text:
\section{Introduction} \label{intro}

Coupled cluster theory is one of the most accurate models
when spectroscopic properties of small and medium sized molecules
are investigated.\cite{WavFuncRev,CCRespFunc, CCRespRev}
Due to its high accuracy and relatively feasible computational scaling
as $\mcl{O}(\NV{4}\NO{2})$,
CCSD is the most widely used variant of coupled cluster.
Despite its accuracy for valence excited states,
larger errors occur when considering core excited states or
double excitation dominated states.
\cite{comp_Xray_review,N2_core,XPS_benchmark,NOCI_core,glycine,CCSDR3}
Including triple excitations in the parametrization of the wave function
improves the description of such states.
However, the computational cost and the memory requirement
increase to $\mcl{O}(\NV{5}\NO{3})$ and $\mcl{O}(\NV{3}\NO{3})$,
respectively for CCSDT.\cite{CCSDT,Bibel}
Approximating triples amplitudes with perturbation theory
can reduce the computational cost to $\mcl{O}(\NV{4}\NO{3})$
and the required memory to $\mcl{O}(\NV{2}\NO{2})$.

Triples corrections can be classified as iterative and noniterative models.
In noniterative models, corrections to the CCSD excitation energy are obtained
by expanding the excitation energy using many-body perturbation theory (MBPT).
The advantage of a noniterative approach
is that the triples correction is only computed once.
The disadvantage,
however,
is that transition moments cannot be easily defined.\cite{CCSDR3,size_int_trans}
The noniterative models include CCSDR(1a), CCSDR(1b) and CCSDR(3)
which are derived from the iterative methods CCSDT-1a, CCSDT-1b and CC3,
respectively.\cite{CCSDR3,CCSDTn,CC3_response,CC3_code,CC3_new}
Other noteworthy examples are CREOM-CCSD(T), EOMIP-CCSD$^*$
---developed specifically for ionized states---
and EOM-CCSD(T)(a)* which introduces
corrections to both the CCSD ground and the excited states.
\cite{CREOMptsd,ccsdstar_1,ccsdstar_2,ccsdptpa}

The best-known methods for including triples excitations iteratively are
CC3 and CCSDT-n.\cite{CC3_response, CCSDTn}
Both CCSDT-1 and CC3 scale asymptotically as $\mcl{O}(\NV{4}\NO{3})$,
but CC3 includes single excitations to infinite order leading to an improved
description of ground and excited states.\cite{CC3_response}
The advantage of iterative models is that they are more robust \cite{triples_properties}
and provide a consistent definition of other properties than the energy.
\cite{cc3_ee_benchmark}
However, that comes at the cost of iteratively converging equations scaling
as $\mcl{O}(\NV{4}\NO{3})$.
Nevertheless, with current implementations systems of around 400 basis functions
can be routinely treated at the CC3 level.\cite{CC3_new}

Due to the success of coupled cluster theory,
schemes have been developed to reduce the scaling while keeping the accuracy.
Pulay and S\ae{}b\o{} advocated the use of localized molecular orbitals (LMOs),
for a compact description of electronic correlation
in M\o{}ller-Plesset (MP) perturbation theory and configuration interaction
singles and doubles(CISD).
\cite{Local_corr_1,Local_corr_2,Local_CI,Local_MP_1,Local_MP_2}
They used Boys localization for the occupied molecular orbitals
and projected atomic orbitals (PAOs) for the virtual space,
and reduced the scaling by neglecting the correlation between distant pairs of localized orbitals.
\cite{Local_corr_2}
Werner and Sch\"utz then extended this model to coupled cluster theory
with and without a noniterative triples correction.
\cite{Local_CC,Local_CCSDpT_1,Local_CCSDpT_2}
Domain based local pair-natural orbital coupled cluster (DLPNO-CC)
methods are also related to this approach.\cite{Neese_LPNO,Neese_LPNO_CC}
The DLPNO-CC approach has recently been extended to
CCSD(T) and also CC3 which was used to calculate the first electronic excited state
of a system with more than 1300 basis functions.\cite{DLPNO_CCSDpT,DLPNO_CC3}
Reducing the size of the active space based on a distance criterium is certainly
successful for ground state properties.
For the description of excitation energies and other excited state properties,
however,
distance measures do not work as well
as more diffuse orbitals become more important.
\cite{Local_EE_CCSD,Local_CC2,Local_CC_prop,Local_laplace_CC2,
PNO_CC2,Towards_local_EE,Accuracy_LocalEOM}
Therefore,
larger active spaces have to be employed in these calculations
and different orbital spaces are used for the ground and excited states.
\cite{Local_EE_CCSD,Local_CC2}

Multilevel and embedding methods treat different regions of a system
with different levels of theory.
The idea of obtaining an accurate description of a large molecular system
by coupling the contributions of its subsystems is exploited in
QM/MM approaches,\cite{QMMM_1,QMMM_2,QMMM_3,QMMM_review_1,QMMM_review_2,PElib}
frozen density embedding,\cite{FDE_1,FDE_2}
subsystem DFT,\cite{SubsystemDFT_1,SubsystemDFT_2}
and the ONIOM, IMOMO and LMOMO methods.\cite{IMOMO,ONIOM,LMOMO}
Another method related to multilevel coupled cluster (MLCC)
was developed by Oliphant and Adamowicz using CCSD for multireference
systems by including selected triple and quadruple substitutions.
\cite{ML_MRCC_1,ML_MRCC_2,ML_MRCC_3}
This scheme was adapted by K\"{o}hn and Olsen to include higher order substitutions
at reduced cost.\cite{Active_CC,Active_CC_TQ}

In multilevel coupled cluster (MLCC) one CC wave function
is used for the full system but different parts of the system
are described with different level of truncation.\cite{MLCCSD_ECC2,MLCC}
Considerable savings are achieved by applying the higher order excitation operators
in a smaller (active) subset of the orbitals.\cite{MLCC3}
The active orbital space can be selected using localized orbitals
--- such as Cholesky orbitals\cite{Cholesky_Orbs} and projected atomic orbitals (PAOs)
\cite{Local_corr_2}
--- or state-selective approaches ---
such as the correlated natural transition orbitals (CNTOs).\cite{MLCC_CNTO_CVS}
As MLCC is designed for intensive properties, excitation energies
or oscillator strengths are accurately reproduced
if an appropriate active space is chosen.\cite{MLCC_CNTO_CVS,MLCC3,MLCC_CVS,MLCC_EOM}
While state-selective approaches are preferred to keep
the active space as compact as possible,
they are less suited for transition properties
especially between excited states,
as a consistent active space is needed for all excited states.\cite{DLPNO_CC3}
Localized orbitals are only suitable in the cases where the target property
is localized in a smaller region of the molecule.

In this paper we report the extension of the MLCC3 method to compute
oscillator strengths with CC3 quality but at significantly reduced cost.
Employing core-valence separation (CVS),
oscillator strengths are also available for core excited states.\cite{CVS,CVS_ADC,CVS_CC}
This allows us to tackle excited states and oscillator strengths of systems
with more than 1000 basis functions.

\section{Theory} \label{Theory}

In this section,
we will introduce the closed shell MLCC3 model within the equation of motion (EOM) formalism.
For a more detailed derivation we refer to Refs \citenum{CC3_response,CC3_new}.
Consider the general cluster operator
\begin{equation}
   T = \sum_{\mu} \tau_\mu X_\mu,
\end{equation}
where $X_\mu$ is an excitation operator that converts the reference
determinant, $\ket*{\R}$,
into the excited determinant, $\nket{\mu}$,
and $\tau_\mu$ is the corresponding amplitude.
In MLCC3 with two levels,
namely CCSD and CC3,
the cluster operator assumes the form
\begin{equation}
   T = T_1 + T_2 + T^{a}_{3}
\end{equation}
with
\begin{equation}
\begin{split}
   T_1 &= \ssum{A}{I} \ta{A}{I} E_{AI} \\
   T_2 &= \frac{1}{2} \ssum{AB}{IJ} \ta{AB}{IJ} E_{AI} E_{BJ} \\
   T^{a}_{3} &= \frac{1}{6} \ssum{abc}{ijk} \ta{abc}{ijk} E_{ai} E_{bj} E_{ck}
\end{split}
\label{eq:T_op}
\end{equation}
where $E_{AI}$ and $E_{ai}$ are singlet excitation operators.
While the operators $T_1$ and $T_2$ excite on the full orbital space
indicated by capitalized indices,
the triples cluster operator $T^{a}_{3}$ only excites in the active orbital space
denoted by lower case indices.
We use the standard notation
where the indices $i$, $j$, $k\dots$ refer to occupied,
$a$, $b$, $c\dots$ to virtual,
and $p$, $q$, $r\dots$ to general active orbitals.
The CC wave function is defined as
\begin{equation}
   \nket{\mathrm{CC}} = \exp(T) \ket*{\R}
\end{equation}
and we introduce the similarity transformed Hamiltonian
\begin{equation}
   \bar{H} = \exp(-T) \hat{H} \exp(T)
\end{equation}
where
\begin{equation}
   \hat{H} = \sum_{pq} h_{pq} E_{pq}
     + \frac{1}{2} \sum_{pqrs} (pq|rs) (E_{pq} E_{rs} - E_{ps} \del{qr}) + h_{nuc}
\end{equation}
is the electronic Hamiltonian.
To obtain the cluster amplitudes a set of biorthogonal determinants
\begin{equation}
   \{\nbra{\mu}\} = \{\nbra{\mu_1}\} \oplus \{\nbra{\mu_2}\} \oplus \{\nbra{\mu_3^a}\}
   \label{eq:bo_space}
\end{equation}
is defined,
where the triply excited determinants, $\mu_3^a$,
are restricted to the active space.
These determinants are generated using the contravariant excitation operator,
$\tilde{X}_\mu$, such that,
\begin{equation}
   \braket{\mu}{\nu} = \bra*{\R} \tilde{X}_\mu X_\nu \ket*{\R} = \del{\mu\nu}.
   \label{eq:Omega}
\end{equation}
The coupled cluster energy, $\mathrm{E_{CC}}$,
and the cluster amplitudes are then obtained by projection
onto the reference determinant and the set of excited determinants,
respectively,\cite{Bibel}
\begin{align}
   \label{eq:energy}
   \mathrm{E_{CC}} &= \bra*{\R} \bar{H} \ket*{\R}
   \\
   \Om{}{\mu} &= \nbra{\mu} \bar{H} \ket*{\R} = 0.
   \label{eq:amplitudes}
\end{align}
To obtain compact equations we incorporate the effect of the singles
cluster operator into the Hamiltonian and obtain the so-called
$T_1$-transformed Hamiltonian,
\begin{equation}
   H = \exp(-T_1) \hat{H} \exp(T_1).
\end{equation}
In analogy to MBPT,
the $T_1$-transformed Hamiltonian is split into an
effective one-particle operator and a fluctuation potential.
\begin{equation}
   H = F + U
\end{equation}
In CC3 the double excitation amplitudes and the fluctuation potential are
treated as first order in the perturbation while the triples amplitudes
are considered second order.
The single excitation amplitudes are included as zeroth order parameters,
as they have a special role as relaxation parameters.\cite{CC3_response,CC3_code}
Inserting eq \eqref{eq:T_op} and eq \eqref{eq:bo_space} into eq \eqref{eq:Omega} and neglecting
all terms of third and higher order in the perturbation,
we obtain the MLCC3 ground state equations,
\begin{align}
   \label{eq:OM_CC3_S}
   \Om{}{\mu_1} &= \nbra{\mu_1} H + [H,T_2] + [H,T^{a}_{3}] \ket*{\R} \\
   \label{eq:OM_CC3_D}
   \Om{}{\mu_2} &= \nbra{\mu_2} H + [H,T_2] + [[H,T_2],T_2] + [H,T^{a}_{3}] \ket*{\R} \\
   \label{eq:OM_CC3_T}
   \Om{}{\mu^a_3} &= \nbra{\mu^a_3} [H,T_2] + [F,T^{a}_{3}] \ket*{\R}.
\end{align}
The Fock matrix is not necessarily diagonal in the local orbital basis,
but it can be block-diagonalized within the active orbital space,
such that the off-diagonal elements do not contribute to the triples amplitudes.
Therefore,
the triples amplitudes can be expressed in terms of the doubles amplitudes
\begin{equation}
   \ta{abc}{ijk} = -\frac{1}{\varepsilon^{abc}_{ijk}} \nbra{\mu^a_3} [H,T_2] \ket*{\R},
\end{equation}
where $\varepsilon^{abc}_{ijk}$ are the orbital energy differences
\begin{equation}
   \varepsilon^{abc}_{ijk} = \varepsilon_{a}+\varepsilon_{b}+\varepsilon_{c}-\varepsilon_{i}-\varepsilon_{j}-\varepsilon_{k}.
\end{equation}

In equation of motion coupled cluster (EOM-CC)
start out from the matrix representation of the similarity transformed Hamiltonian,
\begin{equation}
   \label{eq:H_mat_el}
   \boldsymbol{\bar{H}} =
   \begin{pmatrix}
      \bra*{\R} \bar{H} \ket*{\R}      & \bra*{\R} \bar{H} \nket{\nu} \\
      \nbra{\mu} \bar{H} \ket*{\R} & \nbra{\mu} \bar{H} \nket{\nu}
   \end{pmatrix}.
\end{equation}
If the CC ground state equations, eq \eqref{eq:Omega},
are converged,
the similarity transformed Hamiltonian can be written as,
\begin{equation}
   \label{eq:H_mat}
   \boldsymbol{\bar{H}} =
   \begin{pmatrix}
      0      & \bm{\eta}^T \\
      \bm{0} & \boldsymbol{J}
   \end{pmatrix}
   +
   \mathrm{E_{CC}} \bm{I},
\end{equation}
where $\eta_\nu = \bra*{\R} [\bar{H},X_\nu] \ket*{\R}$
and $\boldsymbol{J}$ is the so-called Jacobian with matrix elements
$\nbra{\mu} [\bar{H},X_\nu] \ket*{\R}$.
The eigenvectors of $\bar{H}$ are the EOM states and the corresponding
eigenvalues the energies of these states.
As the similarity transformed Hamiltonian is non-symmetric,
the left and right eigenvectors are not hermitian conjugates,
but they are biorthonormal.\cite{Bibel}
\begin{equation}
   \boldsymbol{\bar{H}}\boldsymbol{\bar{R}}_m = E_m\boldsymbol{\bar{R}}_m
   \quad
   \boldsymbol{\bar{L}}^T_m\boldsymbol{\bar{H}} = E_m\boldsymbol{\bar{L}}^T_m
   \quad
   \boldsymbol{\bar{L}}^T_m\boldsymbol{\bar{R}}_n = \del{mn}
\end{equation}
From the biorthogonality of the EOM states and the structure of the Hamiltonian matrix,
we obtain the left and the right ground state,
\begin{equation}
   \label{eq:GS_vec}
   \boldsymbol{\bar{L}}_0 =
   \begin{pmatrix}
      1      \\
      \boldsymbol{\lambda}
   \end{pmatrix}
   \quad
   \boldsymbol{\bar{R}}_0 =
   \begin{pmatrix}
      1      \\
      \bm{0}
   \end{pmatrix},
\end{equation}
and the left and right excited states,\cite{CC3_new}
\begin{equation}
   \label{eq:ES_vec}
   \boldsymbol{\bar{L}}_m =
   \begin{pmatrix}
      0      \\
      \boldsymbol{L}_m
   \end{pmatrix}
   \quad
   \boldsymbol{\bar{R}}_m =
   \begin{pmatrix}
      -\boldsymbol{\lambda} \boldsymbol{R}_m \\
      \boldsymbol{R}_m
   \end{pmatrix}.
\end{equation}
The parameters $\boldsymbol{\lambda}$
are determined from
\begin{equation}
   \boldsymbol{\lambda}^T \boldsymbol{J} = - \bm{\eta},
\end{equation}
while the parameters of the excited states are determined as eigenvectors of the Jacobian,
$\boldsymbol{J}$.
The MLCC3 Jacobian is given by\cite{MLCC3}
\begin{equation}\label{eq:jcc3}
\footnotesize
   \boldsymbol{J}^{MLCC3} =
   \begin{pmatrix}
      \nbra{\mu_1}[H + [H,T_2],X_{\nu_1}]\ket*{\R} &
      \nbra{\mu_1}[H,X_{\nu_2}]\ket*{\R} &
      \nbra{\mu_1}[H,X_{\nu^a_3}]\ket*{\R}
      \\
      \nbra{\mu_2}[H + [H,T_2+T^{a}_{3}],X_{\nu_1}]\ket*{\R} &
      \nbra{\mu_2}[H + [H,T_2],X_{\nu_2}]\ket*{\R} &
      \nbra{\mu_2}[H,X_{\nu^a_3}]\ket*{\R}
      \\
      \nbra{\mu^a_3}[H + [H,T_2], X_{\nu_1}]\ket*{\R} &
      \nbra{\mu^a_3}[H,X_{\nu_2}]\ket*{\R} &
      \nbra{\mu^a_3}[F,X_{\nu^a_3}]\ket*{\R}
   \end{pmatrix}.
\end{equation}
The vectors in eq \eqref{eq:GS_vec} and eq \eqref{eq:ES_vec} correspond to operators
which generate the EOM states from the Hartree-Fock determinant.
\begin{align}
   \nbra{\mathrm{\tilde{CC}}} &= \bra*{\R} \Big(1 + \sum_\mu \la{}{\mu} \tilde{X}_\mu \Big) \exp(-T) \\
   \nket{\mathrm{CC}} &= \exp(T) \ket*{\R} \\[0.2eM]
   \nbra{m} &= \bra*{\R} \sum_\mu \La{}{\mu} \tilde{X}_\mu \exp(-T) \\
   \nket{m} &= \Big(\sum_\mu \Ra{}{\mu} X_\mu - \sum_\mu \Ra{}{\mu} \la{}{\mu}\Big)
   \exp(T) \ket*{\R}
\end{align}
Once the ground and excited states are determined,
left and right transition moments can be obtained in terms of
left ($D^{m\text{-}0}$) and right ($\tilde{D}^{0\text{-}m}$) transition densities.
\cite{EOMCC,EOM_densities,EOM_gradient}
\begin{align}
   \nbra{\mathrm{\tilde{CC}}} A \nket{m} &= \sum_{pq} \tilde{D}^{0\text{-}m}_{pq} A_{pq} \\
   \nbra{m} A \nket{\mathrm{CC}} &= \sum_{pq} D^{m\text{-}0}_{pq} A_{pq}
\end{align}
Here,
$A$ is a general one-electron operator $A=\sum_{pq} A_{pq} E_{pq}$.

To obtain accurate excitation energies and transition dipole moments,
the selection of the active orbital space is crucial.
In this paper two approaches are chosen to partition the orbital space.
For the cheaper strategy Cholesky orbitals are used for the occupied space.
To obtain these orbitals the Hartree-Fock density is Cholesky decomposed
using the AOs of the active atoms as pivoting elements.
\cite{Cholesky_Orbs,Cholesky_subsystems}
\begin{equation}
   D_{\alpha\beta} = \sum_J C^a_{\alpha J} C^a_{\beta J} + \Delta D_{\alpha\beta}
\end{equation}
The decomposition is stopped when the size of all active diagonal elements
is below a given threshold and the coefficients are simply the elements
of the Cholesky vectors $C_{\alpha J}$.
The inactive orbitals are then obtained by decomposing the remaining part of the density,
$\bm{\Delta D}$.
Projected atomic orbitals have been shown to give a good description of the
virtual space for solvated systems,
but also adenosine. \cite{MLCC_EOM,MLCC_MLHF,MLCC_Embedding}

The construction of correlated natural transition orbitals is more costly
as they are obtained from excitation vectors of a coupled cluster calculation.
In MLCC3 we use CNTOs constructed from CCSD excited states
to get a compact description of the excited states.
The CNTOs are generated by diagonalizing two matrices,
denoted by $\bm{M}$ and $\bm{N}$,
defined as
\begin{align}
   \label{eq:M}
   M_{ij} = \sum_a R^a_i R^a_j + \frac{1}{2}\ssum{ab}{k} (1+\del{ai,bk}\del{ij}) \Ra{ab}{ik} \Ra{ab}{jk}\\
   \label{eq:N}
   N_{ab} = \sum_i R^a_i R^b_i + \frac{1}{2}\ssum{c}{ij} (1+\del{ai,cj}\del{ab}) \Ra{ac}{ij} \Ra{bc}{ij}.
\end{align}
The eigenvectors of $\bm{M}$ and $\bm{N}$ correspond to the CNTO transformation
matrices for the occupied and virtual CNTOs, respectively.
The CNTOs whose eigenvalues sum up to a certain cutoff are chosen as active space
\begin{align}
   \label{e:cnto_threshold_o}
   1 - \xi_M &< \sum_o \lambda^M_o \\
   \label{e:cnto_threshold_v}
   1 - \xi_N &< \sum_v \lambda^N_v
\end{align}
where $\lambda^M_o$ and $\lambda^N_v$ are the eigenvalues of $\bm{M}$ and $\bm{N}$.
To obtain the most compact basis, separate CNTO bases for each excited state
would be preferable.
However,
due to the non-orthogonality of the orbitals,
subsequent calculation of transition moments between excited states would be complicated.
Therefore,
we choose a state averaged approach,
\begin{equation}
   \bm{M} = \frac{1}{n_{ES}} \sum^{n_{ES}}_i \bm{M}_i, \quad
   \bm{N} = \frac{1}{n_{ES}} \sum^{n_{ES}}_i \bm{N}_i,
\end{equation}
where $\bm{M}_i$ and $\bm{N}_i$ are constructed according to eq \eqref{eq:M}
and \eqref{eq:N} for the $i$-th excited state
and $n_{ES}$ is the number of excited states included in the matrices.

\section{Implementation}\label{Implementation}

The closed shell MLCC3 ground and excited states as well as
EOM transition properties have been implemented in the $e^T$ program package.\cite{eT}
One of the advantages of MLCC3 compared to other reduced cost methods is
that only the space,
in which the triples amplitudes are defined,
is restricted.
Therefore,
we can split the occupied and virtual orbitals into active
and inactive subsets,
and use almost identical code for MLCC3 as for full CC3.
The algorithms employed to calculate closed shell CC3 properties
in $e^T$ have been detailed in Ref. \citenum{CC3_new}
and only a short summary will be given in this paper.
The ground state residual, $\bm{\Omega}$,
and the transformations of a trial vector with the Jacobian
are computed in a restricted loop over the occupied indices $i\geq j\geq k$.
An $\nv{3}$-block of triples amplitudes is constructed for a given
set of indices $\{i,j,k\}$.
Using this structure, the permutational symmetry of the triples amplitudes
can be exploited,
while utilizing efficient matrix multiplication routines
for the contractions of the block of virtual orbitals.
\cite{CCSDpT_Lee,Triples_alg1,Triples_alg2}
By reformulating the equations in terms of contravariant triples amplitudes
\begin{equation}\label{eq:contra_3}
   \tta{abc}{ijk} = 4\ta{abc}{ijk} - 2\ta{bac}{jik} - 2\ta{cba}{kji}
                  - 2\ta{acb}{ikj} + \ta{cab}{kij} + \ta{bca}{jki},
\end{equation}
and residuals,
$\tOm{}{}$,
the number of memory-bound reordering operations is reduced.
After all contributions to the contravariant residual are collected
it is converted back to the covariant form,
using the relations
\begin{align}
   \tOm{A}{I} &= \Om{A}{I} \\
   \tOm{AB}{IJ} &= 2\Om{AB}{IJ} - \Om{BA}{IJ}, \quad
   \Om{AB}{IJ} = \frac{1}{3}(2\tOm{AB}{IJ} + \tOm{BA}{IJ}).
\end{align}
As in CC3,
the $\ta{}{3}$ amplitudes are defined in terms of the $\ta{}{2}$ amplitudes
\begin{equation}
   \label{eq:tau3}
   \ta{abc}{ijk} = -(\varepsilon^{abc}_{ijk})^{-1} P^{abc}_{ijk}
                     \Big(\sum_D \ta{aD}{ij} g_{bDck} -
                     \sum_L \ta{ab}{iL} g_{Ljck}\Big).
\end{equation}
However,
because the triples determinants are restricted to the active space
only the summation indices in the expression for $\ta{}{3}$ are over the full space.
Here,
$P^{abc}_{ijk}$ is a permutation operator creating a sum of all unique permutations
of the index pairs $ai, bj, ck$,
and $g_{pqrs}$ are two-electron integrals in the $T_1$-trasformed basis.\cite{Bibel}
From eq \eqref{eq:tau3} it is evident that the most memory efficient implementation
will make use of two separate arrays for $\ta{ab}{iL}$ and $\ta{aD}{ij}$.
Similarly,
two vectors are needed for the doubles part of the ground state residual
because one index originates from a $T_1$-transformed two-electron integral,
$g_{pqrs}$,
\begin{align}
   \tOm{ab}{iL} &= \ssum{c}{jk} \tta{abc}{ijk} g_{jLkc} \\
   \tOm{aD}{ij} &= \ssum{bc}{j} \tta{abc}{ijk} g_{Dbkc},
\end{align}
Therefore,
the memory requirement and the computational cost of the triples contributions
scale linearly with the full size of the system,
and the overall asymptotic scaling for constructing the ground state residual is
$4\NV{}\nv{3}\no{3}$ floating point operations (FLOP).

The triples amplitudes of the right excitation vector can be expressed as
\begin{equation}
   \label{eq:R3}
   \Ra{abc}{ijk} = -\frac{1}{\varepsilon^{abc}_{ijk} - \omega} P^{abc}_{ijk} \Big(
   \sum_D \bRa{aD}{ij} g_{bDck}   - \sum_L \bRa{ab}{iL} g_{Ljck}
   + \sum_D \ta{aD}{ij} \Ups{bDck} - \sum_L \ta{ab}{iL} \Ups{Ljck} \Big)
\end{equation}
where $\Ups{bDck}$ and $\Ups{Ljck}$ are treated as one-index transformed integrals
\begin{align}
   \label{eq:ups_v}
   &\Ups{bDck} = \sum_E R^E_k g_{bDcE}
               - \sum_M \big(R^b_M g_{MDck} + R^c_m g_{bDMk}\big) \\
   \label{eq:ups_o}
   &\Ups{Ljck} = \sum_E \big(R^E_j g_{LEck} + R^E_k g_{LjcE}\big)
               - \sum_M R^c_M g_{LjMk}.
\end{align}
and $\bRa{ab}{ij} = (1+\del{ai,bj})\Ra{ab}{ij}$.\cite{Bibel}
From eq \eqref{eq:R3} can be seen that the construction of $R_3$ is
twice as expensive as the construction of $\tau_3$.
For the Jacobian transformation the same terms have to be computed
as for the ground state residual,
but $R_3$ is contracted instead of $\tau_3$.
Additionally,
the $\tau_3$ amplitudes are required for a single term
leading to an overall asymptotic scaling of $8\NV{}\nv{3}\no{3}$ FLOP.
It should be noted that the construction of $\Ups{bDck}$
scales quadratically with the full system size.
However,
this term will not be significant compared to the
other terms in the Jacobian transformation.

The transpose Jacobian transformation also scales with $8\NV{}\nv{3}\no{3}$ FLOP,
as the $L_3$ and $\tau_3$ amplitudes need to be constructed and two contractions,
each scaling as $2\NV{}\nv{3}\no{3}$ FLOP, are needed.
The final contractions contributing to the singles part of the transformed vector
contains terms that scale quadratically with the full size of the system.
However,
these terms scale at most as $2\NV{}\NO{}\nv{2}\no{}$ FLOP and are therefore
negligible compared to full CCSD.

To obtain core excited states core-valence separation is employed,
where all non-zero elements of both the trial vector and the transformed vector
need to contain at least one index corresponding to a core orbital.
\cite{CVS_CC,MLCC_CVS,CC3_new}
Therefore,
in this implementation of the Jacobian transformations,
we skip iterations in the loop over $i,j,k$
if all indices correspond to valence orbitals.
This reduces the scaling for both Jacobian transformations to $8\NV{}\nv{3}\no{2}$.

As in the full CC3 code the EOM transition densities are constructed in
a loop over the occupied indices and another loop over the virtual indices.
We calculate all contributions to the density in a loop over the occupied indices,
except for one contribution to the occupied-occupied block of the density
which cannot be efficiently calculated in a loop over $i,j,k$.
\begin{equation}
   \label{eq:DL_oo}
   D^{m\text{-}0}_{kl} \mathrel{-}= \frac{1}{2} \ssum{abc}{ij} \tL{abc}{ijl} \ta{abc}{ijk}
\end{equation}
As shown in eq \eqref{eq:DL_oo} for the occupied-occupied block of the left transition density,
the triples amplitudes that are contracted differ in the occupied indices.
Therefore,
a triples loop over the virtual indices has to be used,
in order to exploit the permutational symmetry of the triples amplitudes.
This leads to an increase in contractions scaling as $2\NV{}\nv{3}\no{3}$ FLOP.
However,
the triples amplitudes have to be reconstructed for the loop over $a,b,c$
which also leads to a larger prefactor in the scaling.
While the contractions inside the triple loops scale linearly with
the full system size,
there exists one term in the right transition density, $\tilde{D}^{0\text{-}m}$,
that requires storing a subblock of $\ta{}{2}$ scaling as $\NV{}\NO{}\nv{}\no{}$
in memory.
This is, however, not an issue as CCSD is used as lower level method
where the full $\ta{}{2}$ array scaling as $\NV{2}\NO{2}$ needs to be kept in memory.

Because the triples amplitudes have to be calculated twice
the overall scaling to construct a single $D^{m\text{-}0}$ amounts to $10\NV{}\nv{3}\no{3}$ FLOP.
The construction of a single $\tilde{D}^{0\text{-}m}$ totals $16\NV{}\nv{3}\no{3}$ FLOP,
as the $\Ra{}{3}$ amplitudes are twice as expensive as the $\La{}{3}$,
and also the $\ta{}{3}$ and $\la{}{3}$ amplitudes are required.
For transition moments from the ground state,
these densities only need to be computed once per state,
compared to the iterative cost (per state) for the Jacobian transformations.

\section{Results and Discussion}\label{Applications}
With the MLCC3 method, we can obtain
excitation energies and oscillator strengths
of CC3 quality at significantly reduced cost.
We compare the MLCC3 results for oxygen core excitations of guanine to the CC3
results.
The scaling with the size of the inactive space is shown for formaldehyde
with up to six explicit water molecules.
To show the capabilities of the method,
the UV/VIS spectrum of azobenzene
and a core excited state of betaine 30 with more than 1000 molecular orbitals
are reported.

\subsection{Guanine}
A single core excited state of the oxygen atom of guanine is calculated
with aug-cc-pCVDZ basis set on the oxygen atom and aug-cc-pVDZ on the remaining atoms
using two Intel Xeon-Gold 6138 with 40 threads in total.
\cite{aug_cc_pVXZ,cc_pCVXZ,cc_pVXZ}
The results and timings per iteration are summarized in Table \ref{t:Gua_1state}
for selected active spaces.
The number of virtual orbitals is chosen to be 10 times larger than the number
of occupied orbitals.
Already with an active space comprising 10 occupied orbitals the excitation
energies improve by 2\,eV compared to CCSD and the difference to CC3 is only 0.4\,eV.
Increasing the active space to 15 occupied orbitals the deviation from the CC3 results
is below 0.2\,eV.
For 15 occupied orbitals
the error of MLCC3 is below the expected error of CC3 for oxygen core excitations.
\begin{table}
\centering
\caption{Timings in seconds to compute a core excited state          from the oxygen atom of guanine
         at the CCSD and MLCC3 level with several active spaces.
         Timings are given, averaged over the number of iterations when solving for
         $\bm{\tau}$, $\bm{\lambda}$, $\bm{R}$ and $\bm{L}$.
         Additionally, timings to construct the ground state density, $\bm{D^{0\text{-}0}}$,
         left transition density, $\bm{D^{m\text{-}0}}$, and right transition density, $\bm{\tilde{D}^{0\text{-}m}}$,
         are reported.
         Note that the MLCC3 and CC3 timings only comprise the triples part.}
\label{t:Gua_1state}
\begin{tabular}{l SS SSSSS}
   \toprule
   & \mco{CCSD} & \mc{5}{c}{MLCC3} & \mco{CC3} \\
   \cmidrule(lr){2-2}\cmidrule(lr){8-8}\cmidrule(lr){3-7}
   $\no{}/\nv{}$ & & \mco{$10/100$} & \mco{$13/130$} & \mco{$15/150$} & \mco{$18/180$} & \mco{$20/200$} &  \\
   \midrule
   $\omega$ [eV] & 535.91 & 533.90 & 533.76 & 533.69 & 533.61 & 533.58 & 533.51 \\
   $f\times 100$ & 3.26 & 2.42 & 2.31 & 2.26 & 2.20 & 2.18 & 2.12 \\
   \midrule
   $\bm{\tau}$    & 15.49 & 3.03 & 10.72 & 24.93 & 70.31 & 125.74 & 2220.55 \\
   $\bm{\lambda}$ & 25.78 & 5.40 & 21.49 & 46.08 & 130.22 & 238.02 & 4157.37 \\
   $\bm{R}$       & 24.48 & 1.72 & 4.82 & 9.22 & 20.90 & 33.13 & 301.98 \\
   $\bm{L}$       & 23.62 & 1.86 & 5.27 & 9.83 & 22.59 & 36.58 & 317.90 \\
   $\bm{D^{0\text{-}0}}$    & 0.59 & 5.80 & 25.76 & 66.43 & 175.06 & 312.30 & 5147.35 \\
   $\bm{D^{m\text{-}0}}$     & 0.21 & 3.68 & 14.76 & 33.33 & 95.24 & 171.81 & 2340.44 \\
   $\bm{\tilde{D}^{0\text{-}m}}$     & 0.71 & 7.29 & 29.97 & 65.50 & 182.68 & 320.64 & 4638.42 \\
   \bottomrule
\end{tabular}
\end{table}
\begin{table}
\centering
\caption{Speed up of MLCC3 compared to CC3 calculated according
         to equations \ref{e:speedup_gs} and \ref{e:speedup_es}.
         The first part shows the speed up for terms that scale asymptotically
         as $\mcl{O}(\NV{}\nv{3}\no{3})$ while the second part summarizes the
         speed up for terms with a cost of $\mcl{O}(\NV{}\nv{3}\no{2})$.}
\label{t:Gua_speedup_1}
\begin{tabular}{l c
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]}
   \toprule
   $\no{}$ && \mco{10} & \mco{13} & \mco{15} & \mco{18} & \mco{20} \\
   $\nv{}$ && \mco{100} & \mco{130} & \mco{150} & \mco{180} & \mco{200} \\
   \midrule
   $\bm{\tau}$      &&  732.9 & 207.1 & 89.1 & 31.6 & 17.7 \\
   $\bm{\lambda}$   &&  769.9 & 193.5 & 90.2 & 31.9 & 17.5 \\
   $\bm{D^{0\text{-}0}}$      &&  887.5 & 199.8 & 77.5 & 29.4 & 16.5 \\
   $\bm{D^{m\text{-}0}}$       &&  636.0 & 158.6 & 70.2 & 24.6 & 13.6 \\
   $\bm{\tilde{D}^{0\text{-}m}}$       &&  636.3 & 154.8 & 70.8 & 25.4 & 14.5 \\
   \cmidrule{1-1}
   $S^{GS}_{theo}$  && 1079.1 & 223.6 & 94.7 & 31.7 & 16.9 \\
   \midrule
   $\bm{R}$         &&  175.6 & 62.7 & 32.6 & 14.5 & 9.1 \\
   $\bm{L}$         &&  170.9 & 60.3 & 32.3 & 14.1 & 8.7 \\
   \cmidrule{1-1}
   $S^{ES}_{theo}$  &&  276.7 & 74.5 & 36.4 & 14.6 & 8.7 \\
   \bottomrule
\end{tabular}
\end{table}
For the smallest active space in Table \ref{t:Gua_1state} the cost per iteration
is much smaller than the CCSD timings.
The CC3 contribution dominates inly in the construction of the densities,
because CCSD densities scale as $\mcl{O}(\NV{3}\NO{2})$ in contrast
to $\mcl{O}(\NV{}\nv{3}\no{3})$ for MLCC3 densities.
Considering active spaces with 13 and 15 occupied orbitals,
the time spent in the MLCC3 part of the code is almost identical to the
time in the CCSD code.
The excited states are significantly cheaper with MLCC3,
as CVS is implemented by skipping iterations in the $i$, $j$, $k$ loop,
effectively reducing the scaling to $\mcl{O}(\NV{}\nv{3}\no{2})$.

In Table \ref{t:Gua_speedup_1} we report speed up compared to CC3.
For terms scaling as $\mcl{O}(\NV{}\nv{3}\no{3})$ the speed up is calculated as,
\begin{equation}
   \label{e:speedup_gs}
   S^{GS} = \frac{t^{it}_{CC3}}{t^{it}_{MLCC3}} \qquad
   S^{GS}_{theo} = \frac{(\NO{}\times \NV{})^3}{(\no{}\times \nv{})^3},
\end{equation}
while for core excited states the reduction in the scaling is given by,
\begin{equation}
   \label{e:speedup_es}
   S^{ES} = \frac{t^{it}_{CC3}}{t^{it}_{MLCC3}} \qquad
   S^{ES}_{theo} = \frac{\NO{2}\times \NV{3}}{\no{2}\times \nv{3}}.
\end{equation}
It should be noted that only the dominating terms are included in this estimate,
but terms with a lower scaling can be significant,
especially for small active spaces.
With an active space of 15 occupied orbitals a speed up of about 90 can be reached,
while the deviation from the CC3 results is below 0.2\,eV.

As we pursue a state-averaged approach in the determination of the active space,
the performance is expected to deteriorate somewhat when more states are considered.
Four core excited states of the oxygen atom of guanine are calculated
with aug-cc-pCVDZ basis set on the oxygen atom and aug-cc-pVDZ on the remaining atoms
\cite{aug_cc_pVXZ,cc_pCVXZ,cc_pVXZ}.
The calculations were performed on two Intel Xeon E5-2699 v4 processors using 40 threads,
so the timings are not directly comparable to Table \ref{t:Gua_1state}.

Instead of specifying active spaces explicitly,
we chose to use the CNTO threshold as defined
in eq \ref{e:cnto_threshold_o} and \ref{e:cnto_threshold_v}.
For a more direct comparison the results of calculations
performed as above are tabulated in the SI (Table \ref{si-t:Gua_4_systematic}).
Both the thresholds for the occupied and virtual orbital space
are reduced from $10^{-1}$ to $10^{-6}$ while keeping both thresholds at the same magnitude.
The size of the active spaces and the full size of the system are summarized
in Table \ref{t:cnto_space_4}.
By using the thresholds,
the ratio between active virtual orbitals and active occupied orbitals
reduces to approximately 7.

The excitation energies, $\omega$,
and oscillator strengths, $f$,
are reported in Table \ref{t:Gua_4states}.
For a threshold of $10^{-1}$ the occupied orbital space
consists only of a single orbital,
such that the triples amplitudes are zero by definition.
The results for this threshold are always identical to CCSD.
\begin{table}
\centering
\caption{Number of occupied and virtual orbitals in the active space
         for guanine for various CNTO thresholds.
         The CNTOs have been constructed from four core excited states obtained
         at the CCSD level of theory.}
\label{t:cnto_space_4}
\begin{tabular}{c SS}
   \toprule
   $\xi$      & \mco{$\no{}$} & \mco{$\nv{}$} \\
   \midrule
   $10^{-1}$  &  1 &   4 \\
   $10^{-2}$  &  5 &   8 \\
   $10^{-3}$  & 16 &  56 \\
   $10^{-4}$  & 26 & 138 \\
   $10^{-5}$  & 29 & 208 \\
   $10^{-6}$  & 32 & 244 \\
   \midrule
   Full space & 39 & 263 \\
   \bottomrule
\end{tabular}
\end{table}
\begin{table}
\small
\centering
\caption{First 4 excited states of guanine with MLCC3 for descreasing CNTO thresholds.}
\label{t:Gua_4states}
\begin{tabular}{c cc cc cc cc}
   \toprule
   $\xi$ &
   \mc{2}{c}{State 1} &
   \mc{2}{c}{State 2} &
   \mc{2}{c}{State 3} &
   \mc{2}{c}{State 4}\\ \cmidrule(lr){2-3}\cmidrule(lr){4-5}\cmidrule(lr){6-7}\cmidrule(lr){8-9}
   &
   $\omega$ [eV] & $f\times 100$ &
   $\omega$ [eV] & $f\times 100$ &
   $\omega$ [eV] & $f\times 100$ &
   $\omega$ [eV] & $f\times 100$ \\
   \midrule
   CCSD      & 535.9067 & 3.20 & 538.4340 & 0.12 & 539.3858 & 0.05 & 539.6794 & 0.08 \\
   $10^{-2}$ & 534.8780 & 2.80 & 536.3546 & 0.08 & 537.7091 & 0.02 & 537.8040 & 0.00 \\
   $10^{-3}$ & 533.9879 & 2.43 & 535.1010 & 0.07 & 535.6097 & 0.11 & 536.1425 & 0.00 \\
   $10^{-4}$ & 533.5776 & 2.17 & 534.5033 & 0.06 & 534.7363 & 0.15 & 535.3402 & 0.01 \\
   $10^{-5}$ & 533.5184 & 2.12 & 534.3886 & 0.05 & 534.6080 & 0.15 & 535.1326 & 0.01 \\
   $10^{-6}$ & 533.5107 & 2.12 & 534.3704 & 0.05 & 534.5925 & 0.15 & 535.0691 & 0.02 \\
   \midrule
   CC3 & 533.5091 & 2.12 & 534.3599 & 0.05 & 534.5888 & 0.15 & 535.0139 & 0.02 \\
   \bottomrule
\end{tabular}
\end{table}
The results of Table \ref{t:Gua_4states} are plotted in Figure \ref{fig:cntoG}
in addition to the CCSD and CC3 results, depicted by the horizontal lines.
Increasing the active space improves the energies until the error is below
the expected error of the full CC3 method at a CNTO threshold of $10^{-4}$.
The oscillator strengths of the first and second state converge smoothly towards
their CC3 values,
however,
larger jumps are found for the third and fourth state.
These jumps are artifacts of the small active spaces,
the plots in the SI show a smooth convergence towards the CC3 values.
For the oscillator strengths the CCSD values have not been plotted
as horizontal lines because they would overload the plot,
and they coincide with the data points for $\xi=10^{-1}$.
\begin{figure}[ht]
   \centering
   \begin{subfigure}{0.56\textwidth}
      \includegraphics[width=\textwidth]{plots/cnto_en_conv_lines.pdf}
   \end{subfigure}
   %
   \begin{subfigure}{0.43\textwidth}
      \includegraphics[width=\textwidth]{plots/cnto_osc_conv_lines.pdf}
   \end{subfigure}
   \caption{Convergence of the first four core excitation energies (left)
            and oscillator strengths (right) of guanine with CNTO threshold.
            Dashed lines are the CC3 results and dotted lines denote the CCSD values.}
   \label{fig:cntoG}
\end{figure}
\begin{table}
\centering
\caption{Timings in seconds to compute four core excited states from the oxygen atom of guanine
         at the CCSD, CC3 and MLCC3 level with decreasing CNTO threshold.
         Timings are given, averaged over the number of iterations when solving for
         $\bm{\tau}$, $\bm{\lambda}$, $\bm{R}$ and $\bm{L}$.
         Additionally, timings to construct the ground state density, $\bm{D^{0\text{-}0}}$,
         left transition density, $\bm{D^{m\text{-}0}}$, and right transition density, $\bm{\tilde{D}^{0\text{-}m}}$,
         are reported.
         Note that the MLCC3 and CC3 timings only comprise the triples part.}
\label{t:Gua_time_4}
\begin{tabular}{l S SSSSS S}
   \toprule
   & \mc{1}{c}{CCSD} & \mc{5}{c}{MLCC3} & \mco{CC3}\\
   \cmidrule(lr){2-2} \cmidrule(lr){3-7} \cmidrule(lr){8-8}
   &  & \mco{$ 10^{-2}$} & \mco{$ 10^{-3}$}
      & \mco{$ 10^{-4}$} & \mco{$ 10^{-5}$} & \mco{$ 10^{-6}$} \\
   \midrule
   $\bm{\tau}$     & 22.8 & 0.08 & 2.75 & 133.79 &  704.15 & 1783.39 & 4180.2 \\
   $\bm{\lambda}$  & 44.2 & 0.13 & 5.68 & 270.98 & 1414.40 & 3408.42 & 8593.9 \\
   $\bm{R}$        & 38.7 & 0.10 & 1.23 &  30.89 &  149.33 &  342.51 &  700.2 \\
   $\bm{L}$        & 43.3 & 0.12 & 1.31 &  32.27 &  145.30 &  318.53 &  702.0 \\
   $\bm{D^{0\text{-}0}}$     &  0.6 & 0.02 & 6.27 & 324.25 & 1658.26 & 4020.82 & 8765.3 \\
   $\bm{D^{m\text{-}0}}$      &  0.3 & 0.01 & 3.57 & 164.82 &  735.92 & 1662.66 & 3033.6 \\
   $\bm{\tilde{D}^{0\text{-}m}}$      &  1.2 & 0.06 & 7.39 & 330.58 & 1546.95 & 3647.72 & 7224.9 \\
   \bottomrule
\end{tabular}
\end{table}
Table \ref{t:Gua_time_4} shows the timings of one iteration of the most expensive
parts of the calculation of MLCC3 oscillator strengths.
For thresholds below $10^{-4}$ the CC3 contribution is negligible
when solving for ground and excited state amplitudes.
However,
the calculation of the EOM densities is already dominated by the CC3 part
at $\xi=10^{-3}$.
Compared to the timings for solving the amplitudes the densities are still
insignificant at a threshold of $10^{-3}$.
At $10^{-4}$ the CC3 contribution dominates all timings,
but compared to a full CC3 calculation the cost per iteration is reduced
by more than a factor of 30 for the ground state equations 20 for the excited states
(SI Table \ref{si-t:Gua_SU_xi}).
Even at $10^{-6}$ there is still a reduction of a factor of two,
despite most orbitals being included in the active space.

Comparing Table \ref{t:Gua_1state} and \ref{t:Gua_4states},
shows that the results with 20 occupied and 200 virtual orbitals are
slightly worse than the first excitation for $\xi=10^{-4}$,
although the latter includes only 6 more occupied but 62 less virtual orbitals.
Therefore,
we included calculations with a lower ratio between active virtual and occupied
orbitals.
Table \ref{t:Gua_1state_lower} shows the results for these calculations,
confirming that significantly less virtual orbitals are needed to obtain
almost identical results.
With 18 occupied and 130 virutal orbitals a speed up of up to 80 is achieved,
and with 20 occupied and 130 virtual orbitals the speed up is still around 50
(SI Table \ref{si-t:Gua_SU_o_to_v}).
\begin{table}
\centering
\caption{Calculations of a single core excited state of guanine from the oxygen atom
         at the CCSD, CC3 and MLCC3 level with varying sizes of the active space.
         Excitation energies, $\omega$, and oscillator strengths, $f$,
         as well as timings to construct the ground state density, $\bm{D^{0\text{-}0}}$,
         left transition density, $\bm{D^{m\text{-}0}}$, and right transition density, $\bm{\tilde{D}^{0\text{-}m}}$,
         are reported.
         Additionally timings are given,
         averaged over the number of iterations when solving for
         $\bm{\tau}$, $\bm{\lambda}$, $\bm{R}$ and $\bm{L}$.
         Note that the MLCC3 and CC3 timings only comprise the triples
         part and that timings are given in seconds.}
\label{t:Gua_1state_lower}
\begin{tabular}{l SSSSSS}
   \toprule
   & \mc{6}{c}{MLCC3} \\
   \cmidrule(lr){1-1}\cmidrule(lr){2-7}
   $\no{}/\nv{}$ & \mco{16/160} & \mco{18/130} & \mco{18/150} & \mco{18/180} & \mco{20/130} & \mco{20/200} \\
   \midrule
   $\omega$ [eV] & 533.66 & 533.64 & 533.62 & 533.61 & 533.61 & 533.58 \\
   $f\times 100$ &   2.23 &   2.24 &   2.21 &   2.20 &   2.22 &   2.18 \\
   \midrule
   $\bm{\tau}$    & 40.09 & 28.09 & 41.22 & 70.31 & 38.32 & 125.74 \\
   $\bm{\lambda}$ & 70.96 & 53.86 & 76.78 & 130.22 & 73.14 & 238.02 \\
   $\bm{R}$       & 12.83 & 8.70 & 12.30 & 20.90 & 10.59 & 33.13 \\
   $\bm{L}$       & 13.43 & 9.69 & 13.23 & 22.59 & 11.88 & 36.58 \\
   $\bm{D^{0\text{-}0}}$    & 83.67 & 69.90 & 103.69 & 175.06 & 94.52 & 312.30 \\
   $\bm{D^{m\text{-}0}}$     & 48.37 & 38.19 & 59.63 & 95.24 & 50.33 & 171.81 \\
   $\bm{\tilde{D}^{0\text{-}m}}$     & 90.03 & 75.51 & 111.44 & 182.68 & 95.11 & 320.64 \\
   \bottomrule
\end{tabular}
\end{table}

\begin{figure}
   \centering
   \includegraphics[width=\textwidth]{plots/guanine_pao_active.pdf}
   \caption{Geometry of guanine showing the active regions for which occupied
            Cholesky orbitals and PAOs have been constructed.
            The labels denote the number of active atoms and hydrogens are always inactive.}
   \label{fig:G_PAO_geom}
\end{figure}
We
have also performed
some calculations with Cholesky occupied orbitals and PAOs for the
virtual space.
The active atoms are shown in Figure \ref{fig:G_PAO_geom} as solid atoms
and $10^{-2}$ was used as threshold for the Choleksy decomposition of the AO density.
\begin{table}
\centering
\caption{Number of occupied and virtual orbitals in the active spaces
         constructed using Cholesky orbitals and PAOs for guanine.}
\label{t:pao_as}
\begin{tabular}{c SS}
   \toprule
   System label (Figure \ref{fig:G_PAO_geom})& \mco{$\no{}$} & \mco{$\nv{}$} \\
   \midrule
   1  &  5 &  26 \\
   4  & 23 &  92 \\
   7a & 33 & 158 \\
   7b & 33 & 158 \\
   11 & 39 & 245 \\
   \midrule
   Full space & 39 & 263 \\
   \bottomrule
\end{tabular}
\end{table}
\begin{table}
\small
\centering
\caption{First 4 excited states of Guanine with MLCC3 calculated with active spaces constructed from Cholesky orbitals and PAOs.}
\label{t:paoG_conv}
\begin{tabular}{r cc cc cc cc}
   \toprule
   &
   \mc{2}{c}{State 1} &
   \mc{2}{c}{State 2} &
   \mc{2}{c}{State 3} &
   \mc{2}{c}{State 4}\\ \cmidrule(lr){2-3}\cmidrule(lr){4-5}\cmidrule(lr){6-7}\cmidrule(lr){8-9}
   &
   $\omega$ [eV] & $f\times 100$ &
   $\omega$ [eV] & $f\times 100$ &
   $\omega$ [eV] & $f\times 100$ &
   $\omega$ [eV] & $f\times 100$ \\
   \midrule
   $1$  & 534.6250 & 2.81 & 537.0755 & 0.13 & 538.2042 & 0.39 & 538.2714 & 0.28 \\
   $4$  & 533.8427 & 2.37 & 534.9479 & 0.07 & 535.9413 & 0.05 & 536.0856 & 0.15 \\
   $7$a & 533.5901 & 2.17 & 534.6548 & 0.06 & 534.9312 & 0.16 & 535.4104 & 0.04 \\
   $7$b & 533.6082 & 2.19 & 534.6045 & 0.06 & 534.8809 & 0.16 & 535.4454 & 0.03 \\
   $11$ & 533.5110 & 2.12 & 534.4149 & 0.05 & 534.5932 & 0.15 & 535.0960 & 0.02 \\
   \midrule
   CC3 & 533.5091 & 2.12 & 534.3599 & 0.05 & 534.5888 & 0.15 & 535.01394 & 0.02 \\
   \bottomrule
\end{tabular}
\end{table}
The size of the active spaces are summarized in Table \ref{t:pao_as}
and the results are reported in Table \ref{t:paoG_conv}.
\begin{figure}[ht]
   \centering
   \begin{subfigure}{0.56\textwidth}
      \includegraphics[width=\textwidth]{plots/pao_en_conv_lines.pdf}
   \end{subfigure}
   %
   \begin{subfigure}{0.43\textwidth}
      \includegraphics[width=\textwidth]{plots/pao_osc_conv_lines.pdf}
   \end{subfigure}
   \caption{Convergence of the first four core excitation energies (left)
            and oscillator strengths (right) of guanine for the five
            active spaces in Figure \ref{fig:G_PAO_geom}.
            Dashed lines are the CC3 results and dotted lines denote the CCSD values.}
   \label{fig:paoG}
\end{figure}
As shown in Figure \ref{fig:paoG} the excitation energies are already significantly
improved when only the oxygen is included in the active space.
However, the size of the active spaces also increases much faster,
because all the atoms contribute to the $\pi$-system.
Despite the active spaces being larger,
the performance of the Cholesky/PAOs is worse than calculations with a similarly large
active space consisting of CNTOs.
The reason for the poor performance of these active spaces
is that we split up the $\pi$-system.
Additionally,
the CC3 excitation vectors consist of multiple similarly large amplitudes
which need to be described accurately by the active space.
An active space consisting of CNTOs is better suited to describe such excted states.

\subsection{Formaldehyde in water}

To investigate the scaling with the size of the inactive orbital space
we consider formaldehyde with several explicit water molecules.
The calculations were performed on two Intel Xeon-Gold 6138 using 40 threads.
Comparing excitation energy and oscillator strength
is not constructive for this system,
because CCSD and CC3 already almost coincide for the first excited state.
The geometry for formaldehyde with six water molecules
is reported in the SI;
it has been adapted from a geometry with 10 water molecules from Ref. \citenum{MLCC_CNTO}.
The other geometries are
generated by subsequently removing water molecules,
starting with the last one.
For a proper investigation of solvent effects,
randomized geometries would have to be extracted from a molecular dynamics
simulation and the results would have to be averaged.\cite{QMMM_ES}

For all calculations we used a aug-cc-pVTZ basis set
and the active space comprises 8 occupied and 136 virtual orbitals.
The sizes of the systems considered are summarized in Table \ref{t:size_fa}.
\begin{table}
\centering
\caption{Number of occupied and virtual orbitals for formaldehyde with
         increasing number of water molecules with aug-cc-pVTZ basis set.}
\label{t:size_fa}
\begin{tabular}{c cc}
   \toprule
   System & \mc{2}{c}{aug-cc-pVTZ} \\
   \cmidrule(lr){2-3}
    \#H$_2$O & \mco{$\NO{}$} & \mco{$\NV{}$} \\
   \midrule
    1 & 13 & 217 \\
    2 & 18 & 304 \\
    3 & 23 & 391 \\
    4 & 28 & 478 \\
    5 & 33 & 565 \\
    6 & 38 & 652 \\
   \bottomrule
\end{tabular}
\end{table}

\begin{figure}[ht]
   \centering
   \includegraphics[width=0.7\textwidth]{plots/scaling_inactive_final.pdf}
   \caption{Average time to calculate one transition density or one
            iteration solving for $\bm{\tau}$, $\bm{\lambda}$, $\bm{L}$ and $\bm{R}$
            with increasing number of water molecules in the inactive space.}
   \label{fig:pao_water}
\end{figure}

Figure \ref{fig:pao_water} shows
the timing breakdown for the MLCC3 contribution in the calculation of EOM oscillator strengths.
As expected the timings for every quantity increase linearly with the number of
water molecules added to the system,
implying the terms scaling quadratically with the full system size
are negligible.

\subsection{Azobenzene}

In the aug-cc-pVDZ basis, azobenzene has 48 occupied and 364 virtual orbitals.
On two Intel Xeon E5-2699 v4 processors using 40 threads
a single iteration of the CC3 ground state equations takes 6 hours.
As the Jacobian transformations are twice as expensive per state,
a CC3 calculation of 10 excited states is costly.

By using an active space containing 34 occupied and 238 virtual orbitals,
the time per iteration of the ground state equations reduced to 36 minutes.
In figure \ref{fig:azobenzene},
the spectra calculated at the CCSD and MLCC3 level of theory are shown
together with the experimental results.
\begin{figure}[h!]
   \centering
   \includegraphics[scale=0.5]{plots/azobenzene_gauss.pdf}
   \caption{UV-VIS absorption spectrum of azobenezene calculated with CCSD
   and MLCC3 employing aug-cc-pVDZ basis set.\cite{aug_cc_pVXZ}
   The theoretical stick spectrum is broadened using Gaussian functions
   with fwhm of 0.5\,eV and the experimental data is
   taken from Ref. \citenum{azobenzene_exp}.}
   \label{fig:azobenzene}
\end{figure}
While the CCSD results are significantly blue shifted,
the broadened MLCC3 values match very well with the experimental bands
at 300 nm and 220 nm.
The very broad band at around 450 nm is not reproduced,
but an almost dark excitation is found around 420 nm.
CCSD predicts this latter excitation to be at 400 nm instead.

\subsection{Betaine 30}

To demonstrate the capabilities of our MLCC3 implementation,
we consider the first core excitation from the oxygen atom in betaine 30.
The geometry is shown in Figure \ref{fig:betaine}.
The system comprises 145 occupied and 992 virtual orbitals
using a aug-cc-pCVDZ basis set for the oxygen atom,
aug-cc-pVDZ for carbon and nitrogen atoms and cc-pVDZ for hydrogen atoms.
\begin{figure}[h!]
   \centering
   \includegraphics[width=0.4\textwidth]{plots/betaine_geom.pdf}
   \caption{Geometry of the betaine 30.}
   \label{fig:betaine}
\end{figure}
\begin{table}[ht]
    \centering
    \begin{tabular}{c S[table-format=3.3] S[table-format=3.3] c c}
        \toprule
        & \mco{$\omega$ [eV]} & \mco{$f\times 100$} & $\no{}$ & $\nv{}$\\ \midrule
        CCSD  & 535.12 & 2.74 &  &  \\
        MLCC3 & 531.50 & 0.67 & 20 & 200 \\
        MLCC3 & 531.29 & 0.63 & 25 & 200 \\
        MLCC3 & 531.32 & 0.63 & 25 & 250 \\
        \bottomrule
    \end{tabular}
    \caption{First core excitation from the oxygen atom calculated at the CCSD level of theory
             and MLCC3 with increasing number of CNTOs in the active space.}
    \label{tab:betaine}
\end{table}
In Table \ref{tab:betaine} we report the excitation energy and oscillator strengths for CCSD
and MLCC3 using three active CNTO spaces of increasing size.
Using CCSD both the excitation energy and especially the oscillator strength are
overestimated compared to the MLCC3 results.
Increasing the size of the active space from 20 occupied and 200 virtual CNTOs
to 25 occupied and 250 virtual orbitals,
only changes the excitation energy by 0.3~eV.
Therefore,
we can assume that the MLCC3 results are within the expected error range of a full CC3 calculation.
\begin{table}[ht]
\centering
\caption{Timings in minutes to compute a core excited state
         from the oxygen atom of betaine 30
         at the CCSD and MLCC3 level with several active spaces.
         Timings are given, averaged over the number of iterations when solving for
         $\bm{\tau}$, $\bm{\lambda}$, $\bm{R}$ and $\bm{L}$.
         Additionally, timings to construct the ground state density, $\bm{D^{0\text{-}0}}$,
         left transition density, $\bm{D^{m\text{-}0}}$, and right transition density, $\bm{\tilde{D}^{0\text{-}m}}$,
         are reported.
         Note that the MLCC3 and CC3 timings only comprise the triples part.}
\label{t:betaine_timings}
\begin{tabular}{l SS SSSSS}
   \toprule
   & \mco{CCSD} & \mc{3}{c}{MLCC3} \\
   \cmidrule(lr){2-2}\cmidrule(lr){3-5}
   $\no{}/\nv{}$ & & \mco{$20/200$} & \mco{$25/200$} & \mco{$25/250$} \\
   \midrule
   $\bm{\tau}$    &  73.2 & 3.1 &  5.6 & 10.7 \\
   $\bm{\lambda}$ & 143.5 & 6.4 & 12.0 & 21.4 \\
   $\bm{R}$       & 122.6 & 1.2 &  1.7 &  2.8 \\
   $\bm{L}$       & 130.8 & 1.3 &  1.9 &  3.2 \\
   $\bm{D^{0\text{-}0}}$    &   0.5 & 8.0 & 14.6 & 28.6 \\
   $\bm{D^{m\text{-}0}}$     &   0.5 & 5.2 &  9.4 & 18.3 \\
   $\bm{\tilde{D}^{0\text{-}m}}$     &   1.0 & 9.1 & 16.5 & 31.2 \\
   \bottomrule
\end{tabular}
\end{table}

Due to the significant size of the system the time spent calculating
the contribution of the triple excitations is small compared to the timings of CCSD,
as shown in Table \ref{t:betaine_timings}.
For the densities the triples contribution dominates,
however,
the time used to construct densities is still small compared to
determining the ground and excited states.

\section{Conclusion}\label{Conclusion}

The multilevel CC3 method provides a framework,
with which intensive molecular properties can be calculated
at an accuracy approaching that of the CC3 method.
For sufficiently large inactive spaces the computational cost
will tend towards that of CCSD.
Compared to Cholesky PAOs,
CNTOs provide smaller orbital spaces without sacrificing accuracy.
However,
the cost of constructing CNTOs is significant,
as the CCSD ground and excited state equations need to be solved.

There is some ambiguity regarding the selection of the active space using CNTOs.
We can either specify the number of occupied and virtual orbitals explicitly
or use a cutoff, $\xi$,
and include the orbitals whose eigenvalues sum up to $1-\xi$.
The first approach gives great flexibility,
but several calculations are typically needed to confirm that the excitation
energies actually converged.
Using a cutoff on the other hand is a more blackbox approach,
as $\xi=10^{-4}$ gives accurate results,
but the active spaces can become larger than required.
Further benchmarking, especially on larger systems,
is needed to obtain a rule of thumb for the selection of an active space.

Two bottlenecks were identified that limit the size of the systems we can treat:
First, the convergence behaviour of the solvers is diminished,
due to the change of the orbital basis.
The start guess could be improved by transforming the CCSD amplitudes
from canonical MOs to the CNTO basis.

For large systems with several hundered to a thousand MOs,
CCSD becomes a bottleneck and
another layer could be introduced at the CCS level of theory.
For the multilevel CC3 model with CC3 in CCSD in CCS,
it has to be investigated how the orbital space is set up effectively,
as NTOs obtained from CCS will not provide a suitable active space.
One possibility could be the approximated CNTOs introduced by Baudin and Kristensen,
or CNTOs obtained from a MLCCSD calculation.\cite{cornflex}

\begin{acknowledgement}

We acknowledge computing resources through UNINETT Sigma2
- the National Infrastructure for High Performance Computing
and Data Storage in Norway, through project number NN2962k.
We acknowledge funding from the Marie Sk{\l}odowska-Curie European Training Network
``COSINE -- COmputational Spectroscopy In Natural sciences and Engineering'',
Grant Agreement No. 765739 and
the Research Council of Norway through FRINATEK projects 263110, CCGPU,
and 275506, TheoLight.

\end{acknowledgement}

\clearpage

\subsection*{Guanine}

Table \ref{t:Gua_4_systematic} summarizes the results from calculations
using MLCC3 with active spaces where $\nv{} = 10\no{}$.
These results are also visualized in Figure \ref{fig:Gua_4_systematic}
showing a smooth convergence of both excitation energies and oscillator strengths
towards the CC3 results.

\begin{table}[h!]
   \centering
   \caption{Excitation energies and oscillator strengths for the first four
            excited states of Guanine with MLCC3 for active spaces with increasing size.
            For the MLCC3 values the number of occupied and virtual orbitals
            is reported in the left column.
            The total system contains 39 occupied and 263 virtual orbitals.}
   \label{t:Gua_4_systematic}
   \begin{tabular}{c cc cc cc cc}
      \toprule
      System &
      \mc{2}{c}{State 1} & \mc{2}{c}{State 2} & \mc{2}{c}{State 3} & \mc{2}{c}{State 4} \\
      \cmidrule(lr){1-1} \cmidrule(lr){2-3} \cmidrule(lr){4-5}  \cmidrule(lr){6-7} \cmidrule(lr){8-9}
      CCSD & 535.91 & 3.26 & 538.44 & 0.12 & 539.39 & 0.05 & 539.68 & 0.07 \\
      \phantom{1}8/\phantom{1}80  & 534.13 & 2.45 & 535.20 & 0.06 & 536.22 & 0.10 & 536.34 & 0.00 \\
      10/100 & 533.94 & 2.39 & 534.99 & 0.06 & 535.79 & 0.11 & 536.08 & 0.00 \\
      13/130 & 533.79 & 2.30 & 534.78 & 0.06 & 535.43 & 0.13 & 535.77 & 0.01 \\
      15/150 & 533.73 & 2.26 & 534.66 & 0.06 & 535.18 & 0.14 & 535.64 & 0.01 \\
      18/180 & 533.66 & 2.21 & 534.55 & 0.05 & 534.94 & 0.14 & 535.44 & 0.01 \\
      20/200 & 533.62 & 2.18 & 534.49 & 0.05 & 534.83 & 0.16 & 535.32 & 0.01 \\
      24/240 & 533.55 & 2.14 & 534.41 & 0.05 & 534.69 & 0.17 & 535.14 & 0.02 \\
      CC3 & 533.51 & 2.12 & 534.36 & 0.05 & 534.59 & 0.15 & 535.01 & 0.02 \\
      \bottomrule
   \end{tabular}
\end{table}

\begin{figure}[ht]
   \centering
   \begin{subfigure}{0.555\textwidth}
      \includegraphics[width=\textwidth]{plots/systematic_energy_conv_lines.pdf}
   \end{subfigure}
   %
   \begin{subfigure}{0.435\textwidth}
      \includegraphics[width=\textwidth]{plots/systematic_osc_conv_lines.pdf}
   \end{subfigure}
   \caption{Convergence of the first four core excitation energies (left)
            and oscillator strengths (right) of guanine with the size
            of the active space.
            Dashed lines are the CC3 results and dotted lines denote the CCSD values.}
   \label{fig:Gua_4_systematic}
\end{figure}

\begin{table}
\centering
\caption{Speed up of MLCC3 compared to canonical CC3
         for the calculation of four core excited states of guanine.
         Speed ups calculated according to equations
         47 and 48 in the main document.
         The first part shows the speed up for terms that scale asymptotically
         as $\mcl{O}(\NV{}\nv{3}\no{3})$ while the second part summarizes the
         speed up for terms with a cost of $\mcl{O}(\NV{}\nv{3}\no{2})$.}
\label{t:Gua_SU_xi}
\begin{tabular}{l c
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]}
   \toprule
   $\xi$ && \mco{$10^{-3}$} & \mco{$10^{-4}$} & \mco{$10^{-5}$} & \mco{$10^{-6}$} \\
   \midrule
   $\bm{\tau}$     && 1520.1 & 31.2 & 5.9 & 2.3 \\
   $\bm{\lambda}$  && 1505.2 & 31.6 & 6.0 & 2.5 \\
   $\bm{D^{0\text{-}0}}$     && 1397.9 & 27.0 & 5.3 & 2.2 \\
   $\bm{D^{m\text{-}0}}$      &&  849.7 & 18.4 & 4.1 & 1.8 \\
   $\bm{\tilde{D}^{0\text{-}m}}$      &&  977.8 & 21.9 & 4.7 & 2.0 \\
   \cmidrule{1-1}
   $S^{GS}_{theo}$ && 1500.2 & 23.4 & 4.9 & 2.3 \\
   \midrule
   $\bm{R}$        &&  537.8 & 21.4 & 4.4 & 1.9 \\
   $\bm{L}$        &&  502.8 & 20.4 & 4.5 & 2.1 \\
   \cmidrule{1-1}
   $S^{ES}_{theo}$ &&  615.4 & 15.6 & 3.7 & 1.9 \\
   \bottomrule
\end{tabular}
\end{table}

\begin{table}
\centering
\caption{Speed up of MLCC3 compared to canonical CC3
         for the calculation of a single core excited states of guanine.
         Speed ups calculated according to equations
         47 and 48 in the main document.
         The first part shows the speed up for terms that scale asymptotically
         as $\mcl{O}(\NV{}\nv{3}\no{3})$ while the second part summarizes the
         speed up for terms with a cost of $\mcl{O}(\NV{}\nv{3}\no{2})$.}
\label{t:Gua_SU_o_to_v}
\begin{tabular}{l c
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]
                S[table-number-alignment = center]}
   \toprule
   $\no{}$ && \mco{16} & \mco{18} & \mco{18} & \mco{18} & \mco{20} & \mco{20} \\
   $\nv{}$ && \mco{160} & \mco{130} & \mco{150} & \mco{180} & \mco{130} & \mco{200} \\
   \midrule
   $\bm{\tau}$     && 55.4 & 79.1 & 53.9 & 31.6 & 57.9 & 17.7 \\
   $\bm{\lambda}$  && 58.6 & 77.2 & 54.1 & 31.9 & 56.8 & 17.5 \\
   $\bm{D^{0\text{-}0}}$     && 61.5 & 73.6 & 49.6 & 29.4 & 54.5 & 16.5 \\
   $\bm{D^{m\text{-}0}}$      && 51.5 & 61.4 & 41.6 & 25.4 & 48.8 & 14.5 \\
   $\bm{\tilde{D}^{0\text{-}m}}$      && 48.4 & 61.3 & 39.2 & 24.6 & 46.5 & 13.6 \\
   \cmidrule{1-1}
   $S^{GS}_{theo}$ && 64.3 & 84.2 & 54.8 & 31.7 & 61.4 & 16.9 \\
   \midrule
   $\bm{R}$        && 23.5 & 34.7 & 24.6 & 14.4 & 28.5 & 9.1 \\
   $\bm{L}$        && 23.7 & 32.8 & 24.0 & 14.1 & 26.8 & 8.7 \\
   \cmidrule{1-1}
   $S^{ES}_{theo}$ && 26.4 & 38.9 & 25.3 & 14.6 & 31.5 & 8.6 \\
   \bottomrule
\end{tabular}
\end{table}

\clearpage

\subsection*{Geometries}

Here we list the geometries of the molecules used in the calculations
presented in the application section of the paper.

\begin{table}
   \centering
   \caption{Geometry of guanine in {\AA}ngstr{\o}m.}
   \begin{tabular}{c S[table-format=3.6] S[table-format=3.6] S[table-format=3.6]}
      \toprule
      Atom & \mc{1}{c}{x} & \mc{1}{c}{y} & \mc{1}{c}{z} \\
      \midrule
      O  &   2.400416 &   1.186125 &  0.000000 \\
      N  &  -2.164547 &   0.729374 &  0.000000 \\
      C  &  -1.823669 &   2.066210 &  0.000000 \\
      N  &  -0.540931 &   2.253857 &  0.000000 \\
      C  &   0.000000 &   0.987621 &  0.000000 \\
      C  &   1.368570 &   0.557966 &  0.000000 \\
      N  &   1.424157 &  -0.869681 &  0.000000 \\
      C  &   0.356682 &  -1.723002 &  0.000000 \\
      N  &   0.627528 &  -3.053172 &  0.000000 \\
      N  &  -0.882076 &  -1.320799 &  0.000000 \\
      C  &  -0.996160 &   0.028079 &  0.000000 \\
      H  &  -2.573196 &   2.842649 &  0.000000 \\
      H  &   2.367552 &  -1.232740 &  0.000000 \\
      H  &   1.561780 &  -3.418613 &  0.000000 \\
      H  &  -0.152003 &  -3.687334 &  0.000000 \\
      H  &  -3.088910 &   0.328741 &  0.000000 \\
      \bottomrule
   \end{tabular}
\end{table}

\begin{table}
   \footnotesize
   \centering
   \caption{Geometry of formaldehyde with 6 explicit water molecules in {\AA}ngstr{\o}m.
   Adapted from a geometry with 10 water molecules from Ref. \citenum{MLCC_CNTO}.}
   \begin{tabular}{c S[table-format=3.7] S[table-format=3.7] S[table-format=3.7]}
      \toprule
      Atom & \mc{1}{c}{x} & \mc{1}{c}{y} & \mc{1}{c}{z} \\
      \midrule
      C &    0.24155 &  -0.26233 &   0.50653 \\
      O &    1.08878 &  -0.29115 &   1.39233 \\
      H &   -0.09479 &  -1.18677 &   0.01481 \\
      H &   -0.21855 &   0.68784 &   0.17709 \\
      O &    1.67506 &   2.52513 &   1.36591 \\
      H &    1.64135 &   1.57595 &   1.59689 \\
      H &    1.72610 &   2.51833 &   0.38456 \\
      O &    1.75008 &  -0.31632 &  -1.77458 \\
      H &    1.57721 &   0.65833 &  -1.80806 \\
      H &    2.61183 &  -0.36928 &  -1.33501 \\
      O &    1.48197 &  -3.01167 &   1.26413 \\
      H &    2.11276 &  -3.43941 &   1.86016 \\
      H &    1.49199 &  -2.05596 &   1.51182 \\
      O &   -2.40632 &  -1.19477 &   0.86990 \\
      H &   -2.04899 &  -2.10772 &   0.67851 \\
      H &   -3.05560 &  -1.30821 &   1.57778 \\
      O &   -0.89752 &   3.33556 &   1.62275 \\
      H &    0.06715 &   3.09459 &   1.64454 \\
      H &   -0.91078 &   4.27966 &   1.83820 \\
      O &   -1.16871 &   2.71932 &  -1.00701 \\
      H &   -1.22105 &   2.98736 &  -0.05388 \\
      H &   -1.77348 &   1.94185 &  -1.10382 \\
      \bottomrule
   \end{tabular}
\end{table}

\end{suppinfo}

\clearpage

redpajama_set_name: RedPajamaArXiv


text:
Biz Break: Apple naysayers: Sudden trouble for…
Biz Break: Apple naysayers: Sudden trouble for iPad, iPhone maker?
By Frank Michael Russell | Mercury News, Bay Area News Group
Today: Apple stock drops after a rare analyst downgrade of the "i" device maker. Plus: Google news. And: Silicon Valley tech stocks.
Apple naysayers
Apple's stock dropped today after a rare analyst downgrade of the Cupertino maker of Mac computers and "i" devices including the iPad, iPhone and iPod touch.
According to Bloomberg News, JMP Securities lowered its rating on Apple shares to "market perform" from "market outperform."
In an interview with Tiernan Ray of Barron's Tech Trader Daily blog, JMP analyst Alex Gauna said he cut his rating on Apple shares in response to slowing revenue growth at Taiwan-based Hon Hai Precision — the parent of contract manufacturer Foxconn Technology Group. But the analyst also said the intensifying disaster in Japan could hurt Apple.
Gauna still expects Apple to meet its forecast of $22 billion in revenue for the current quarter. However, analysts on average have been expecting Apple to pull in just over $23 billion — and the company routinely beats Wall Street forecasts.
In an e-mail today, Ticonderoga Securities analyst Brian White noted that the crisis in Japan "will have far-reaching implications" for tech manufacturers and suppliers.
"At the same time, we believe Apple has enough pull in the supply chain due to its size, supply agreements with upfront payments and success of its products to get more than its fair share of supplier output," White wrote.
Analysts also have noted that demand for Apple's iPad 2 since its release Friday appears to have exceeded supply. Today on Apple's online store, the company is scheduling shipping for the iPad 2 in four to five weeks.
Apple shares finished regular trading today at $330.01, down $15.42, or 4.5 percent — a somewhat steeper fall than the decline today in the tech-heavy Nasdaq. Earlier, Apple shares dropped as low as $326.26.
Verizon iPhone: In a blog post today, Boy Genius Report founder and editor-in-chief Jonathan Geller said the Verizon iPhone may be no better choice than the AT&T model.
Geller — who is based on the East Coast — complained today about dropped calls and 2G connections on his Verizon iPhone in Connecticut and New York City.
"In the end, my personal experience with Verizon's iPhone in and around New York City ended up being about the same as it was when I was on AT&T," he wrote. "This, combined with other advantages AT&T's network has, has made me finally decide to switch back."
Android army: Motorola Mobility today announced that a Wi-Fi version of its Xoom tablet computer — which runs Google's Android operating system — will be available March 27 with a suggested price of $599. The Xoom has 32 gigabytes of storage.
By comparison, Apple's 32GB Wi-Fi-only iPad 2 also costs $599.
Verizon Wireless, meanwhile, will sell its first 4G LTE smartphone starting tomorrow. The HTC ThunderBolt — which also runs Android — will cost $249.99 for customers who agree to a new two-year contract with Verizon.
Google Docs: The Mountain View Internet juggernaut is encouraging a wave of comments in documents created with its Google Docs online applications.
According to a blog post today, Google is introducing the discussions feature "to encourage rapid and seamless discussions, help the right people participate, as well as integrate discussions with e-mail in an intuitive way," Google Docs group product manager Scott Johnston wrote.
In another post, software engineer Nick Cooper wrote that Googlers have been testing the new feature and "have seen it make the feedback cycle shorter and get more people involved."
Wholesale food and energy costs skyrocketed last month, sending the Producer Price Index up 1.6 percent, the U.S. Labor Department reported today.
Food prices jumped 3.9 percent from the month before, and energy prices climbed 3.3 percent. Excluding often volatile food and energy costs, though, wholesale prices were up 0.2 percent from the month before.
Silicon Valley tech stocks
Up: Gilead Sciences.
Down: Apple, Google, Oracle, Intel, Cisco Systems, Hewlett-Packard, eBay, VMware, Juniper Networks.
The tech-heavy Nasdaq composite index: Down 50.51, or 1.9 percent, to 2,616.82.
The blue chip Dow Jones industrial average: Down 242.12, or 2 percent, to 11,613.30.
And the widely watched Standard & Poor's 500 index: Down 24.99, or 1.9 percent, to 1,256.88.
Check in weekday afternoons for the 60-Second Business Break, a summary of news from Mercury News staff writers, The Associated Press, Bloomberg News and other wire services. Contact Frank Russell at 408-920-5876. Follow him at Twitter.com/mercspike.
Frank Michael Russell

redpajama_set_name: RedPajamaCommonCrawl


text:
Skip to main content Food Voraciously Recipe Finder Going Out Guide Tom Sietsema Tim Carman Nourish Dinner in Minutes Wine Spirits
'The line is crossed, and it's crossed daily': The struggles of female bartenders
By M. Carrie Allan
M. Carrie Allan
Bio Follow
Bartender Rachel Sergi makes drinks at the Quarter + Glory. (Marvin Joseph/The Washington Post)
Back in the '90s, Allegra Lucier had an exhausting bartending gig at a rock bar in the East Village. Night after night, she got hit on.
"So this one gentleman passed me a note one evening, and I was like, 'I'm not doing this,' and I passed the note back. He passed it again, I passed it back, he passed it again, and I was like, 'If you want me to get you a drink, I'll get you a drink — other than that . . . leave me alone.' He passed the note again. And I'm like, 'Oh my God, I'm going to get this person kicked out.' I'm so sick of it. So I open the note: Hello. I am deaf."
She was mortified. But it was also a signal flare, a reminder of how jaded you can get in an environment where some of the clientele have messed-up presumptions about what "hospitality" should entail.
Those were the days of Long Island iced teas and rum-and-Cokes, before the craft cocktail renaissance. As that movement gained steam, Lucier — now head bartender at Osteria Morini in New York — moved into it. She's happy she did. The environment is more creative and rewarding, less harassment-prone, one in which women bartenders can create a real career, even as they — the horror! — get older.
Yet she noticed another difference.
"In the rock-and-roll world, it's all about women behind the bar — maybe because it's about sex, it's about sales," she says. "When I first got into the craft cocktail world, the first thing you realize is you're very much alone."
Genders behind the blenders
The cocktail world is full of talented female bartenders. And yet both men and women will tell you that, especially in some markets, gender biases are still a problem.
Rachel Sergi strains the contents of a drink into a glass before serving. (Marvin Joseph/The Washington Post)
Bartending was considered a woman's job in England, but here, that began to change around the time of the Revolution, says cocktail historian David Wondrich. During Prohibition, women came to speakeasies as customers. They came back as bartenders when men were away at war; when the men came back, women got pushed out. They were seen as taking men's jobs, says Wondrich. A notion that women needed protection from the moral vice of alcohol lingered, too.
It wasn't until the '70s that, thanks to the 1964 Civil Rights Act, laws prohibiting women from bartending began to get struck down.
The shift toward male bartenders in the 19th century, Wondrich says, "partly had to do with the increased status of the bartender," a boost he captured in "Imbibe!" "It's kind of a vicious circle. The status rises, so more men get into it, and more men get into it, so the status is raised."
Which sounds a lot like what we've seen with the craft cocktail renaissance.
In its first decade, the movement often focused on digging up old drinks that had all but disappeared. It's a subculture obsessed with history — old distilling techniques, ancient botanicals — and inclined to romanticize its past, resurrecting everything from "speakeasies" to sartorial style. The image of a bearded bartender in old-timey suspenders, geeking out on artisanal bitters has become a bit of a joke.
Yet there's a grain of truth in it. Maybe a whole slice of bread. I regularly visit cocktail dens where the crew behind the stick is entirely or almost entirely male. Add throwback costuming and decor, and some bars can feel like you've stepped into a time warp — which is part of their appeal.
But it's made me wonder: When a subculture identifies deeply with a historical heyday in which women and minorities had little place, does some of that baggage seep into modern iterations, disguised as simple aesthetics?
In "A Proper Drink," his new history of the craft cocktail renaissance, Robert Simonson devotes extensive copy to Audrey Saunders and Julie Reiner, two pioneers who opened groundbreaking bars Pegu Club and the Flatiron Lounge and trained a cadre of New York bartenders who went on to become major influencers.
But he's quick to acknowledge that in his years writing about cocktails for the New York Times, "I spend a lot of my time interviewing white men."
Fom left, Sarah Rosner of Radiator, Rachel Sergi of Quarter+Glory, Megan Barnes of Espita Mezcaleria, Chantal Tseng of Reading Room DC, Gina Chersevani of Buffalo & Bergen, Andrea Tateosian of Urbana, Danielle Paulson of District Distilling Company and Angie Fetherston of Drink Company. (Marvin Joseph/The Washington Post)
'We all have biases'
This spring, a social media storm exploded around Employees Only, an influential speakeasy-style bar in New York. The bar had posted a hiring notice for its new Singapore location: "NOT JUST A BOYS CLUB! . . . We are looking for badass cocktail waitresses and supervisors to join our team!"
At a glance, the ad seemed harmless, even purposefully inclusive. But EO had stepped in an issue that has dogged the industry: The career path from barback — assistants who help keep the bar stocked with booze, clean glasses and perform other thankless tasks — to bartender has long been an easier one than that from cocktail waitress to bartender. Since bars have traditionally hired men as barbacks and women as servers, women have found it harder to advance.
So EO's ad asking women to apply for non-bartending positions didn't sit well with some and ended up in a full-scale Internet flame-and-shame war. (In EO's defense, a spokeswoman says the bartender positions in Singapore had already been filled, and the location has a female bar apprentice.)
The organizers of Tales of the Cocktail had already been digging into diversity issues when the blowup happened, producing a white paper, making recommendations and holding a session on gender issues during the July conference. Among the findings: "Employer biases" and "customer biases" were the two most common responses to a question about barriers to women trying to build bartending careers. A New York survey found nearly 60 percent of bartenders in fine-dining establishments were male, compared to 45 percent in family-style restaurants (where earnings and prestige are lower). "In other words, despite comprising a majority of the bartending workforce, females are underrepresented in the most lucrative and highest profile positions within the industry."
"You find a similar thing with African Americans and Hispanics," says Ann Tuennerman, founder of Tales. "Yes, they have a high percentage in the hospitality industry, but in less-prominent positions."
The Bureau of Labor Statistics 2015 numbers indicate that 60 percent of bartenders now are women. But the picture is complex. Women reported easily getting gigs at sports bars and "breastaurants" such as Hooters, where a good headshot can be more important than a good Manhattan. In such venues, and in particular markets (Vegas, Miami and L.A. were mentioned), men reported facing hiring barriers themselves.
In the craft cocktail world, where the bartender role is more prestigious and less sexualized, it was more of a mixed bag. Several women said they felt their gender had occasionally been an advantage, with employers looking to add a woman to their bartending lineup. Others, especially in smaller markets, reported struggles to advance.
Sarah Rosner, Danielle Paulson and Andrea Tateosian. (Marvin Joseph/The Washington Post)
Lots of folks agree that gender issues persist, but the best way to address them is not always clear.
Some have focused on cultivating female talent. In 2011, bartenders Ivy Mix and Lynnette Marrero started Speed Rack, a bartending competition for women, "because there weren't any female bartenders in the best bars in the world, and there was a problem with that," Mix says. The popular competitions now take place around the country and internationally, and Mix says they've built a lot of camaraderie.
After winning the Bols spirits company-sponsored world bartending championship in 2014, bartender Kate Gerwin started Girls with Bols, a program that pairs up-and-coming women with female (and some male) mentors. That program, too, has grown by leaps and bounds and helped many women.
Derek Brown, owner of multiple D.C. bars and founder of hospitality group Drink Company, says building a diverse bar takes effort. "It's not this knee-jerk 'Let's make our staff Benetton,' but more a thoughtful approach that says, 'Let's be careful not to stack our staff with all the same kind of people, because that doesn't reflect the people who will come to our bars.'"
Being intentional in hiring is key, says David Kaplan, a founder of Death & Co., another highly influential speakeasy-style cocktail bar in New York.
Over the years, Death & Co. has had female head bartenders, female general managers, men and women servers. Kaplan's proud of the year when all the New York Speed Rack finalists were from the company's family of bars. But when Death & Co. first opened, "we did have an all-female floor staff, and . . . I didn't question it. Only later I realized, 'Oh, I'm doing this just because I've seen everyone else doing it.' "
"We all have biases," he says. "The thing is realizing they're there and working to counter them."
The bad apples
Angie Fetherston, Gina Chersevani and Rachel Sergi. (Marvin Joseph/The Washington Post)
Many women I talked to had rueful stories of how the "Bartenders are male" bias had played out. Rachel Sergi, bartender at Quarter + Glory in the District, related a common theme: She'll be behind the bar with a male colleague, and customers will ask him to make their drink. Or customers will ask her when the bartender will be there.
Megan Barnes, beverage director at Espita, recalls a customer who complimented her male barback on the drink she had made. "Because if a man and a woman are standing behind a bar together, the man is clearly the bartender and the female is a server or hostess, right?"
Gina Chersevani of Buffalo & Bergen gets people who assume someone else (a man) owns her bar and call asking to talk to "Gino." Even good looks can be a double-edged sword: Lydia Ballard, a bartender at Rue St. Louis in New Orleans, says some people seem to think a male bartender "is there because he's skilled, but I'm there because I'm pretty."
Most women shake off the casual sexism. But harassment is a different beast. It's less common in the craft cocktail world, but women had stories ranging from obscene comments to actual fondling and groping by customers. (One survey cited in the Tales research found that women in the hospitality industry filed sexual harassment charges at more than five times the rate of the general female workforce.)
"The line is crossed, and it's crossed daily," says Gerwin, who's working to develop an anti-harassment program for bars.
Many women I spoke to described men who had given them their first breaks or trained them behind the bar — mentors, bosses, allies and fellow bartenders — as best friends and brothers. "Our male friends are often our biggest champions," says Tyler Hudgens, bar director at the Dabney. Mix points out that half of the people who come to watch Speed Rack are men. Overall, women seemed to feel that good guys make up the vast majority in the craft cocktail world.
But bias and harassment aren't just coming from the other side of the bar. Many women had work stories that ranged from "mildly discouraging" to "boss may actually have been a caveman." They had been passed over for jobs in favor of far less-experienced men. They had been hit on by supervisors or colleagues, sometimes to the point where they had quit. Hiring managers had told them women weren't welcome as bartenders. A cocktail competition judge had made innuendos about the genitals of a female competitor. There were managers who had taken a "customer is always right" approach to harassment, in one case firing a woman who had objected to being groped.
Bosses (male and female) had made sexist comments, a few going on tirades about women's lack of competence and strength. (The ability to move a keg, Wondrich says, is something women "get ragged on for by idiots. . . . Many women can move kegs. And many of the men who are saying that are so out of shape they couldn't move a keg anyway.")
Chantal Tseng of Reading Room DC and Megan Barnes of Espita Mezcaleria. (Marvin Joseph/The Washington Post)
'I'd rather hear I'm talented'
Bartenders hate complainers, and women bartenders are no exception. The job requires a physical and emotional toughness, and the perceived pressure for bartenders to grin and bear whatever they get is substantial.
My conversations indicated that bars need to make clear that there are circumstances in which staff should complain. Customers are not always right, and a work culture that tells staff to tolerate situations that are at best exhausting and at worst downright dangerous are setting them up for discouragement, failure and career change for the wrong reasons.
Drink Company's Angie Fetherston, who has worked with Brown to get their staff training from Safe Bars, says managers need to empower staff of any gender to 86 a customer who's out of line.
Bartenders "think they're supposed to get people to buy drinks and tip well . . . so they just have to endure this treatment," she said. "And they absolutely don't. We don't want customers like that."
When I asked women who've been in the industry for years for advice for women starting out in the field, they had a lot to say.
Don't allow others to hijack your plans. If you hear "no," find a job where you'll hear "yes." Become your own best advocate. You may be working in a man's world, but remember that warmth and compassion are strengths. Don't play the gender card, but don't let others play it against you either. The woman who works harder — who cleans the bar, reads the books, masters technique, learns everything she can about spirits and flavors and customer service and smart business practices — be her.
And to customers encountering her? You may not see old-timey suspenders, which don't sit right if you have breasts. But check the tattoos, the grin, the shake-hardened arms and the killer martini you're drinking, and remember: She's a bartender. If you want to show appreciation, tip well and direct your compliments appropriately. "It's nice when I have people tell me a drink was amazing, the best Negroni in town, and have that be the compliment and not that I'm a girl who's pretty," says Lucier. "I'd rather hear I'm talented."
Wine drinkers, rejoice. If you have a bottle of wine on hand that's pumping out bad smells, the American Chemical Society has a cheap chemistry life hack to help save your wine. (YouTube/ACS Reactions)
Allan is a Hyattsville, Md., writer and editor. Follow her on Twitter: @Carrie_the_Red.
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M. Carrie Allan Carrie Allan is a writer and editor who lives in Hyattsville, Md. Her Spirits column appears regularly. Follow


This is an article I wrote seven years ago that was published on GracieMag.com. Let's revisit it, and at the end, I'll address if anything has changed since then!
We watched Renzo Gracie get obliterated on his feet, BJ Penn had his belt taken from him on his feet, and Damian Maia lost his title shot to what started as a very impressive performance but turned into three rounds of running around the ring by Anderson Silva.
Renzo Gracie, BJ Penn, and Damian Maia – you would be hard-pressed to find three better men to represent the art of Brazilian Jiu Jitsu in the UFC. So is this the end of an era?
Jiu Jitsu dominated the UFC in the early years, was it just a phase?
Let's imagine for a second that football has been around since the beginning of time, but all anyone ever did was a passing game. Then, all of a sudden in 1993 a team came out with a running game, went undefeated and won the super bowl.
For the next few years, other teams started implementing running games into their arsenal and before you knew it – EVERY team had at least some running game in their playbook.
Now, this year in the playoffs all of the matches were running teams versus passing teams. All of the passing teams won. After so much success, should we stop using the running game? It seems ridiculous to even ask such a question. Of course not, on this night the passing teams had the running teams numbers, and nobody could do anything about it. They just came out with a better strategy and implementation.
Jiu Jitsu is not dead, not by any means. In fact, there were some aspects of those fights last night that proved how alive it truly is.
Anderson Silva and Matt Hughes, arguably two of the best fighters in the history of the sport said that there was no way they were going to the ground. They trained to keep that fight on the feet, just as the jiu jitsu players trained to get it to the ground, the Jiu Jitsu players just couldn't pull it off.
If anything is to be taken from these fights, it is the evolution of all martial artists. Jiu Jitsu in the United States has evolved tremendously. Fighters are taking the words of Bruce Lee to heart and using no way as way. Matt Hughes' Jiu Jitsu includes more aspects of fighting than Royce Gracie's. His wrestling skills combined with the training he has in Jiu Jitsu enabled him to take out some of the best of the Gracie Family.
So what will I train? I will continue to train my jiu jitsu skills, both the sportive aspect as well as the street. I will continue to train my standup skills, but I will not limit myself to Boxing or Muay Thai, my standup will include Kenpo, Kali, Wing Chun, Muay Thai, Western Boxing, Wrestling, Jiu Jitsu, Judo, and other martial arts that our family has incorporated into what we teach.
Where we believe some schools error is in calling their singular art "THE WAY." There is no way, and once someone starts to tell you that this is the way, and no other martial arts are worth learning, be wary.
However, don't be fooled by the hype of the outcomes of these fights, on any night anything can happen. Watch them, appreciate their place as a competitive sport in which some aspects of the martial arts can be proven on the canvas battleground, and continue to train a very well-rounded program.
Jiu Jitsu is not dead!
So 7 years after posting this article, has anything changed? If we look at that stats it seems that more fights (while still close) are being won by the strikers rather than the grapplers.
No this does not mean Jiu Jitsu is dying but in fact the opposite. More and more fighters are learning it, which makes them much better at defending against it. Why are they learning it? Because the early success of Jiu Jitsu in this format proved it is a necessity.
However, every round starts standing up, and this plays into the hands of the striker - the fight starts where they want to be, so they just have to avoid letting the grappler get it to where he wants to be.
So, what are you training? Are all three sides of this triangle covered? If not, there could be a huge hole in your ability to fight in all scenarios.


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Missed it? Mondays: Wknd of 8/22-8/23 Love, Park and Soul Summit edition Edition
This past weekend started with the threat of messy storms and ended (for me at least) with a purifying rain dance.
The weekend was just getting going Friday when I can across this young brother,
I don't know the specific why he was at this bus stop near Classon Av, but he was playing a soulful brand of bluesy sound all of a sudden.
Like to hear it, here it go!
(warning there will be a loud burp, not me, but my apologies)
After last Friday's controversial debate which resulted in the Michael Jackson/Spike Lee Block Party being moved from Fort Greene to Prospect Park I decided Saturday to refresh my memory of the area and see if it was as far from a grocery store, deli, bodega, restaurant and or cafe as I remember. It is.
As you can see from the pix, it's a lovely plot of land, but expect a walk to get to the back of the bus park, Nethermead.
My travels through the park brought me close enough to the heart of Flatbush, to be lured by nostalgia. I lived a lot of years in Flatbush and yet somehow it doesn't make it's way into my blog as much as it's in my heart.
I'm reminded every time i pass this way how much of a shopping/commercial center this part of the borough is, on pare with Fulton Street(Downtown and Bed-Stuy), Pitkin Av, in the way retail centers used to be arranged but not totally unified, the way a strip mall would be. It's also impressive to see the amount of people and business that are still out here, from Sears, to Staples, Rainbow shops these are the businesses local residents rely on for their shopping needs. One aside, it never made sense to drive through this part of Flatbush, and as you can see, it still doesn't.
And then I decided to look for food, and I really was looking for some Jerk Chicken, or Veggie Roti, but my fave Jerk spot has gone (was on Flatbush between Clarkson and Lenox Rd) morphed into a vegetarian restaurant called "Zen" (but no Palet). So I trekked on seeking Caribbean culinary flare and wound up here:
Why? Because I haven't had a slice here in at least a decade and if memory serves this is the first place I was introduced to pizza. I used to live (everywhere in Brooklyn) and among many addresses I lived just off Cortelyou Road with my Mom, as a child. We'd take the bus from Crown Heights, and wait forever for the B23 (which used to start it's run right in front of the pizzeria) to come take us down to East 3rd and Cortelyou. I remember one particularly long wait led my mom to go in and the rest was history, or at least the subject of a longer post, which I'll write later.
So I stopped. And thought to myself,"how many years have these guys been here?" And in answer to my query there was the sign adorning the top of the joint, signaling it's 40 year anniversary. So I went in. The place is changed, but then when I lived here there were still solid vestiges of the 40s and 50s visible in this part of Flatbush. For example a theater on the slender side of Cortelyou at Flatbush Avenue had been there since vauville, it was closed when I was a kid but still very prominent in it's antiquey details. The Albemarle was still there and it's where I saw the Empire Strikes Back (I came out of that screening so despondent at Luke's predicament that my mom consoled me with the very first McDonald's "Happy Meal". It worked. When the Albermarle closed in the 80's it became this church:
Not to be confused with the long dormant Loews Kings Theater (below), one of the few things I truly agree with the Boro Prez on, (that the theater should be preserved and reused as such.
These are a few examples of why it's so amazing that Antonios' Pizza is still going. Up until the 70's this area was a mix of Italian, Irish and African-Americans with trace amounts of Middle Easter and Hispanic pops, now if I don't hear a Caribbean accent I feel almost certain I'm listening to a new-comer.
Anyway as I'll detail later, I had a little convo with the workers there, before gobbling down my slice with sausages (not how I used to but times change) and taking off again.
Eventually I was surrounded by residences and block parties:
and I was so far from the city side of Brooklyn that it only made sense to head for the sea. I was especially curious if I'd see any effect from the then Hurricane Bill on the shore.
I headed aimlessly on to Midwood, another place I've spent a chunk of life-time and all I got was the remembrance that Midwood streets (in addition to being well served by the city, thanks to an influential constituency) are really wide. Insanely wide. It most have been part of the planning when these tracts of land were made, to create boulevard style lanes, but damn, you could build new blocks in the center of these streets.
Ocean Parkway isn't much different, but at least it calls it self a parkway:
On the way, I had to stop in Brighton Beach.
After all if I shows love to my Caribbean Gangsters (not really) how can I neglect my Russian Mobsters (really not really). I strolled down the ave and this is what I saw:
Russian Signage! The next time the "English as official Language" choir starts up, demanding all Spanish language signs come down, I'd like to see them pitch their shtick out here in "Little Odessa". If Boris doesn't have to write signs in English, why should Juan have to?
Gawking ate signs gave way to staring at rows of pastries
which I ate
and ate
Btw this placed just opened:
and they were having beer specials
(shout out to my comrades!)
Finally I reached the ocean (not really) and at Coney Island there was...Dancing!
I'd totally forgotten about the long running Coney Island Dancers' Boardwalk Dance Party.
It's free, fun and every Saturday during the summer. The Coney Island Dancers (who dance in many places actually) have a myspace page with event info, you can also join the Organic (dance) Movement, another group dedicated to social dancing, here.
Saturday ended with nightfall at Coney, no Hurricane in sight, but I did spot a Cyclone.
Followed by a frigid Q train home.
Three words. Soul Summit, baptismal.
I got confirmation earlier that yesterday would be the last Soul Summit of the year and peoples and nature proved yet again that Fort Greene Park can handle a party.
As hearts, hours and rhythm pulsed on, all things were joined by a trickle of rain that became a downpour. Each boost of rain intensity was answered by joyous shouts and enraptured words from the crowd. Then the music stopped, and the party..?
See for yourself.
And that was my weekend. Only a few summer weekends left, don't miss them.
Labels: Bedford-Stuyvesant, Brighton Beach, Coney Island, East Flatbush, Flatbush, Flatbush Av, Fort Greene, Fort Greene Park, Midwood, missed it mondays, Party
Arlene...blackorchid August 24, 2009 at 10:36 PM
Soul Summit. That youtube clip put a smile on my face from the memories of that fabulous sunday party of people of every size, shape, color enjoying music and dancing. How beautiful!!!!!


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Q: download file to update-independent directory in objective c I'm developing an IOS app which download some video and save it, but after update app or reinstall it the directory of app change, and app can not access to previous downloaded files.
Is there any way to save downloaded file to location out of application domain directory?
the code for generating path to save file is.
  NSURL *documentsDirectoryURL = [[NSFileManager defaultManager] URLForDirectory:NSDocumentDirectory inDomain:NSUserDomainMask appropriateForURL:nil create:NO error:nil];

  return [documentsDirectoryURL URLByAppendingPathComponent:[response suggestedFilename]];

A: I cannot verify the update part of your question.
I use the application's Documents all the time and after an update that is untouched, so I can still use any files added to it in a previous version.
For the reinstalling (i.e. first delete the app, then re-download it from the AppStore and run it) there is obviously no such way, unless you consider what ravi.p suggested in his comment (adding it to PhotosAlbum). That would beat the entire purpose of a reinstall. If a user deletes the app they want to delete all its data. That's why the warning dialog specifically makes that clear. If you could circumvent this would beat the intention, wouldn't it?
The previous Documents directory isn't changed in this case, it is deleted and on the reinstall a new one is created.
I didn't check it recently, but I believe even the full path of the Documents directory doesn't change after an update, including the hashed part that is created by the sandboxing mechanism. My guess is that you're either confusing something with the update process or simply get a different file name in the newer app version.
Edit:
Okay, so apparently the application's folders can change on an update, at least according to what you further explained in your comment. :)
Then I am wondering how you can find your sqlite file again, but in ay way there is an easy solution to your problem:
Do not save the full path in your database. That is bad practice anyways, since the method you already used to get it in the first place (after downloading the file) is meant to be used for accessing the folder. So you only save
[response suggestedFilename]

in your database (going from your posted code).
In places where you need to access the file you then simply rebuild your path in just the same way you do in the first line of code you posted.
You can even write a convenience method for this in some place (a model class or the class taking care about DB access).
And by the way: Again, updating and reinstalling are two different things, especially the process in which Xcode copies your development build onto your development device is a different one from how users ultimately update your app from the store.

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Mount Lowman () is a mountain,  high, on the east-central slopes of Pomerantz Tableland,  southeast of Rinehart Peak, in the Usarp Mountains of Antarctica. It was mapped by the United States Geological Survey from surveys and U.S. Navy air photos, 1960–62, and was named by the Advisory Committee on Antarctic Names for Henry R. Lowman III, a United States Antarctic Research Program biologist at McMurdo Station, 1967–68.

References

Mountains of Victoria Land
Pennell Coast

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