agreement and for the second maximum still in good agreement with the experimental values\cite{soper,badyal} (see table (\ref{tab_rdf})). The overall shape of the RDF looks as expected, apart for some noisy features due to relatively poor sampling.
This agreement shows that the environment of the QM water molecule and especially the hydrogen-bonded neighbours are described well with our QM/MM implementation. Compared to the pure SPC/E model, the QM water appears to rigidify the local structure of its first neighbours, with a higher first peak, and a lower first minimum, regardless of the QM level of theory, in agreement with what has been observed in past studies on QM water models\cite{lin,lin2,miceli}.

\begin{table}[ht]\centering
\begin{threeparttable}
\caption{First and Second Peak of the Oxygen--Oxygen RDF\textsuperscript{\emph{a}}}
\label{tab_rdf}
\begin{tabular}{lccccccc}
\toprule \toprule
maxima & HF & MP2 & CCSD(T) & CAS(6,6) & BLYP & SPC/E & exp.\cite{soper} \\
 \midrule
1. $r_{\mathrm{OO}}$ & 2.82 & 2.80 & 2.81 & 2.80 & 2.81 & 2.89 & 2.8 \\
2. $r_{\mathrm{OO}}$ & 4.55 & 4.80 & 4.75 & 4.24 & 4.54 & 4.61 & 4.5  \\
\bottomrule  \bottomrule
\end{tabular}
\textsuperscript{\emph{a}} The distances (in \AA{}) for the first and second peak of the oxygen--oxygen radial distribution functions (RDFs) between the QM and MM oxygen atoms at 300~K are obtained from QM/MM-MD simulations within the NVE ensemble using the SPC/E water model. The cc-pVTZ basis was used for the wavefunction-based QM methods.
\end{threeparttable}
\end{table}

\subsubsection{Vibrational frequencies}

To test the quality and reliability of the dynamical properties obtained by our implementation, we calculated vibrational frequencies from MD  trajectories,\cite{thaunay,thomas,wang,vitale,silvestrelli2,praprotnik,liu,giovanni}
obtaining them from the Fourier transform of the dipole-moment autocorrelation function.\cite{thaunay,wang,thomas,vitale}

\begin{figure}[ht!]
    \centering
        \begin{subfigure}[h]{1.0\textwidth}
            \centering
            \includegraphics[width=\textwidth]{vib_spce.png}
            \caption{ }
            \label{ir_spce}
        \end{subfigure}\vspace{0.5cm}
        \begin{subfigure}[h]{1.0\textwidth}
            \centering\footnotesize
            \begin{tabular}{lcccccc}
                \toprule \toprule
                     Mode & SP & AIMD & QM/MM & \makecell{exp. gas \\ (harm.)\cite{toukan}} & \makecell{exp. gas \\ (fund.)\cite{lemus}} & \makecell{exp. liquid \\ (fund.)\cite{walrafen}}  \\
                 \midrule
                 bend & 	1667.3		&	1667.6	&	1772.0	&	1648 	&	1595		&	1640 \\
                 asym. stretch & 3858.3	&	3863.1	&	3477.5	&	3832		&	3657		&  3450	 \\
                 sym. stretch & 	3964.0	&	3969.1	&	3643.2	&	3943		&	3756		& 3615	 \\
                \bottomrule  \bottomrule
            \end{tabular}
            \caption{ }
            \label{tab_ir}
        \end{subfigure}
    \caption{IR spectra (a) and frequencies (b) of gaseous and liquid water obtained from single-point (SP) calculations as well as AIMD (at 1~K) and QM/MM-MD simulations (at 300~K within the NVE ensemble. The CCSD(T)/cc-pVTZ level of theory was used throughout and the SPC/E water model was used for QM/MM. Experimental harmonic and fundamental frequencies are included for comparison. Frequencies are given in cm$^{-1}$.}
    \label{vib_2}
\end{figure}

Figure (\ref{ir_spce}) reports the IR spectrum of gaseous and liquid water using the same trajectories as in section \ref{dipole}. For the gaseous water molecule, we also calculated single-point harmonic vibrational frequencies at the CCSD(T)/cc-pVTZ level to compare to the AIMD results and to experiment, shown in figure (\ref{tab_ir}). The frequencies derived from AIMD simulations agree well with the frequencies obtained from the single-point calculation and also with the harmonic experimental values. Because AIMD simulations ran at very low temperature (1~K) we expected negligible temperature effects and no appearance of anharmonic deviations. For the solvated water system dynamical environment effects are essential for the position and the shape of the IR peaks. The IR spectrum obtained from the QM/MM-MD simulation has the typical broad band around $3500-3700$ cm$^{-1}$ that is caused by hydrogen-bond interactions interfering with the stretching modes. The obtained frequencies for the two stretching modes (3477.5 cm$^{-1}$ and 3643.2 cm$^{-1}$) are in a reasonable agreement with the experimental values (3450 cm$^{-1}$ and 3615 cm$^{-1}$). The position of the bending mode (1772.0 cm$^{-1}$) is at a higher frequency than the experimental value (1640 cm$^{-1}$). The comparatively large blue shift of the bending mode indicates the relatively strong influence of the water model. The solvent induced blue shift of the bending mode and the red shift of the stretching modes are qualitatively well reproduced which is another indication of a correct implementation of the QM/MM interface.

\subsection{Speeding up simulations}\label{speedup}
The use of highly accurate quantum-chemical methods in MD simulations is computationally very expensive. Therefore it is important to find ways to reduce the cost and to increase the efficiency of the implementation. Here we present two methods implemented in the CFOUR interface to MiMiC to speed-up simulations.

\subsubsection{Long-range interactions}\label{sectionlr}

Hierarchical treatment of the long-range electrostatic coupling is an excellent strategy to reduce the time per MD step in the simulation.\cite{laio} In the present implementation, the long-range electrostatic interactions are implemented in the CFOUR code, because of the integral form of the multipoles and their derivatives and the use of atom-centered GTO basis functions in the QM part. To investigate the effectiveness of the new implementation in reducing the computational cost, as well as the dependence of the numerical accuracy on the number of MM atoms in the short-range region, we performed single-point QM/MM calculations and QM/MM-MD simulations of one QM water molecule surrounded by 12000 SPC/E water molecules, which is a typical system size in studies of enzymatic reactions, using different cutoff distances $d_{\mathrm{cut}}$. The accuracy of the QM and QM/MM energy and forces as well as the dipole moment of the QM subsystem is tested by single-point calculations. The MD simulations show the stability of the long-range implementation and of the obtained properties. We compared the obtained values with calculations where all MM atoms are in the short-range region.

\begin{figure}[ht!]\centering
     \includegraphics[width=1.0\textwidth]{lr_sp.png}
    \caption{Convergence of the a) energy, b) forces, and c) dipole moment, and the d) absolute time with respect to the number of MM atoms in the short-range region for the calculation of the short- and long-range electrostatic QM/MM interactions in a single-point HF/cc-pVTZ calculation on one snapshot of a water system with 12001 water molecules. The reference is a calculation with all MM atoms in the short-range region. The energy in a) is the full QM energy plus the electrostatic QM/MM interaction energy. In b) the mean absolute error of the AIMD and electrostatic QM/MM forces on four different groups of atoms is shown (the three QM atoms, the three short-range MM atoms nearest the center of mass of the QM subsystem, the three nearest long-range MM atoms, and the three farthest long-range MM atoms). Plot c) shows the dipole moment of the QM subsystem and d) shows the relative time for the calculation of the QM/MM interactions (energy and forces).}
    \label{sp_lr}
\end{figure}

Figure (\ref{sp_lr}) shows the results of the single-point calculations. The convergence criterion for the density matrix in the solution of the HF equations for the single-point calculations was $10^{-12}$ a.u.\ which is much tighter than what we usually use in QM/MM-MD simulations ($10^{-7}$ - $10^{-9}$ a.u.).
It is seen that the errors are small for all numbers of MM atoms in the short-range region except of very low numbers (less than 5-10 $\%$ short-range atoms). We achieve an accuracy of about $10^{-9}$~a.u.\ for the energy by including only $10$ $\%$ of the MM atoms in the short-range region. This error is negligible compared to the fluctuations of the energy because of the time discretization error and thermal energy fluctuations at 300~K (compare \ref{energycons}).  Including more atoms in the short-range region improves the energy only slightly. The full convergence to the short-range value is only achieved if nearly all atoms are included.
This behaviour is also seen for the forces on the different groups of atoms, except for the three long-range atoms that are furthest from the QM subsystem, where the force is already exact even for very few short-range atoms. For the dipole moment the accuracy is about $10^{-8}$~D with $10$ $\%$ short-range atoms. This accuracy is sufficient for QM/MM-MD simulations where we usually use convergence criteria of similar magnitude. Thus, the number of MM atoms in the short-range region that are needed to guarantee stable simulations with the same accuracy as pure short-range simulations is about $10$ $\%$ for this system ($3600$ atoms). Nevertheless, this number can be different for other systems, e.g., with a larger or differently shaped QM subsystem, and should therefore be checked before performing a simulation. Figure (\ref{sp_lr}d) shows the reduction in computational cost for the electrostatic QM/MM interactions.
As expected, the time for the short-range interactions increases linearly with the number of MM atoms in the short-range region. The time for the calculation of the long-range interactions is negligible in comparison to the time spent calculating the short-range interactions and increases only slightly with increasing number of long-range MM atoms. For example, the calculation of the short-range QM/MM interactions with all MM atoms in the short-range region took 102 seconds. The calculation of the QM/MM interactions with only $4000$ atoms ($11$~$\%$) short-range MM atoms took $9$ seconds, thereof only $0.3$ seconds were needed for the calculation of the long-range QM/MM interactions. Therefore, as expected, also in the present implementation the use of long-range interactions drastically reduces the computational cost without any significant loss of accuracy.

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{lr_sim.png}\centering
\caption{Fluctuation of the energy per particle for different cutoff distances for the long-range coupling. The system consisting of 12001 water molecules was simulated within the NVE ensemble at the HF/cc-pVTZ level of theory and using the SPC/E water model.}
\label{sim_lr}
\end{figure}

The fluctuation of the energy during a QM/MM-MD simulation with different cutoff distances is shown in figure (\ref{sim_lr}). There is a drift of the energy for the $5$ a.u.\ cutoff distance. No drift is observed for all other cutoff distances and the fluctuations are very small and of the same magnitude as for the full short-range coupling case. The standard deviation of the fluctuations of the energy per particle is between $3.0 \cdot 10^{-4}$ and $7.0 \cdot 10^{-5}$ a.u.\ for the different cutoff distances (excluding the $5$ a.u.\ cutoff). This shows that a cutoff distance of $7.5$ a.u.\ (which is only 35-50 MM atoms in the short-range region) is enough for a stable simulation. However, this would affect the accuracy compared to a full short-range treatment as discussed earlier. For comparison, a cutoff distance of $35-40$ a.u.\ corresponds to $10$ $\%$ MM atoms in the short-range region.

Table (\ref{lr_dip}) shows the average dipole moment and associated standard deviation for different cutoff distances. The dipole moments are all in the same range and within the standard deviation of the full short-range coupling case. They should converge to the same value when simulating long enough considering the precision given in the table and the accuracy that can be obtained (see figure (\ref{sp_lr}c)). This shows that even small cutoff distance like $10$ a.u., where only 60-90 MM atoms are in the short-range region, can be sufficient to adequately describe the polarisation of the electronic structure of the QM region.

\begin{table}[ht]\centering
\begin{threeparttable}
\caption{Dipole Moment of the QM Water Molecule\textsuperscript{\emph{a}}}
\label{lr_dip}
\begin{tabular}{lrrrrrrrrr}
\toprule \toprule
 $d_{\mathrm{cut}}$  & 5 & 7.5 & 10 & 20 & 30 & 40 & 50 & 80 & only sr \\
 \midrule
 $\mu$      & 2.811   & 2.639  & 2.753  & 2.637  & 2.748   &  2.692  & 2.706  & 2.719  &  2.711  \\
$\sigma$    &  0.147  & 0.150  & 0.150  & 0.144  &  0.181  &  0.185  & 0.154  & 0.171  &  0.178   \\
\bottomrule  \bottomrule
\end{tabular}
\textsuperscript{\emph{a}} The average dipole moment and associated standard deviation (in D) of the QM water molecule in the system with 12001 water molecules is obtained from a QM/MM-MD simulation at the HF/cc-pVTZ level of theory and using the SPC/E water model. The values are obtained for different cutoff distances for the long-range coupling and compared with the full short-range case.
\end{threeparttable}
\end{table}

\subsubsection{QM/QM multiple time step dynamics}\label{sectionmts}

Another method to speed-up the simulation is the use of an MTS algorithm.\cite{martyna,tuckerman,liberatore} This reduces the number of calculations needed at the high-accuracy quantum-chemical level. Because the maximum time step $\delta t$ used in the integration of the equation of motion is limited, MTS algorithms separate different degrees of freedom which can be integrated at different rates. The MTS algorithm implemented in CPMD\cite{liberatore} is an adaptation of the rRESPA\cite{tuckerman2} scheme and enables the use of a combination of quantum-chemical methods within a simulation. Here we explore the combination of BLYP and CCSD(T). Instead of using CCSD(T) in every step of the simulation, we use BLYP as the reference method, while CCSD(T) is used only at larger time steps as a correction.

\begin{figure}[hbt]
\includegraphics[width=1.0\textwidth]{mts_vib.png}\centering
\caption{Vibrational spectra of hydrogen fluoride in vacuum obtained from AIMD simulations at the combined CCSD(T)/cc-pVTZ and BLYP/PW levels of theory with CCSD(T)/cc-pVTZ calculations only every $n$th step where $n = 2, 4, 6, 10, 15,$ or $20$. Frequencies are given in cm$^{-1}$.}
\label{hf_mts}
\end{figure}

We performed AIMD simulations on hydrogen fluoride, which has only one vibrational mode so that no other effects can interfere, to investigate the use of the MTS scheme within our implementation. To obtain reference data, we first performed simulations with a standard time step of 10 a.u.\ ($\approx$ 0.2 fs) at the CCSD(T)/cc-pVTZ or BLYP/PW levels of theory. Then, we performed simulations at the BLYP/PW level of theory with the use of CCSD(T)/cc-pVTZ calculations every $n$th time step (the MTS factor $n$ being $2, 4, 6, 10, 15,$ or $20$) as well as a simulation at the CCSD(T)/cc-pVTZ level of theory with a time step of 50 a.u.\ ($\approx$ 1.2 fs) to demonstrate that a CC simulation with an increased time step without any reference forces at lower level does not reproduce the correct value. The obtained spectra are given in figure (\ref{hf_mts}) and the energy fluctuations for the MTS simulations are given in the appendix.

The frequency obtained from BLYP/PW and CCSD(T)/cc-pVTZ simulations using the 10 a.u.\ time step differ substantially as expected. All BLYP/CCSD(T) MTS-MD simulations, except for the one with the largest MTS factor of 20, reasonably reproduce the pure CCSD(T) frequency. The simulation with an MTS factor of 4 has a deviation of $+6$ cm$^{-1}$ and the simulation with the MTS factor of 10 has a deviation of $-4$ cm$^{-1}$. The other simulations have deviations smaller than $\pm1$ cm$^{-1}$. However, the simulation with the largest MTS factor does not give reasonable results. Also the CCSD(T)/cc-pVTZ simulation with a time step of 50 a.u.\ does not reproduce the correct frequency because the time step is to large to describe the vibrational mode of hydrogen fluoride. Remarkably, the BLYP/CCSD(T) MTS-MD simulation can reproduce the pure CCSD(T) frequency even though a CCSD(T) calculation is only performed every 15th step (150 a.u. or $\approx$ 3.6 fs). All MTS-MD simulations reproduce the coupled-cluster average bond length of HF of $0.916 \pm 0.002~\AA$. Even the simulation with $n=20$, with an average bond length of $0.9120 \pm 0.03~\AA$,  reproduces reasonably well the CC value.

\begin{figure}[hbt]
\includegraphics[width=1.0\textwidth]{mts_bond.png}\centering
\caption{Fluctuation of the bond length of hydrogen fluoride in vacuum obtained from AIMD simulations at the combined CCSD(T)/cc-pVTZ and BLYP/PW levels of theory.}
\label{mts_bond}
\end{figure}

Figure (\ref{mts_bond}) shows the fluctuation of the bond length of hydrogen fluoride. Panel a) shows that in the MTS simulation a correction due to the CC calculations is introduced. These corrections appear in the dynamics as fast oscillations along the CC trajectory with a period corresponding to that of the correction rate. The oscillation of the correction and the physical oscillation remain well separated until the MTS factors are small enough, but for an MTS factor of $n=20$ the interval for the corrections is too big to reproduce the CC trajectory. The vibration introduced by the correction steps can also be seen in the obtained vibrational spectra. The MTS factor $n=2$ corresponds to a very high correction frequency of 68900 cm$^{-1}$. The correction frequency for the MTS factor of $n=20$ is at 6890 cm$^{-1}$ which is rather close to the hydrogen fluoride vibration. The critical value for the MTS correction to well reproduce the  CCSD(T) vibrational frequency is n=15 (with a correction frequency of 9187 cm$^{-1}$). Considering that one period of the hydrogen fluoride vibration takes around 33 time steps, we deduce that the MTS factor should be at least smaller than half of the period of the fastest vibrational mode that needs to be accurately reproduced. This is in agreement with the literature describing limitations of the MTS procedure and possible solutions to the resonance problem.\cite{liberatore, minary, leimkuhler, morrone}

Another limitation to the maximum speedup of the method described by Liberatore et al.\cite{liberatore} is the increased number of SCF cycles needed in the wavefunction optimization in the correction steps for larger MTS factors. In our case this is negligible. The relative speedup for the simulation with the MTS factor $n=20$ is 19.78. This has two reasons: The number of the SCF cycles increases only slightly from 9/10 cycles in the case of a pure CCSD(T) simulation to 10/11 in the case of the simulation with MTS factor $n=20$. Furthermore, the time needed for the optimization of the wavefunction is negligible compared to the time needed for solving the CC equations which is independent of the initial guess of the wavefunction.

This means that a substantial speedup of the simulation can be achieved with little to no loss in accuracy using MTS. However, the magnitude of the speedup can differ for bigger and more complicated systems and according to the different properties for which a higher-level correction is required.

\section{Summary and outlook}

We presented a wavefunction-based electrostatic-embedding QM/MM implementation enabled by the coupling of the CFOUR program package to the MiMiC framework. This allows the use of various QM methods like HF, MP2, CC, and CAS-SCF in AIMD and QM/MM-MD simulations. The implementation features an efficient long-range electrostatic coupling akin to the one in MiMiC but based on a GTO basis rather than a PW basis. The interface in CFOUR is based on a loose-coupling scheme facilitated by the light-weight MPI-based MiMiC communication library.

For AIMD and QM/MM-MD implementations using post-HF methods, the reduction of the computational cost is very important. We presented two methods that drastically reduce the computational cost without substantial loss of accuracy, namely a long-range coupling scheme and the use of a QM/QM MTS algorithm.

To verify the functionality and stability of our implementation, we performed simulations of gaseous water and a small and large liquid water system consisting of 1012 and 12001 water molecules, respectively, of which one molecule is treated by QM and the remainder by MM. The large water system was used for the investigation of the long-range electrostatic coupling. We showed that the energy fluctuations during an NVE simulation are very small and that the energy is conserved over time for all tested QM methods. The quality of the electrostatic coupling in QM/MM-MD simulations was investigated by comparison of RDFs, dipole moments, and vibrational frequencies. We showed that all of the mentioned properties agreed well with experimental data and with other theoretical studies.

With this coupling of CFOUR to MiMiC, we have an AIMD and QM/MM-MD implementation that is flexible in terms of the choice of QM method (e.g., DFT, MP2, CC, or CAS-SCF), and that has several methods to increase the computational efficiency of the simulations. The next step is to implement other quantum-chemical methods included in CFOUR like EOM-CC and to use the flexibility of the MiMiC framework to couple QM/MM-MD schemes with on-the-fly evaluation of molecular properties using a broad family of electronic-structure methods. Also, interfacing fast DFT-based AIMD codes to CFOUR, naturally opens to the further development of hierarchical QM/QM embedding schemes within MiMiC.

\section{Appendix}

\subsection{Multipole expansion for basis functions}

Here we give the explicit expressions for the multipoles used in eq. (\ref{multe}) and for the forces due to the long-range interactions. The integral form of the charge $C$, the dipole moment $\mu^\alpha$, the quadrupole moment $\Theta^{\alpha \beta}$, the octopole moment $\Omega^{\alpha \beta \gamma}$, and the hexadecapole moment $\Phi^{\alpha \beta \gamma \epsilon}$ of an electron density are

\begin{equation}
C = \sum_{\mu, \nu} D_{\mu\nu}\langle \chi_\mu | \chi_\nu \rangle,
\end{equation}

\begin{equation}
\mu^\alpha = \sum_{\mu, \nu} D_{\mu\nu}\langle \chi_\mu | \alpha | \chi_\nu \rangle,
\end{equation}

\begin{equation}
\Theta^{\alpha \beta} = \sum_{\mu, \nu} D_{\mu\nu}\langle \chi_\mu | 3 \alpha \beta - |\boldsymbol{r}|^2\delta_{\alpha \beta}  | \chi_\nu \rangle,
\end{equation}

\begin{equation}
\begin{split}
\Omega^{\alpha \beta \gamma} & = \sum_{\mu, \nu} D_{\mu\nu}\langle \chi_\mu | 15 \alpha \beta \gamma - 3|\boldsymbol{r}|^2\left(\gamma \delta_{\alpha \beta} + \beta \delta_{\alpha \gamma} +\alpha \delta_{\beta \gamma} \right) | \chi_\nu \rangle,
\end{split}
\end{equation}

and

\begin{equation}
\begin{split}
\Phi^{\alpha \beta \gamma \epsilon}  & =
 \sum_{\mu, \nu} D_{\mu\nu}\langle \chi_\mu | 105 \alpha \beta \gamma \epsilon + 3 |\boldsymbol{r}|^4\left(\delta_{\alpha \beta} \delta_{\gamma \epsilon} + \delta_{\alpha \gamma} \delta_{\beta \epsilon} + \delta_{\alpha \epsilon} \delta_{\beta \gamma} \right) \\
& - 15 |\boldsymbol{r}|^2\left( \alpha \beta \delta_{\gamma \epsilon} + \alpha \gamma \delta_{\beta \epsilon} + \beta \gamma \delta_{\alpha \epsilon} + \alpha \epsilon \delta_{\beta \gamma} + \beta \epsilon \delta_{\alpha \gamma} + \gamma \epsilon \delta_{\alpha \beta} \right) | \chi_\nu \rangle.
\end{split}
\end{equation}

The forces on the atoms are calculated via the negative derivative of the electrostatic potential $V_{iA}$ given in eq. (\ref{multe}) with respect to the coordinates of the long-range MM atoms $R_A$ and with respect to the coordinates of the QM atoms $R_I$ at which the basis functions are centered. The forces on the long-range MM atoms are given by

\begin{equation}\label{lrmmf2}
\begin{split}
F_{iA}^\alpha(A) = -\frac{\delta V_{iA}}{\delta R_A^\alpha} & = q_A \Biggl[ C \frac{R_A^\alpha}{|\boldsymbol{R}_A|^3} -   \mu^\alpha \frac{1}{|\boldsymbol{R}_A|^3} + \sum_\beta \mu^\beta \frac{3R_A^\alpha R_A^\beta}{|\boldsymbol{R}_A|^5} \\
 & - \sum_\beta \Theta^{\alpha \beta} \frac{R_A^\beta}{|\boldsymbol{R}_A|^5} + \sum_{\beta, \gamma} \Theta^{\beta \gamma} \frac{2.5 R_A^\alpha R_A^\beta R_A^\gamma}{|\boldsymbol{R}_A|^7} \\
 & - \sum_{\beta, \gamma} \frac{1}{2} \Omega^{\alpha \beta \gamma} \frac{R_A^\beta R_A^\gamma}{|\boldsymbol{R}_A|^7} + \sum_{\beta, \gamma, \epsilon} \frac{7}{6} \Omega^{\beta \gamma \epsilon} \frac{R_A^\alpha R_A^\beta R_A^\gamma R_A^\epsilon}{|\boldsymbol{R}_A|^9} \Biggr].
\end{split}
\end{equation}

The forces on the QM atoms at which the basis functions are centered are given by

\begin{equation}\label{lrqmf2}
\begin{split}
F_{iA}^\alpha(I) = -\frac{\delta V_{iA}}{\delta R_I^\alpha} & = \sum_A q_A \Biggl[ C^{\bar{\alpha}} \frac{ 1}{|\boldsymbol{R}_A|} + \sum_\beta \mu^{\beta,\bar{\alpha}} \frac{ R_A^\beta}{|\boldsymbol{R}_A|^3} + \frac{1}{2} \sum_{\beta, \gamma} \Theta^{\beta \gamma, \bar{\alpha}} \frac{R_A^\beta R_A^\gamma}{|\boldsymbol{R}_A|^5} \\
 & + \frac{1}{6} \sum_{\beta, \gamma, \epsilon} \Omega^{\beta \gamma \epsilon, \bar{\alpha}} \frac{R_A^\beta R_A^\gamma R_A^\epsilon }{|\boldsymbol{R}_A|^7} + \frac{1}{24} \sum_{\beta, \gamma, \epsilon, \kappa} \Phi^{\beta \gamma \epsilon \kappa, \bar{\alpha}} \frac{ R_A^\beta R_A^\gamma R_A^\epsilon R_A^\kappa }{|\boldsymbol{R}_A|^9}   \Biggr],
\end{split}
\end{equation}

with $C^{\bar{\alpha}}$, $\mu^{\beta,\bar{\alpha}}$, $\Theta^{\beta \gamma, \bar{\alpha}}$, $\Omega^{\beta \gamma \epsilon, \bar{\alpha}}$, and $\Phi^{\beta \gamma \epsilon \kappa, \bar{\alpha}}$ the derivatives of charge, dipole moment, quadrupole moment, octopole moment, and hexadecapole moment with respect to the coordinates of the QM atoms $R_I^\alpha$. $C^{\bar{\alpha}}$ and $\mu^{\beta,\bar{\alpha}}$ are given by
\begin{equation}
C^{\bar{\alpha}} = \frac{\delta C}{\delta R_I^\alpha} = \sum_{\mu, \nu} D_{\mu\nu} \left[ \left\langle \frac{\delta \chi_\mu}{\delta R_I^\alpha}  \bigg\vert \chi_\nu  \right\rangle + \left\langle \chi_\mu \bigg\vert \frac{\delta \chi_\nu}{\delta R_I^\alpha}  \right\rangle \right]
\end{equation}
and
\begin{equation}
\mu^{\beta,\bar{\alpha}} = \frac{\delta \mu^{\beta}}{\delta R_I^\alpha} = \sum_{\mu, \nu} D_{\mu\nu} \left[ \left\langle \frac{\delta \chi_\mu}{\delta R_I^\alpha}  \bigg\vert \beta \bigg\vert\chi_\nu  \right\rangle + \left\langle \chi_\mu \bigg\vert  \frac{\delta \beta}{\delta R_I^\alpha} \bigg\vert \chi_\nu  \right\rangle + \left\langle \chi_\mu \bigg\vert \beta \bigg\vert \frac{\delta \chi_\nu}{\delta R_I^\alpha}  \right\rangle \right].
\end{equation}
The other multipole derivatives are calculated in an analogous manner.

\subsection{Energy conservation for MTS simulations}

\begin{figure}[h!]\centering
     \includegraphics[width=0.85\textwidth]{mts_nrg_cons.png}
    \caption{Fluctuation of the total energy per atom for hydrogen flouride in vacuum obtained from AIMD simulations at the combined CCSD(T)/cc-pVTZ and BLYP/PW levels of theory with CCSD(T)/cc-pVTZ calculations only every $n$th step where $n = 2, 4, 6, 10, 15,$ or $20$.}
    \label{nrg_mts}
\end{figure}

Figure (\ref{nrg_mts}) shows the energy conservation in AIMD simulations at the combined CCSD(T)/cc-pVTZ and BLYP/PW levels of theory for the different MTS factors. The fluctuations of the energy increase with increasing MTS factor. The stepped structure arise from the corrections steps which lead to jumps in the energy. However, there is no drift in energy seen during the simulations.

\section{Acknowledgement}
The authors acknowledge funding by the Deutsche Forschungsgemeinschaft
(DFG) within the project B5 of the TRR 146 (Project No.
233630050). Authors also acknowledge the support of the Research Council of Norway through the CoE Hylleraas Centre for Quantum
Molecular Sciences (Grant No. 262695), and the Norwegian
Supercomputing Program (NOTUR) (Grant No. NN4654K).
J.M.H.O. acknowledges financial support from VILLUM FONDEN (Grant No. 29478).

redpajama_set_name: RedPajamaArXiv


text:
DOWNLOAD THE LATEST ISSUE OF ROOOAR MAGAZINE – FREE
8 Powerful Traits That Define a Strong Woman Leader
"Power is taking action in a moment that could make you feel powerless. Never let anyone define you. Only you define who you are."
– Ginni Rometty, Chief Operating Officer, IMB
Although there have been many influential women throughout history, from Amelia Earhart to Rosa Parks, the rise of the strong woman leader has become increasingly common in recent times, and for good reason!
These women disrupt gendered norms and enable equality not only within the workplace but also within the world. In doing so, they pave, the way for future generations of women.
So, what defines a powerful woman?
A confident leader tries her best, is good at what she does, and treats others with respect. There are many different traits which define strong leaders, but here are 8 of the most powerful ones.
Something about a strong woman leader draws attention from people around her and calls for respect. While most men can dedicate themselves entirely to their career or chosen goal, many women balance their jobs with caring for children and running households. This is a trait often seen in millennial women, who have proven time and time again that it's possible for a woman to have a successful career without sacrificing her personal life. She can embrace both parts of her life without putting one before another.
Male-dominated societies often mean that women work harder to prove themselves. But a strong leader will inspire other women to own the challenge of juggling their career while being a mum. She will act as a role model for emerging leaders and show younger generations that women can achieve anything that they set their mind to. Women who earn leadership roles in male-dominated societies are a great inspiration to other women who want to follow the same path, showing that these positions aren't out of reach.
Self-confidence is vital in reaching the top of any business ladder. A woman who is confident will have the courage to assert herself in a male-dominated workplace and achieve her goals. While confidence is a trait that doesn't always come naturally to everyone, it can be learnt through coaching and mentorship. Through coaching, women who are less self-confident can learn to recognise their worth, power and purpose, which will help give them the confidence to apply for leadership roles. This is necessary if we want to achieve gender diversity and parity in the workplace.
At the same time, a leader should balance confidence with compassion and fairness to ensure her rise to power is not achieved at the expense of others. Knowing who she is and what she wants gives a leader the confidence to achieve their goals. However, a good leader won't let this turn into overconfidence – she will know when to admit she needs help and will ask for it graciously. Humility and knowing her limits are equally crucial to confidence.
Strong leaders are honest and open to scrutiny. They welcome feedback and have a continuous desire to develop. When a leader is transparent, she builds trust with the people who work under her, allowing them to see both her strengths and weaknesses.
Honest leadership helps contribute to a deserved positive reputation. A leader sets an example for others by letting them know the truth-telling the truth with kindness is not always easy but is a discipline that will serve her well for the rest of her life.
Motivation from Vision
An inspirational leader worth following always has a clear plan of where she is going and how she intends to get there. She will be prepared to stand out on her own and even go against the flow sometimes. Leaders who think outside of the box and look at things differently inspire others to support them. Ambition is a strong motivating trait, but a good leader won't set unrealistic goals to override her natural integrity or sway her from her vision.
While every leader needs a clear plan, she also must be flexible with that plan as necessary. Strong leaders can discern when to let go of mindsets and ideas that don't work. A good leader listens to feedback and closely monitors their environment, adapting her tactics accordingly so she can keep progressing to her leadership goals.
A good leader is focused on what next steps they should take towards their goals. Many women are naturally articulate about their feelings and are good at accurately detecting the emotions of other people. A good leader can focus on the reactions of their team as well as the task at hand – and can empathize with even the most challenging people, understand their motives, and use this information to convince them to see problems and issues in a new light.
A leader should nurture and strengthen her emotional health so she can focus on your goals with minimal worries. A good leader is not taken aback by mistakes but is inspired to keep her efforts and actions consistent.
She leader knows how to look after herself and her team, listen carefully to good advice and learn from her mistakes. After looking after herself, a good leader will have the determination and the willpower to keep on striving to her leadership goals.
Hard work and perseverance are vital to obtaining a leading role and can only be achieved if the leader is genuinely passionate about what she is doing. A great leader's vision and passion will inspire her team to help achieve their shared goals.
Women who are filled with enthusiasm and love for their work will inspire both men and women to work harder alongside them.
guest writer:
Maia Fletcher is an aspiring creative writer who enjoys writing articles on all kinds of topics, from travel to home decor and sustainable living.
Find Maia at maiafletcher.wordpress.com
Form B2B To E-commerce
Whether you're new to business or a seasoned entrepreneur, most of us will be using technology to run and grow our businesses. For some it's easy peasy, for others it's their daily struggle. Doing what I do for a living, which involves managing Facebook ads, and...
Continue Binge Reading Our Latest Blogs
Technology: The Good, The Bad And The Ugly
As a marketing strategist who started my business in the social media early years, I've spent a lot of time using and observing technology and how it impacts us and our business. I've come to realise, now more than ever, there is good, bad, and ugly with technology....
Movers, Shakers And The Cookie Baker
At this point in time, I have lived my life 50/50 in the Philippines and Australia, I am determined to make a positive impact in both countries I consider my home. Through Baked by Erica, I endeavour to spread joy and happiness to everyone I meet through delicious...
THE ROOOAR ROOM
Roooar is fuel for fire, inspiration for growth, and that one place you can turn up where everyone just gets you.
Welcome, fierce female holding her own as an entrepreneur…
get the latest issue of roooar magazine free

redpajama_set_name: RedPajamaCommonCrawl


An n-tersection is defined as a location in n-dimensional space, n being a positive integer, having all non-negative integer coordinates. For example, the location (1,2,3) represents an n-tersection in three dimensional space. Two n-tersections are said to be adjacent if they have the same number of dimensions and their coordinates differ by exactly 1 in a single dimension only. For example, (1,2,3) is adjacent to (0,2,3) and (2,2,3) and (1,2,4), but not to (2,3,3) or (3,2,3) or (1,2). An n-teresting space is defined as a collection of paths between adjacent n-tersections. Finally, an n-credible maze is defined as an n-teresting space combined with two specific n-tersections in that space, one of which is identified as the starting n-tersection and the other as the ending n-tersection.
The input file will consist of the descriptions of one or more n-credible mazes. The first line of the description will specify n, the dimension of the n-teresting space. (For this problem, n will not exceed 10, and all coordinate values will be less than 10.) The next line will contain 2n non-negative integers, the first n of which describe the starting n-tersection, least dimension first, and the next n of which describe the ending n-tersection. Next will be a non-negative number of lines containing 2n non-negative integers each, identifying paths between adjacent n-tersections in the n-teresting space. The list is terminated by a line containing only the value –1. Several such maze descriptions may be present in the file. The end of the input is signalled by space dimension of zero. No further data will follow this terminating zero.
For each maze output it's position in the input; e.g. the first maze is "Maze #1", the second is "Maze #2", etc. If it is possible to travel through the n-credible maze's n-teresting space from the starting n-tersection to the ending n-tersection, also output "can be travelled" on the same line. If such travel is not possible, output "cannot be travelled" instead.


For this print, I was inspired by medieval stained glass designs. The repeated frame pattern is a variation from one that I saw at Beauvais Cathedral in France. The central design is a view of Mount Hood in Oregon. From a window I saw a beautiful view of the mountain with an orchard in the foreground and a clear dark sky behind. To stylize the mountain, I thought about looking at a stained glass window from the outside (one only sees dark lines of the leading). So I broke down the mountain into its simplest lines to create sense of leaded glass.
To the rest of the scene I added the clouds and the stream. My inspiration for the clouds came from Japanese woodblock prints that include long wisps of colorful clouds that slither across the sky. In my print, the speedy movement of clouds in contrasted with the slowly moving water of the stream.
Now on sale in my ETSY STORE!


Source And Destination Fields Are Blank On The Create Buy Order Movements With Best Itinerary Result Screen.
When running Order Release action "Order Management -> Manage Buy Order Movement -> Show Itineraries", the confirmation page displays the "Source" and "Destination" as empty instead of populating the actual values. Drilling down into the Order Movement shows that the Source and Destination are there. The problem is only on the action results screen.


text:
Q: Not able to see google map in intel xdk using Google Map API JS This is my first Google Map API project, and I am creating a transport app but unfortunately it does not work, earlier it was working but now it is only working in browser not on mobile and emulator.
In emulator it only shows Google logo and Terms Link.
I am using this reference google link
<script type="text/javascript" src="http://maps.google.com/maps/api/js?key=MYKEY&libraries=places"></script>

my JS CODE : (mapwork.js)
function currentpostionmap()
{
     if ( navigator.geolocation ) {

        function success(pos)
         {
             var latlng = new google.maps.LatLng(pos.coords.latitude, pos.coords.longitude);
             var myOptions = {
            zoom: 15,
            center: latlng,
            mapTypeId: google.maps.MapTypeId.ROADMAP
        };
        map = new google.maps.Map(document.getElementById("map"), myOptions);
          var image123 = 'https:///developers.google.com/maps/documentation/javascript/examples/full/images/beachflag.png';
             var bounds = new google.maps.LatLngBounds();
        marker = new google.maps.Marker({
            position: latlng,
            map: map,
            icon: image123

        });
              bounds.extend(latlng);
                    map.fitBounds(bounds);
//
                    multimarker(map);
//

        }
        function fail(error) {
           var latlng = new google.maps.LatLng(18.5204, 73.8567);
             var myOptions = {
            zoom: 10,
            center: latlng,
            mapTypeId: google.maps.MapTypeId.ROADMAP
        };
            map = new google.maps.Map(document.getElementById("map"), myOptions);

            marker = new google.maps.Marker({
            position: latlng,
            map: map

            });

        }
        // Find the users current position.  Cache the location for 5 minutes, timeout after 6 seconds
        navigator.geolocation.getCurrentPosition(success, fail, {maximumAge: 500000, enableHighAccuracy:true, timeout: 6000});
    }
}
function multimarker(map)
{
          jQuery.ajax({
    url: baseurl +  "getdriverlocation.php",

    async: true,
    success: function(data){
       var myArray = jQuery.parseJSON(data);// instead of JSON.parse(data)

        jQuery(myArray).each(function( index, element ) {
        driverlat = element.driver_lat;
        driverlng = element.driver_lng;
        locations.push([driverlat , driverlng])
});

 for (i  = 0; i < locations.length; i++)
                 {
                var latlng1 = new google.maps.LatLng(locations[i][0], locations[i][1]);

            drivermarker=new google.maps.Marker({position:latlng1});
            drivermarker.setMap(map);

           google.maps.event.addListener(drivermarker, 'click', (function(marker, i) {
            return function() {

            //DRIVER CLICK EVENT
        }
      })(drivermarker, i));

                 }

}

});

}
 function watchDriverPosition(userid)
{
    function success(pos)
    {
         window.setInterval(function(){
          saveDriverLocation(pos.coords.latitude, pos.coords.longitude,userid);
        }, 50000);
    }
    function fail()
    {
        alert ('Fail to watch drivers Position');
    }
    watchId = navigator.geolocation.watchPosition(success, fail, {maximumAge: 500000, enableHighAccuracy:true, timeout: 6000});

}
function saveDriverLocation(latc,lngc,userid)
{

     jQuery.ajax({
url: baseurl + "postdriverlocation.php",
data:'latitude='+latc +'&longitude='+lngc+'&login_id='+userid,
type: "POST",
success:function(response){
    response = $.trim(response);
    if (response == "false"){
       console.log(response);

  }else{
      console.log(response);
  }

},
error:function (){}
});
}

CALLING MAP FUNCTION HERE(main.js)
function showmap(usertype,userid)
    {
        if (usertype==1)
            {
                          changepage('#main');
                currentpostionmap();

            }
        else if (usertype==0)
            {

                watchDriverPosition(userid);

            }
        else{
            alert('You are not logged in.');
            changepage('#login');
        }
    }

It is working on Every browser but not on EMULATOR or MOBILE PHONE.
Please let me know why it is happening and provide a better solution
Thanks

A: Wrap your map code to
 $( document ).on( "pageshow", "#YOUR_MAP_PAGE", function() {

//your map code...

});

redpajama_set_name: RedPajamaStackExchange


text:
Ethos & Legal
Hospice Outreach Service (HOS)
Volunteering Your Time
Cancer Relief Centre Gibraltar
Welcome to the Cancer Relief Centre. We have been providing support to people living with cancer in the community for over 30 years. Here at the Centre, we understand that a diagnosis of cancer can be a life-changing event and we are here to help. All our services are free and are aimed at helping you and your family live life to the full. We are also here to support health care professionals in their roles. The Centre's services can be used by anyone affected by cancer, whether it is for a one-off chat or more continued support. We offer a warm, welcoming environment where you can always find someone to talk to, whatever your needs.
Our team is made of our hospice outreach service team, our Centre team, as well as trustees, senior management, administration, fundraising, and equipment maintenance. We work together to provide the highest quality care and services to our community.
Gráinne McKenna
Grainne McKenna – Charity CEO
Gráinne has been with the charity for seven years. She joined the Charity at the beginning of our redevelopment and restructuring period in 2013, which saw the establishment of charity services at the new Cancer Relief Centre. She was one of the charity's first clinical employees during this new phase and has naturally transitioned into her current role as CEO. She is credited for the development, delivery and management of the Centre's current services and operations. Under her guidance and vision the charity has grown into the organisation we are all so proud of today. Together with Cancer Relief's dedicated staff, volunteers, supporters and donors she works hard to continue to grow services and shape practices to secure our patients and their families the best care possible. Gráinne considers her role a great honour and holds value in the trust placed in her in shaping the charity's future.
Karen Richards
Karen Richards – Centre Nurse
Originally from Hartlepool, Karen began her nursing career serving in the QARNNS Royal Navy nursing service, after qualifying at Portsmouth University. After serving 9 years at various postings she left for motherhood and the first of her four children.
She continued nursing in a variety of positions across the UK before moving for the sunnier climates of the Mediterranean, working at RNH Gibraltar and PRMC until their closure in 2014 when she moved to St Bernard's Hospital. With over 30 years of nursing experience, Karen is enjoying her role as part of the CRC team.
Raynelah Osborne
Raynelah Osborne – Hospice Outreach Service (HOS) nurse
Ray joined the Cancer Relief in May 2020 and has come from looking after complex needs patients in the community setting across London and the Home Counties. Having trained at Guys & St Thomas Lane Fox unit, Ray developed her experience in invasive and non invasive home ventilation. Ray has previously worked in a Gibraltar as a registered nurse and has around 10 years experience in nursing. Ray is very passionate about end of life care and keen to get stuck into her new role.
Nic McCheyne
Nichola McCheyne – Operational & Clinical Services Administrator
Nic moved to Gibraltar in October 2018 searching for sunshine and an escape from the daily London commute. After completing a degree in European Business at Loughborough University Nic began a career in Consumer Research, most recently working as a Research Director, leading a team and managing several client accounts.
Nic started out as a volunteer at Cancer Relief and moved to work full-time within the team in March 2019 to support the operational and administration needs of the charity. Nic loves the varied nature of her work and the sunshine that not only shines on her daily commute but that the lovely team around her bring.
Laina Sultana
Angela Duthie
Laina Sultana – Marketing and Brand Officer
Laina is the marketing and brand officer at the centre who's just started in August 2022. She has recently graduated from Leeds Beckett University, completing a BA (Hons) in Marketing with Advertising Management. During the three years spent studying, Laina has gained multiple skills and knowledge within the field of marketing and is looking forward to applying them to her new role at such a meaningful charity. With the passion and now expertise Laina has for marketing, she hopes to use it towards to vision and goals of Cancer Relief and bring them to life. Laina is very excited to finally put what she has learnt in these three years to use and is eager to take on this new role as Marketing and Brand Officer.
Angela Duthie – Office admininistrator
Angela came to Spain in 2003 with her husband looking for a slower pace of life with that extra bit of sunshine. Three boys later in 2011 they decided to move to Gibraltar. In 2017 she decided to give up her fast-paced work life in gaming to spend more time with her family. She soon realising that she had some spare time on her hands to do something worthwhile which is where Cancer Relief came in. Angela volunteered with us for two years helping at our weekly day support days and absolutely loved the fact that she was able to give something back. When the role of office admin support became available, she couldn't refuse the opportunity to work with such an awesome team of people like Cancer Relief Gibraltar.
Dr. Bronwen James
Dr. Bronwen James – Hospice Outreach Service (HOS) Medical Lead
Bronwen James joined the Cancer Relief team officially in April 2019 but has been associated with them for several years. Bronwen, originally from Wales, qualified in 2007 following an intense 12 years of studying science, including a PhD in Neuroscience and then graduate medicine in Cambridge. She worked in London for her early training before moving to Gibraltar where she worked as a staff grade in the medical department of St Bernard's Hospital. She now works part time providing medical care to residents in the elderly residential services and as part of the HOS team, CRC. She gained her post graduate diploma in palliative medicine (distinction) in 2015 from Cardiff University and has recently gained her Specialty Certificate (SCE) in Palliative Medicine. She has a passion for delivering high quality hospice care and is involved in education & service development. She loves living in her adopted country and is committed to developing a centre of excellence for the people of Gibraltar. Outside of medicine she is mum to 2 small boys and enjoys running and being in the countryside.
Deborah Reason
Deborah Reason – Hospice Outreach Service (HOS) nurse
Debbie trained in Dundee and started her nursing career as a district nurse in Moss side, Manchester. In 2014, she came to Gibraltar for a sailing holiday and never left. Debbie spent 3 years working on John Mackintosh acute medical ward at St Bernard's Hospital. She returned to the UK for a short spell, working as a hospice at home nurse until she was chosen for the role of Hospice Outreach Nurse with Cancer Relief.
When she's not working, she prefers spending her time with horses and dogs, yoga and bakes a mean brownie.
Rowena Wallace
Rowena Wallace – Fundraising, Communications and Events Manager
Rowena obtained a BA in Psychology and, before her return to Gibraltar, worked in clinical trials pharmacy in Southampton University Hospital Trust, working closely with the Wellcome Trust, Cancer Research and major drug companies to conduct research in over 200 trials, and as clinical trial co-ordinator in the paediatric cancer ward, ensuring the smooth and efficient running of all children's cancer trials in the hospital. Keen to continue working within the cancer community, Rowena joined Cancer Relief in 2014 as Centre administrator, transitioning into the newly created fundraising department in 2019. Her aim is to ensure the charity receives the support it requires to continue providing much-needed services to our community. She is proud to be part of such a dynamic team and honoured to work for a charity that means so much to so many.
Samir Smirass
Samir Smirass – Hospice Outreach Service (HOS) Health Care Assistance (HCA)
Samir completed his general nurse diploma in Morocco 2014, and has since worked in a voluntary basis in public health. He moved to Gibraltar in 2015, working as a health care assistant in Dementia elderly residential services and volunteering for Cancer Relief. Happily, he also says his dream came true when he began working for the charity as a health care assistant in December 2018.
Samir is passionate about providing his patient with the best possible care, always with a smile.
Vanessa Cross
Kate Howarth
Georgia Casson
Vanessa Cross – Senior Centre Nurse
Vanessa is one of the Centre Nurses who joined the Cancer Relief team in May 2019. She has worked within oncology since qualification at The Royal London Hospital in 1992. She specialized in the field of breast cancer from 2001, first as a Research Nurse and then as a Clinical Nurse Specialist. She completed her Master's Degree during this time focusing on the psycho-social aspects of breast cancer and uses her knowledge and experience to provide emotional support, advice and information to all Cancer Relief patients and their families, in addition to managing day to day life at the Centre.
Kate Howarth – Hospice Outreach Service (HOS)
Kate joined the charity in 2010 originally in a volunteer capacity. She later joined the nursing complement as Centre Nurse for the Day Support Services and has now joined the expanding the Hospice Outreach Nursing Team.
Having completed her nurse training in Leeds, U.K. in 2002, Kate always wished her nursing career to incorporate caring for people affected by cancer. This was inspired by the care her father received that facilitated his wish to die peacefully
at home and the supportive care offered by the home nursing teams to not just her father but her mother and herself.
Kate has a wealth of nursing background citing experience in various cancer inpatient and outpatient facilities, plus hospice inpatient care skills from her time in St. Gemma's Hospice in Leeds, U.K.
She is a trained Chemotherapy and Systemic Anti-Cancer Therapy Nurse having practised at The Royal Brisbane Hospital in Australia; The Christie Hospital, Manchester U.K and Clatterbridge Cancer Centre, Liverpool U.K. She was part of the Chemotherapy Outpatient Unit in Gibraltar in more recent years treating our community locally. Kate is also trained in the Complementary Therapy 'HEARTS' (Hands-on, Empathy, Aromas, Relaxation, Textures, Sound).
Georgia Casson – Clinical Support Worker
Georgia has worked within the health and social sector for eleven years. Her primary background is disabilities however has worked with the elderly in England and Gibraltar also. She has a NVQ2 in health and social care. Georgia moved to Gibraltar in 2017 and previously worked with the Hospice Outreach Service team. She has come back to Cancer Relief in 2022 to join the Centre team. Georgia says "Cancer Relief are a family and I am truly grateful to be a part of something so special and meaningful."
Julie Gurney
Julie Gurney – Hospice Outreach Service (HOS) Health Care Assistance (HCA).
Julie moved to Spain in 2014 from Buckinghamshire. She has a history of working within Social Services, working with the Complex Care team across a variety of challenging situations. Julie had retired but found the position within Cancer Relief too good an opportunity to pass up, so was delighted to join the Cancer Relief team in January 2020. Julie enjoys the variety of her role and getting to know the community of Gibraltar.
Alejandro Ocaña Ruiz
Alejandro Ocaña Ruiz – Hospice Outreach Service (HOS) nurse
Alejandro is one of the Hospice Nurses at Cancer Relief. He completed his Nursing Degree at the University of Huelva (Spain) in 2015, specialising in Critical Care, also undertaking training in cancer care and palliative care management. He began work in Gibraltar in 2015, at the Learning Disability Service. Alejandro joined the Cancer Relief team in June 2019 and became part of the Hospice Outreach Service Team, providing advice, support and respite to cancer patients and families. End of life care is one of his passions, focusing on the holistic approach to try to provide the best quality of care for anyone affected by cancer in Gibraltar.
Annabelle Camino
Annabelle Camino – Hospice Outreach Service (HOS) Health Care Assistance (HCA)
Annabelle has many years of care experience in many fields, from cardiothoracic, adults with learning disabilities and dementia. She joined Cancer Relief in June 2019, the charity being something very close to her heart. She feels she has found her perfect place, supporting patients and their families in the most difficult of times.
Stephanie Satterley
Stephanie Satterley – Hospice Outreach Service Nurse (HOS)
Stephanie graduated from Plymouth University in 2008 with a First Class hons Degree in Adult Nursing. With a passion and dedication to Oncology Nursing, Stephanie has worked in a variety of different clinical settings including acute medicine, intensive care, chemotherapy and stem-cell transplants. She thoroughly enjoyed her time at the Royal Marsden Hospital where she undertook a managerial role. Prior to leaving the UK she was working as a Specialist Chemotherapy Nursing for a Homecare company delivering specialised treatments in the comfort of patient's own homes. Moving to Gibraltar in November 2020 with her husband and 5 year old son, Stephanie found the Cancer Relief Centre website and instantly knew this was where she was supposed to be. She joined as a HOS Nurse in June 2021 and is looking forward to serving the community of Gibraltar.
Alberto Sanchez
Alberto Sanchez – Hospice Outreach Service Healthcare Assistant
Originally from Los Barrios (Spain), Alberto moved to UK in 2015 looking for a new challenge. He developed his training as a Healthcare Assistant in the Royal Berkshire NHS Foundation Trust in Reading, working in an acute surgical ward and after a year, becoming a Senior Healthcare Assistant. During his career in UK, he has also worked in a care agency in different specialities (ICU, Orthopaedics, Urology, respiratory, elderly care). Alberto moved back to Spain in January 2021. He joined an elderly care agency to get to know Gibraltar, before joining the Cancer Relief team in June. He feels he has found a new challenge to keep developing his skills and knowledge and most enjoys interacting with the community and helping them in the best way he can. In his spare time, Alberto enjoys lots of different sports and training.
Maria Lopez – Hospice Outreach Service nurse
María graduated and completed her Nursing Degree in Córdoba University (Spain) in 2013 and, following advice from a very good friend, decided to move to the UK and start working at the Royal Berkshire Hospital in Reading. Here she worked in numerous clinical settings (all around the oncological patient) from a Urological surgical ward to Intensive Care Unit and finally as an Uro-oncology Clinical Nurse Specialist. Due to the pandemic, along with her husband and 1-year-old baby, she decided to move closer to her family and start a career in Gibraltar in January 2021. Finding an advert to work at the Cancer Relief for the Gibraltarian community was a great surprise and she feels it is like a reward after being away for such a long time. In her free time, Maria loves to spend time with her family, especially at the seaside.
The Cancer Relief Centre is part of the Gibraltar Society for Cancer Relief (GSCR),
The Gibraltar Society for Cancer Relief was first registered as a charity with the Charity Commission under the Friendly Societies Act (registered charity number 38) on 23rd May 1983. In 2017 the Cancer Relief registered a company limited by guarantee with the Registrar of Companies in Gibraltar (registered company number 106292). However, we retain our Registered Charity number 38. The charity is administered by seven trustees who each bring their own experience and expertise to the running of the society. The trustee board meet once a month to discuss on-going operational needs, concerns and future plans. There is an annual general meeting, usually held at the beginning of summer. Dates are advertised in local media so society members can attend.
We currently have 180 members and subscription is open to all.
Click here to download a subscription form.
Marisa Desoiza
Marisa Desoiza, Cancer Relief Chairperson
Marisa trained as a nurse in the 70's and became involved with the charity in the early 80's as a volunteer driver when she took a career break to raise her family. In 1993, Marisa was employed as the Lady Williams Centre Manager for 11 years. During this time, she recognised the incredibly positive impact of palliative care on the quality of life of people with advanced cancer and became increasingly interested in developing this service locally. As a result of this, the then "Hospice at Home nursing service" and a cancer support group were started. Marisa then went on to study for a Master's degree in Health Care Management which she completed in 2004. When she left the Lady Williams Centre to take up employment elsewhere, she remained on the charity's committee on a voluntary basis. When Mrs Lillian Pitaluga, who was the Chairperson retired, Marisa was invited to take the Chair, a position she holds to date. Marisa was instrumental in the move in 2013 from the Centre in Devil's Tower Road to Cancer Relief's present premises in South Barrack Road. Together with her fellow Trustees and the Centre's Team, Marisa has overseen enormous developments in the cancer support services offered by the charity. She considers it an honour to serve as part of the Team that has supported so many people who have been affected by cancer over the years.
Dr. Nathan Chichon
Dr. Nathan Chichon, Trustee
Nathan was born in 1973 in Gibraltar where he has lived most of his life. He spent 14 years in Aberdeen, Scotland, where he trained and worked as a medical practitioner. It was there he met his wife Emma, both returning to Gibraltar in 2004 where their daughter Bethany was born shortly after. He now has the privilege to serve the people of Gibraltar as a GP working for the GHA and as one of the GP leads at the Primary Care Centre. He also worked as the GFA's Chief Medical Officer during the first years of joining UEFA (2013-17). Nathan's hobbies include drawing & painting, fishing and reading sci-fi graphic novels, but his passion is football and in particular the English Premier League. Nathan had the privileged of being appointed a CRC Trustee in 2018 and, God willing, can continue to work with this inspirational group of people for years to come.
Christopher Pitaluga
Christopher Pitaluga, Trustee
Chris graduated from Oxford in 1984 with a degree in English Literature but has spent his career as a professional trustee, specialising in private wealth and corporate structuring. After some years in banking, during which he qualified as a Chartered Banker and TEP, he joined PricewaterhouseCoopers / Abacus in 1995 and became a Partner in 2001. He has been the CEO of Abacus since 2010 but still makes time for his five children (and wife), a passion for running (slowly) and the habitual disappointment of being a supporter of Arsenal football club. Chris is the trustee of a number of charitable trusts and was appointed a trustee of Cancer Relief in 2013. In his role as a trustee he supports the activities of the charity in the community and, in common with other trustees, upholds the vision of the charity and ensures its financial stability and integrity.
Geoff Harding
Geoff Harding, Treasurer & Trustee
Born in London and having qualified in Engineering and Accountancy, Geoff worked in UK, Africa and the Middle East before relocating to Gibraltar in 1981. He quickly resolved to make Gibraltar his permanent home and is now semi-retired but still active as a Management Accountant. He retains involvement in a number of businesses here and acts as a Non Executive Director of several Gibraltar companies, as well as pursuing his interests in exotic holidays and football. Geoff joined the Charity as a volunteer in 2006 because he wanted to give back some of his time and expertise to the people of Gibraltar. He helped with the reorganisation of the charity structure and was appointed Trustee in 2011. He is an integral part of the management team and took over the role of Treasurer in 2019, bringing his many years of experience in management and finance to the Board.
Fabian Vinet
Fabian Vinet, Trustee
Fabian is a Barrister by profession, having been Called to the Bar of England and Wales in 1999 and thereafter to the Bar of Gibraltar. He is a former Government Minister and former Chairman of Gibtelecom, AquaGib and the Gibraltar Electricity Authority, as well as having served on the Government's Land Management Committee and Development Appeals Tribunal. More recently, he was appointed a member of the Commission on Democratic and Parliamentary Reform, making formal recommendations on all aspects of our parliamentary and electoral systems, and headed the commercial operations for the Gibraltar 2019 NatWest International Island Games. Fabian has a keen interest in (or arguably unhealthy obsession with) music, writing, travelling and politics and is incredibly proud to be associated with Cancer Relief Gibraltar.
Clare Bensadon
Kevin Bastone
Clare Bensadon, Trustee
After graduating with a first class in Economics and Mathematics, Clare was selected to join one of the top graduate programmes in the UK, Teach First. Teach First is a charity which aims to address educational disadvantage and develop participants into leaders in all fields via a robust and intense programme. After returning to Gibraltar, Clare worked in banking whist lecturing Economics and Statistics at the University of Gibraltar. Clare continues lecturing and is now running a small business she started. Clare is passionate about her role as trustee because she knows cancer affects us all and so Cancer Relief plays a vital and important role in the community. As trustee, she believes she can contribute in a positive way to the overall mission and purpose of the charity.
Kevin Bastone, Trustee
Kevin has spent his entire career in finance, working in the UK, Europe and Asia. He has experience of retail banking, shipping finance, private banking, family offices, trust and company management, pensions and funds, and has managed companies within these sectors. Kevin spent three years in Gibraltar in the late 90's and returned to reside here in 2009. He hopes that he can use his business skills to help the charity as it continues to evolve and provide the specialist support that is very much needed and valued by the community.
The Centre simply couldn't function without our wonderful team of volunteers. Covering a wide range of roles, each brings something unique to the charity and we enjoy working with them immensely. They are a vital support, ensuring we can provide our services successfully to as many people as possible. Their impact on the charity should never be underestimated and, while we don't have the space to name them all individually, we consider every single one of them part of the Cancer Relief family and are so grateful for their time and hard work.
Volunteering is a great way to support Cancer Relief and enjoy the benefits it can offer. We are always looking for new volunteers across the various roles available at the Centre. If you are interested in finding out more about becoming a Cancer Relief volunteer, visit our 'Volunteering your time' page.
We are open 9am to 5pm, Monday to Friday (excluding bank holidays) and HOS is available out of hours. If you would like to use the Centre services or would like more information about us and what we do, our details are as follows:
Cancer Relief Hospice Outreach Team: Available daily until 11:30pm. Call 20042392 for the details of the nurse-on-call mobile number
Call: (00350) 20042392
Email: info@cancerrelief.gi
Get Involved Blog
Cancer Relief Centre,
5 South Barracks Rd,
Copyright 2015 Cancer Relief Gibraltar


text:
How turn tyres in jobs and art?
23 July 2022 | 2:01 pm
Nigerian artist Blessing Ibie transforms abandoned tyres into impressive sculptures, creating job opportunities for young people in his community. He pays the kids to collect tyres off the streets and at the same time they clean up the environment.
Fine art photography at Arles: Mitch Epstein on capturing 1980s India with his camera
The French city of Arles becomes a Provençal headquarters for fine art photography every summer, as the "Rencontres d'Arles" festival brings together imagery from all over the world through dozens of exhibitions, screenings and events. We sit down with Mitch Epstein, who tells us about revisiting the pictures that make up "In India: 1978-1989".
New antisemitism scandal at Germany's documenta art exhibition
More controversial images have been found at a show racked by accusations of incompetence and antisemitism. Some say the whole event should simply be shuttered.
London Museum will return stolen Art to Nigeria
London's Horniman Museum and Gardens has agreed to return 72 looted objects to the Nigerian government. All objects were taken from the Kingdom of Benin, now part of southern Nigeria, during a British military operation in 1897.
Shopify to cut 1,000 jobs
Shopify is to cut almost 1,000 jobs after overestimating the need for workers during the COVID-19 pandemic.
Ford cuts 3,000 jobs in drive towards electric vehicles
The US automaker has announced it is shedding 3,000 jobs in North America and India to cut costs and simplify processes. The company aims to accelerate its transition to electric vehicles.
Haute Couture, winter 2022/2023: The art of balance
Haute couture is a sartorial discipline revered in France and across the world, but at its best it's also an expression of often complex philosophical ideas and convictions. Designers are continually grappling with the tension between body and spirit, between being and merely appearing, between functionality and seduction. FRANCE 24 takes a deep dive into the latest Haute couture collections from Iris van Herpen, Yuima Nakazato, Imane Ayissi, Adeline André and Alexandre Vauthier.
Young Nigerian builds robot for dangerous jobs
Isah Barde's robot is made of recycled materials. The 17-year-old Nigerian believes it could help with jobs that are dangerous for humans.
Germany agrees to return looted art to Nigeria
French art historians have estimated that some 90% of Africa's looted cultural heritage is believed to be in Europe. Germany has signed an agreement to transfer ownership to Nigeria of the Benin Bronzes, among Africa's most culturally significant artefacts, looted in the 19th century.
'Great Resignation' hits France as employees search for more meaningful jobs
Like the US and other European countries, France is experiencing its own "Great Resignation". Between the end of 2021 and the beginning of 2022, resignations hit an all-time high, at almost 520,000 per quarter. The previous record dated from 2008, just before the financial crisis.
Bringing art therapy to Lagos hospitals
Kunle Adewale uses art therapy to help patients in Lagos hospitals recover. He uses music, painting, and dance to treat psychological disorders and promote mental health and believes that creative expression can foster healing and mental well-being.
Calls for Nazi art in Munich to be taken down
A work by Nazi painter Adolf Ziegler hangs in Munich's Pinakothek museum, and German artist Georg Baselitz says it should be removed. Ziegler persecuted Jewish and "degenerate" artists under Hitler.