Can I do anything meaningful, helpful?
At age 56, I am raising a child again. She is age 7.
I am a full-time, stay-at-home mom and homemaker. It is my job to take care of my child's basic needs, such as roof, food, clothes, health care.
But since I am her mother, and not her babysitter, it is also my responsibility to show and teach her kindness, tolerance, self-control, critical thinking. Is it enough?
Am I doing my part to make the world a better place? To stand up against injustice?
I was an active member of the PTA. I was a voting delegate to conventions for different organizations. I chaired committees and held office in good-works charities and municipal boards. I testified before a state Senate committee.
I wrote three ordinances, currently on the books. I attended peaceful protests. I wrote letters to the editor. Various issues. Many places. Different times.
My current circumstances limit my ability and desire to join with activists, attend meetings, march.
But I can tell my young child that hate is always wrong.
By my own behavior, I can show her that I am not a racist or a sexist or a bigot of any stripe.
I can tell her as many times that I tell her to look both ways before crossing the street that bigotry is wrong; intolerance is wrong; hate is wrong.


The seismic survey indicated that a reflection inside the crater area shown on the Little Peck section also occurs on the Maben-Hill section outside the Panther Mt. region. This does not support the crater hypothesis however, more seismic surveys, to see if the reflector at .7s is disrupted in the crater, are needed.


text:
Being an Atheist in Alcoholics Anonymous
Posted in Alcoholism, Helpful Articles on July 25, 2016
Life as an atheist or agnostic in recovery may seem isolating at first glance. A higher power or deity is often strongly associated with mutual aid support groups like Alcoholics Anonymous (AA) and Narcotics Anonymous (NA). But the truth is that there are many ways those who don't believe in a higher power can still benefit from these groups and find fellowship and support to stay sober.
One Atheist's Experience in AA
John S. is an atheist and recovering alcoholic who came into AA in July 1988 and practiced the program as a believer. After 25 years, he realized that he was an atheist and at that point began to express his recovery in secular terms.
"I spent a lot of time speaking like everyone else was speaking," John says. "I realized I was an atheist and started talking about the program from this new perspective and got a lot of pushback." Feeling uncomfortable in his current group, John started "We Agnostics" in Kansas City. Ever since, he has been part of a growing number of groups and resources for agnostics in AA. In addition to his work with these AA groups, John helps manage a website and hosts a podcast popular in the secular AA community called "AA Beyond Belief."
Making the 12 Steps Work as an Atheist or Agnostic
While there are thousands of secular mutual aid support groups around the world, online agnostic AA meetings and forums, as well as 12-step alternatives such as SMART Recovery, LifeRing and Refuge Recovery, nonbelievers could find themselves in traditional 12-step groups depending on their circumstances — if they're in a drug or alcohol rehab grounded in 12-step meetings or in a particular region, for example. Maybe they live in a small town or are traveling outside of their local community where agnostic meetings aren't offered and they prefer an in-person group to an online forum. This shouldn't prevent anyone from getting the help they need.
"The big obstacle for some [atheists] is they think you must have a belief in a higher power. It doesn't necessarily mean that," John says. He explains that it's really about getting to that point where you realize you have a problem that is bigger than you can handle on our own. You turn for help wherever that might be: AA, a therapist or an addiction treatment program.
John offers some ways you can adjust your experience in a traditional AA meeting and find support as an agnostic or atheist in recovery.
Revise the Language for Your Needs
The 12 steps originated from Alcoholics Anonymous: The Story of How Many Thousands of Men and Women Have Recovered from Alcoholism (aka "The Big Book") by AA cofounder Bill W. Six of the 12 steps refer to God or a higher power. If you can't get past these references, try rewriting them in a way that resonates with your personal values. John created a secular version of the steps. For example, Step 5 reads: "Admitted to God, to ourselves and to another human being the exact nature of our wrongs." John's version simply omits the phrase "to God." Step 5 still works for him because he believes there is something innately healing about being honest with ourselves and sharing our struggles with other humans, whether that is a therapist, AA members or others. Research backs up the benefits of self-disclosure to other people. Opening up to others about our painful experiences can help us overcome shame and begin mending emotional wounds, with or without God.
Be Honest About Your Nonbelief
Be upfront about your viewpoints from the beginning. "If you're not honest about your beliefs, you're not going to meet someone who shares your beliefs, and they're usually there," John says. Alcoholics Anonymous and Narcotics Anonymous don't require you to believe in a certain way. "Most people in AA are very welcoming and open to agnostics and atheists. It's the minority of the people who give us a hard time," John says.
Focus on Other People
In meetings, John concentrates on his connection with others, not a higher power. "My higher power is the people in the room. It's the experience of the people in the room that can support me and my desire to stay sober," he says. When John feels uplifted after a meeting, he attributes it to the emotional high he gets from the support of others in AA. Other people in the room may attribute that same feeling to spirituality or a higher power. "So often in those meetings, it's language. We're doing the same thing but we're describing it differently," he says. Try focusing on fellowship and the actions behind the words. Appreciate the language as a way to convey an idea without taking it literally.
Don't Jump to Judgment
Don't judge AA or NA by the first meeting you attend. Every meeting is different. If one meeting doesn't resonate with you, give it another shot, or try out a different meeting. For example, some meetings close with the Lord's Prayer. This can be uncomfortable for an atheist or agnostic. If you find yourself in a meeting with the Lord's Prayer, John has some advice. "I would encourage the newcomer to be honest about their nonbelief and if they are not comfortable reciting the prayer, to know they are free to abstain," he says. "They can either stand there quietly as the others pray or simply leave the room."
Connect With Other Agnostics/Atheists
You'll likely find other atheists and agnostics in traditional Alcoholics Anonymous and Narcotics Anonymous meetings. Also know that there are many resources, agnostic AA groups, online agnostic forums and groups, social media communities, books, podcasts, conferences and events where you can connect with likeminded people in recovery. Additionally, alternative groups like SMART Recovery and Refuge Recovery are growing in number. If you're in a 12-step-based treatment program, you can still benefit from the fellowship and core principles of the 12 step programs. If you choose to seek out more secular options when you leave drug rehab, there are plenty available.
Remember, We're All in This Together
The bottom line is that people in mutual aid support groups have much more in common than they might think. Whether your path to sobriety involves a higher power or not, the benefits of the connection, support, honesty, acceptance and accountability you'll find in these communities can help you stand strong in sobriety. John says that the rooms of AA can sometimes be uncomfortable for an atheist or agnostic, but it's not impossible to make it work. "Once we're in that room, the real connection with the people has a way to make the other stuff less important," he says.
What to Expect at Your First AA Meeting
Support Group Meetings Vital to Your Recovery
Why Do Alcoholics Hoard?
Why Christian Rehab?

redpajama_set_name: RedPajamaCommonCrawl


William Shawcross is the distinguished journalist, historian and author. He is also the son of Winston Churchill's lawyer, the prominent former Nuremberg prosecutor and Labor MP Sir Hartley Shawcross. He thus provides something of a living link to Churchill whom we are especially proud to claim as a friend of our site.
Mr. Shawcross's new book — Justice and the Enemy: Nuremberg, 9/11, and the Trial of Khalid Sheikh Mohammed — has just been published. It is a book that addresses a subject close to our hearts. Indeed, it is one that we have written about here frequently over the years and a few of our items appear in the text and footnotes to the book.
The book has been favorably reviewed by John Yoo in the Wall Street Journal, where a related column by Mr. Shawcross also appeared. Today the Journal also publishes Mr. Shawcross's selection of Five Best books on the Nuremberg trials.
I blithely thought, Why not? It would be nice to write a little of my father, whom I loved and admired, and Nuremberg was a part of my growing up. I used to listen to fragile 78 rpm records of my father's speeches for the prosecution. I found his descriptions of Nazi crimes chilling.
I am not a lawyer and so I found the book much harder than I expected. But it is now complete and just published — Justice and the Enemy: Nuremberg, 9/11 and the Trial of Khaled Sheikh Mohammed.
What I have tried to do is to put the proposed trial of Khaled Sheikh Mohammed into the context of Nuremberg. I have sought to explain the extraordinarily difficult dilemmas that would have faced any US Government after the horrific attack of 9/11 — particularly in light of bin Laden's repeatedly stated ambition to acquire and use WMD against the world.
I agree with Obama that Nuremberg was a success and should not be dismissed as "victors' justice." But what he failed to acknowledge was that the defendants at Nuremberg had far fewer rights than those at Guantanamo under the Military Commissions created by President Bush. Indeed, were a Nazi transported by time machine from Nuremberg to Guantanamo he would be astonished by the privileges and safeguards which were suddenly available to him.
The most fundamental is this: at Nuremberg there was no right of appeal against the judgement of the Military Tribunal. By contrast anyone convicted at Guantanamo can appeal all the way to the Supreme Court. In other words he will have all the safeguards of anyone convicted in an Article III court. That is worth remembering in the months ahead as reformed military tribunals come under sustained attack from the left and from powerful human rights organisations.
That is another huge difference from 1945. At that time none of the human rights organisations that are so influential today even existed. Apart, that is, from the US Armed Forces and their democratic partners. The US military was then, and still is today, the greatest defender of human rights that the world has ever seen. Think of the millions rescued from tyranny by American forces throughout the 20th century – and in the first ten years of this decade. Without the extraordinary commitment of American blood and treasure the world would not have enjoyed any such stability as it finally won during the century of totalitarians and mass graves.
I live in London and believe very strongly that we Europeans are shockingly casual about the debt we owe those mostly young men and women from all over the United States. And that is why I fear Obama's refusal to accept the concept of American exceptionalism. Without American commitment, a free Europe will be under serious threat. The last one hundred years have shown that only America has the power and the optimism to defeat the forces of nihilism, whether they are fascist, communist or radical Islamist.
We are most grateful to Mr. Shawcross for allowing us to draw our readers' attention to his new book with these personal reflections.


Start of another week in the 'Dream Factory' and Noel SHOUTS the question DEAL OR NO DEAL in the intro today!!!! It has certainly livened up the pilgrims!!!
It's Lynne's turn in the 'Crazy Chair' today and she receives a very LOUD welcome as she takes the walk of wealth with box 8. Noel asks if the box feels like it has the £250,000, she says it does. Lynne is a freelance writer of short stories for magazines, Noel asks if there are any stories from the contestants hotel that might appear soon!! She has her husband in the audience for support today.
11 - £250,000 Not again!!! It's not going to be the big fairytale ending now !
2 - £100,000 It gets worse!!! Noel calls it the script from hell!
Lynne says she writes 'twist endings' so that this could all still turn around. The banker loves it that Lynne has killed off the 2 big characters in the story so early!! The banker reminds everyone to remember that the banker NEVER forgets anything a contestant says and his offer is based on something Lynne mentioned earlier!! It's Lynne's room number in the hotel!! He offers £111, Lynne says NO DEAL.
A very nice all blue round for Lynne and the banker says it's a slight improvement, although he gets unhappy when the 1p and 50p disappear! He offers £4,111, Lynne says NO DEAL.
Noel potentially jinxes the round now by mentioning the number of blues Lynne has knocked out!
15 - £10 Noel doesn't jinx a round for a change!!
It's another all blue round, Unbelievable says the banker! He wants a word with Lynne to come to an agreement!! He says his favourite novel is Catch 22 and then offers £11,111. Lynne wants a quick sweep, everyone says NO DEAL, Lynne says NO DEAL.
Noel describes the board as fantastic now, although the banker says he is unhappy after that round, he offers £21,111. Lynne goes to Ned for some advice, he says to carry on as she should still be OK after another round, Lynne says NO DEAL.
Lynne starts to choose another box until Noel shouts NOOOO at her!! Noel says the banker should be worried as it looks as though Lynne is prepared to go all the way now. The banker offers £19,111, Lynne goes back to Ned and he says it is a really tempting offer and to seriously consider it, Lynne says you are only in the chair once though and NO DEAL.
That round creates a massive gap in the final 2 values, which are 10p and £75,000! Lynne says that now she needs some guts and she says she hopes he offers her £76,000 to get rid of her! The banker offers £22,076, Lynne wants a sweep and the question is do they think Lynne has the guts to go on? Everyone says YES, the banker calls back and says NO!! Lynne says NO DEAL and the whole studio goes wild!!
Lynne provided an incredible game today and despite taking out the 2 largest values in the very first round, she managed to turn around her fortunes and show great courage in going to the end and risking all for the big win.


text:
In Our productions, Short film by Paprika 6 November 2017
Paul, epitome of the young man who comes up to Paris, is looking for an apartment. It's not easy when you don't earn much, have parents who are not subject to wealth tax and that you don't want to live in an insalubrious cellar or a broom cupboard… Suddenly, lady luck comes his way in the form of a nicely sized, bright and inexpensive apartment. How lucky to meet such a friendly, well-meaning landlord! Paul, happy, settles into his new home. But, something's not quite right… there are strange mechanical noises in the night, a pair of boxer shorts he finds under a wall, a neighbour who comes into his flat through the window…! As incredible as it may seem, he's going to have to face up to facts: the apartment is shrinking!!
Year of production : 2014
Format : Short film – 18′
Director : Matthieu LANDOUR
Scenario : Matthieu LANDOUR & Nicolas BOVORASMY
With Anthony SONIGO, Clémence ANSAULT, Silvie LAGUNA, Majid BERHILA & Rudy MAYOUTE
Sales : Salaud Morisset
Broadcast : Canal+
Laureate of the Beaumarchais Foundation: Funding from the Procirep, Angoa and the Mairie de Paris
Prizes and Awards :
Public Prize and Best Actor Award for Anthony Sonigo at the Festival Catacumba 2015, Spain
Rock Award at the Asiana International Short Film Festival 2015, Japan
Best Direction Award at the Festival Eurydice 2015 in Fécamp, France
Special Mention at the 2015 Brno 16mm Festival, Czech Republic
Special Mention at Protesta Festival 2016, Spain
Main official selections :
Bruxelles Short Film Festival 2015, Palm Springs International Film Festival 2015, Milwaukee Film Festival 2015, Hamptons Films Fest 2015, Chicago International Film Festival 2015, Saint- Louis international Film Festival


text:
\section{Introduction}
The hopping matrix element $t$ quantifies the quantum-mechanical coupling
between frontier orbitals on a pair of nearby molecules.
$t$ is important in describing transfer of electrons or holes
between moieties in close proximity,
which governs the mobility of carriers in molecular solids\cite{Kwon:tt}.
In ordered molecular solids, $t$ controls the valence and conduction bandwidths\cite{Kwon:tt},
and thereby determines the group velocity of electron and hole wave packets\cite{Cheng:2003bs}.
In disordered materials, $t$ influences the diffusivity of holes and electrons,
which in turn governs their drift mobilities\cite{Deng:ud}.

Because $t$ depends sensitively on geometry and molecular structure,
it would be useful to have a simple, efficient, generally applicable method
to compute $t$ between arbitrary pairs of small molecules in arbitrary geometries.
Such a method could for example be applied
to explore heterogeniety in disordered molecular solids,
by computing $t$ for many thousands of pairs of moieties in different arrangements,
extracted from configurations obtained from molecular dynamics simulations.
Extensive sampling of $t$ over many arrangements could be useful
to investigate heterogeniety in charge transport,
or in the energetics of charge-transfer excitons at bulk heterojunction interfaces,
or to gain insight as to what molecular structures and arrangements give large values of $t$\cite{Troisi:us,miller2019machine,wang2020artificial}.

Indeed, a common task in quantum chemistry calculations more generally
is to determine the Hamiltonian matrix element
that couples diabatic states on two nearby moieties.
(By ``diabatic states'', here we mean frontier orbitals on each of the two moieties,
which are eigenstates for each moiety in isolation, but not for the interacting pair.)

Because of their central importance,
many techniques have been developed to calculate hopping matrix elements.
One longstanding approach is the Mulliken-Hush method,
originating in discussions of electron transfer reactions
\cite{Hush1968,Mulliken1952,Cave1996,Cave1997}.
(A useful pedagogical treatment of the MH method
is given by Creutz et al.\cite{Creutz1994}.)
The essence of the method is as follows.
First, a simplified 2x2 matrix Hamiltonian is written
to represent an interacting system
of localized states on each of two nearby moieties $a$ and $b$,
for which bonding and antibonding eigenstates and energies
can be computed exactly in terms of the matrix elements.

Then, the dipole matrix element coupling the bonding and antibonding states
is related to the Hamiltonian matrix element between the two localized states,
under two physically reasonable assumptions:
1) weak direct overlap between the localized states,
so that $\mu_{ab}$ is small
compared to the separation between the two moieties;
and 2) the dipole matrix element between the bonding and antibonding states
points along the separation vector between the two moieties.

This argument results in the relation
\begin{equation}
H_{ab} = \frac{ \mu_{12} \Delta E_{12}}{\Delta \mu_{ab}}
= \frac{\mu_{12} \Delta E_{12}}{(\Delta \mu_{12}^2 + 4 \mu_{12}^2 )^{1/2}}
\end{equation}
Here subscripts $a$ and $b$ refer to the moieties,
and 1 and 2 refer to the bonding and antibonding states
of the interacting pair;
$\Delta E_{12} = E_1 - E_2$ is the splitting;
and $\mu_{12}$ the dipole matrix element coupling the bonding and antibonding states.
Finally, $\mu_{12} = \mu_1 - \mu_2$ is the difference in dipole moments
of the two diabatic states, measured with respect to a common origin,
and typically approximated by the separation vector between the moieties
\cite{Cave1996,Cave1997}.
This expression was originally used to obtain
Hamiltonian matrix elements from experimental absorption intensities,
but has also been applied to compute Hamiltonian matrix elements
from dipole matrix elements and energy differences
computed using density functional theory.

Following the work of Mulliken and Hush,
many extensions, improvements, and new approaches
have been introduced for computing matrix elements
between nearby moieties.

The MH method has been generalized by Cave and Newton
to systems in which more than two localized states interact
\cite{Cave1996,Cave1997}.
Voityuk et al.\ introduced an analysis analogous to MH,
but focusing on charge transfer between moieties
rather than dipole matrix elements,
to relate the Hamiltonian matrix element to orbital energy differences
and charge transfer between donor and acceptor
resulting from an excitation
from the bonding to the antibonding eigenstate
\cite{Voityuk2002}.
With the advent of widespread density functional codes,
direct evaluation of Hamiltonian matrix elements became practical,
by analytically computing matrix elements of the Fock operator
(i.e., the effective 1-body Hamiltonian, obtained from an SCFT treatment).
Related approaches focus on more efficient analytical
evaluations of matrix elements the effective 1-body Hamiltonian
for some representation of the interacting states,
for example the fragment-orbital DFT approach of Senthilkumar et al.
\cite{Senthilkumar2003}.
However, these approaches are not readily available
to end users of commonly available DFT platforms such as Gaussian,
which do not give easy access to Fock operator matrix elements
between frontier orbitals.

Kirkpatrick developed an approximate method using ZINDO,
which avoids a full SCF treatment of the pair of interacting moieties,
requiring only an SCF treatment of each moiety separately
\cite{Kirkpatrick2008}.
However, this approach is limited by the ZINDO semi-empirical approximation,
which results in factor-of-two discrepancies with more exact calculations,
while properly capturing trends with changing molecular arrangements.

Finally, in some cases it can be challenging
to obtain appropriate diabatic states;
Wu and van Voorhis address this problem
by applying constrained DFT to force charges to reside
exclusively on the starting and ending moieties
\cite{Wu2006,Wu2006b}.

In this paper, we present a simple numerical approach to extract $t$
from DFT calculations of orbital energies and wavefunctions.
The method uses results generated by the quantum chemistry package Gaussian,
and requires no sophisticated coding or access to orbital expansion coefficients.

Compared to previous methods briefly discussed above,
our elementary approach relates most closely to the original MH method.
However, we circumvent the need for dipole matrix elements
(and attendant approximations of MH),
preferring to work directly with the effective 2x2 system,
as characterized by readily accessible DFT results,
namely the orbital energies and wavefunction cube files.

In essence, we project the complex multielectron system
to the 2x2 space of interacting frontier orbitals on each moiety,
both with respect to the Hamiltonian
and the resulting frontier orbitals of the interacting pair,
consistent with the spirit of tight-binding models.
It can be shown that our approach reduces to MH,
in limit of localized diabatic states well separated in space
and transition dipole pointed along the separation vector.

To demonstrate the utility of our method, we use it to investigate how $t$ depends
on the relative placement and identity of nearby pairs of molecules.
Previous investigations of this sort have been performed
on pairs of identical molecules in idealized geometries,
including a pair of ethylene molecules
\cite{Valeev2006,Kirkpatrick2008},
pairs of parallel-oriented pentacene or hexabenzocoronene molecules
\cite{Kirkpatrick2008},
and neighboring oligoacenes in a crystal
.\cite{JeanLucBredas:2004bt,Kwon:tt,AlessandroTroisi:2005et,
Troisi:us,Hummer:2005kr,Tiago:2003dm}.

In what follows, we first validate our approach
by comparing to previous results for tetracene and ethylene.
Then, we investigate a variety of molecular pairs,
both identical and dissimilar,
with structures relevant to organic photovoltaics.
For a given molecular pair, we perform scans
in which we either translate or rotate one molecule with respect to the other.
In such scans, the onsite energy of the molecules in the pair
and the relative placement of their hybridizing orbitals vary systematically,
both of which in turn affect $t$.
From such scans, we can gain insight
as to what electronic and geometric factors
lead to sizable hopping matrix elements between nearby molecules.

\section{Orbital interactions}

When two molecules are brought close together,
their frontier orbitals hybridize to form the frontier orbitals of the pair.
Typically, the frontier orbitals of the pair consist predominantly
of one particular orbital from each molecule;
for example, the HOMO of a pair may consist mainly
of a linear combination of the HOMOs on each molecule.
Our calculations and discussion make this simplifying assumption,
which can be checked as part of the calculation.

Quantum packages and orbital visualizations give insight
into how individual molecule orbitals hybridize to form pair orbitals.
Pair orbital images can typically be recognized
as made from identifiable orbitals of the two individual molecules,
and clearly display how the wavefunction is distributed between the two.
In this paper, the two molecules within a pair will be referred to
as the ``monomers'' that constitute the pair.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.45\textwidth]{ThioBondVsAnti.pdf}
\caption{HOMO-1 and HOMO of thiophene-thiophene pair at 4.0 \AA\ separation.}
\label{fig:ThioBondAntiEx}
\end{center}
\end{figure}

Fig.\ \ref{fig:ThioBondAntiEx}
shows how the HOMOs of two thiophene monomers hybridize
to form the HOMO and HOMO-1 of the pair.
The pair HOMO-1 in Fig.\ \ref{fig:ThioBondAntiEx}
is evidently a bonding orbital of the molecular HOMOs,
in which the lobes of the wavefunction on each molecule are adjacent
to lobes of the same sign on the opposing molecule.
This arrangement avoids gradients within the pair orbital wavefunction,
lowering its kinetic energy.
By ``lobe'', we mean a region of the wavefunction of a given sign,
indicated by color in Fig.\ \ref{fig:ThioBondAntiEx}.
The thiophene HOMO has four lobes.

Likewise, in the HOMO of Fig.\ \ref{fig:ThioBondAntiEx},
the lobes on one molecule are adjacent to lobes of opposite sign on the opposing molecule,
forming an antibonding orbital.
This arrangement gives rise to nodes between opposing lobes,
resulting in wavefunction gradients that raise the kinetic energy.

The example of Fig.\ \ref{fig:ThioBondAntiEx} is a special case,
in which the constituent monomers are identical and symmetrically related.
As a consequence, the pair HOMO and HOMO-1 wavefunctions
have mirror symmetry with respect to the two molecules
and thus equal magnitude on both molecules,
as evident in the figure.
This mirror symmetry holds regardless of how strongly or weakly
the orbitals interact with one another through hybridization.

For this special case,
the onsite energies of the constituent monomers must be equal by symmetry,
and $t$ can be calculated directly from the splitting
of the bonding and antibonding pair orbitals
\cite{Valeev2006}.
This symmetry holds for identical molecules,
so long as they are symmetrically placed.
For example, if we translate or rotate the molecules in Fig.\ \ref{fig:ThioBondAntiEx}
with respect to the central orthogonal axis,
the arrangement remains symmetric.

However, not all arrangements of identical molecules are symmetric.
In general, each monomer perturbs the orbital energies of the other monomer to some extent.
When the monomers are not symmetrically placed,
these perturbations need not be equal,
and so the effective values of the onsite energy on each monomer may differ.
As a consequence, the pair orbitals will no longer have mirror symmetry,
and the wavefunction may be unequally distributed between the two monomers.

Of course, asymmetric distributions of pair orbitals also result from using different constituent monomers,
as shown for a pyrrole-thiophene pair in Fig.\ \ref{fig:ThPyrOrbitals}.
Once again, the HOMO of thiophene hybridizes with the HOMO of pyrrole within the pair.
However, now the resulting bonding and antibonding orbitals form the HOMO-2 and the HOMO of the pair
(the pair HOMO-1 is an unrelated orbital, not participating in this hybridization).
The pyrrole HOMO is significantly higher in energy than for thiophene,
but the orbitals have roughly the same shape.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.45\textwidth]{ThPyrOrbitals}
\caption{HOMO-2 and HOMO of thiophene-pyrrole pair at 4.0 \AA\ separation.}
\label{fig:ThPyrOrbitals}
\end{center}
\end{figure}

In Fig.\ \ref{fig:ThPyrOrbitals},
the pair orbital wavefunction is not equally distributed between the two moieties.
The lower-energy bonding orbital resides mainly on the lower-energy HOMO of thiophene,
while the antibonding orbital resides primarily on the higher-energy HOMO of pyrrole.
Importantly, each monomer perturbs the onsite energy of the other,
to an unknown and unequal extent.
Thus, we cannot assume the onsite energies of the two molecules in proximity
are the same as when isolated,
so we cannot calculate $t$ from the pair orbital energy splitting alone.
To compute $t$ in such cases,
we need an additional piece of information,
as we shall show in the next section.

\section{Tight-binding model}

To represent the hybridization of one orbital on each of two molecules,
we write a simple $2 \times 2$ tight-binding model,
for which the Hamiltonian matrix is
\begin{equation}
H = \left\lbrack
\begin{array}{ccc}
  \epsilon_1& -$t$ \\
  -$t$& \epsilon_2  \\
\end{array}
\right\rbrack
\label{eqn:Hamiltonian Matrix Eq}
\end{equation}
Here $ \epsilon_1 $ and $ \epsilon_2 $ are the onsite energies
of the relevant frontier orbitals on the two monomers,
and $t$ the hopping matrix element between these orbitals.
Our sign convention is that $t>0$ corresponds to the case
in which monomer orbitals with amplitudes of the same sign form a bonding orbital.

The simple two-state Hamiltonian in Eqn.\ \ref{eqn:Hamiltonian Matrix Eq}
is evidently a drastic simplification of the full quantum mechanics
describing the pair of interacting molecules;
the active space is projected down to a single pair of orbitals.
The frontier orbital of the pair is correspondingly written
as a linear combination of the two interacting monomer orbitals.
Nonetheless, this simple two-site model reasonably represents
interacting molecules that are close enough to hybridize
but not so close that their charge distributions drastically overlap.

The energy eigenvalues of the 2x2 Hamiltonian take the familiar form
\begin{equation}
	\lambda_\pm=\frac{\epsilon_1 + \epsilon_2 \pm \sqrt{(\epsilon_1 - \epsilon_2)^2+4t^2}}{2}
	\label{eqn:EigenvaluesHam}
\end{equation}
with the splitting between the two states $ \Delta E = \lambda_{+} - \lambda_{-} $ given as
\begin{equation}
	\Delta E=\sqrt{(\epsilon_1-\epsilon_2)^2+4t^2}
	\label{eqn:EigenvaluesDiff}
\end{equation}

Evidently, the splitting $\Delta E$ depends on both $t$
and the onsite energy difference $\epsilon_1 - \epsilon_2$.
Only for the special case of identical monomers symmetrically arranged
does $\epsilon_1 - \epsilon_2$ vanish,
whereupon the splitting alone determines $t$, as $|t|= \Delta E/2$.
This limit corresponds to the energy-splitting in dimer (ESD) method
\cite{ottonelli2012koopmans}.
Otherwise, when the onsite energies are not forced by symmetry to be equivalent,
we need more information about the pair system to calculate $t$.
In short, we get this information by measuring the coefficients of the pair wavefunction.

The corresponding eigenvectors $e^+ = \{e^+_1, e^+_2\}$ and $e^- = \{e^-_1, e^-_2\}$
of $H$ take the form
\begin{equation}
\left\lbrack
\begin{array}{ccc}
  e^+_1& e^-_1 \\
  e^+_2&e^-_2  \\
\end{array}
\right\rbrack = \frac{1}{\sqrt{1+\alpha^2}}\left\lbrack
\begin{array}{ccc}
  1& \alpha \\
  -\alpha& 1  \\
\end{array}
\right\rbrack
\label{eqn:HamiltonianEigenvectors}
\end{equation}
in which $\alpha$ is given by
 \begin{equation}
	\alpha=\frac{1}{2t}(\sqrt{(\epsilon_1-\epsilon_2)^2+4t^2} - (\epsilon_1-\epsilon_2))
	\label{eqn:Diffebefsdaa}
\end{equation}

Here we have adopted conventions such that $\epsilon_1 > \epsilon_2$,
and interpret the square root as positive,
so that $0 \leq \alpha \leq 1$,
and $\lambda_+$ approaches $\epsilon_1$ as $t$ becomes small.
Solving Eqn.\ \ref{eqn:EigenvaluesDiff} and Eqn.\ \ref{eqn:Diffebefsdaa}
for the onsite energy difference and $t$ in terms of $\alpha$ and $\Delta E$,
we obtain
 \begin{equation}
	\epsilon_1-\epsilon_2=\frac{1-\alpha^2}{1+\alpha^2}\Delta E
	\label{eqn:Diffebea}
\end{equation}
\begin{equation}
	t=\frac{\alpha}{1+\alpha^2}\Delta E
	\label{eqn:Finalt}
\end{equation}

We extract $\alpha$ from DFT results
by projecting the relevant pair orbitals onto the constituent monomer orbitals
to obtain the $2 \times 2$ matrix of eigenvectors.
Thus the eigenvector coefficients $e^\pm_i$ in Eqn.\ \ref{eqn:HamiltonianEigenvectors}
are given by
\begin{equation}
e^\pm_i = \langle \psi_\pm | \phi_i \rangle
\label{eq:project}
\end{equation}
in which $\psi_+$ and $\psi_-$ are the two hybridized pair orbitals,
and $\phi_1$ and $\phi_2$ the constituent orbitals on the two monomers.

In writing Eqn.\ \ref{eq:project}, we are assuming for simplicity
that the frontier orbitals on the two monomers have negligible overlap,
compared to their projections onto the hybridized dimer orbital.
This is the case for all examples presented in this paper.
More generally, we can construct using standard linear algebra techniques
a dual basis of two mostly-localized states $\{ \tilde \psi_i \}$
that satisfy $\langle \tilde \psi_i | \psi_j \rangle = \delta_{ij}$,
which we can use to extract the expansion coefficients $\{ e^{\pm}_i \}$.
See Appendix for details.

We calculate the projections numerically,
representing the orbitals to be integrated
as spatially discretized ``cube files'',
which can be readily obtained from Gaussian.
To facilitate this approach,
we ensure that the cube files for the pair and both monomer orbitals
are computed on the same grid of sampling points.
In our Gaussian calculations,
we use the B3LYP function with the 6-31g(d,p) basis set.
See Supplemental Information for details.

If our simple $2 \times 2$ model adequately represents the real system,
the eigenvectors generated should be approximately in the form
given by Eqn.\ \ref{eqn:HamiltonianEigenvectors}.
Otherwise, some other monomer frontier orbitals must contribute to the pair wavefunction,
and our simplifying assumption of two interacting orbitals fails.
For all examples results here, the eigenvectors are well represented by this form.

To input, multiply, and integrate cube files,
we employ a set of Python scripts called {\tt cube\_tools}
(available in GitHub at https://github.com/funkymunkycool/Cube-Toolz).
We have modified these scripts to eliminate unnecessary text output,
so they can be used more conveniently as command line tools.
Details about our modified scripts can be found in Supplemental Information.

The resulting ``Frontier Orbital Numerical Projection'' method
is computationally efficient, simple, and versatile.
In the next section, we use it to investigate
how hopping matrix elements and onsite energy shifts vary
with the identity and placement of interacting molecules.

\section{Scans}
Scans explore how the matrix hopping element varies
as we vary the relative location of the two molecules in a pair.
In the scans presented here, one molecule in a pair
is rigidly translated or rotated while the other is held fixed.
Along the scan, the energy splitting $\Delta E$ and eigenvector coefficient $\alpha$
are calculated from DFT results and used to calculate $t$.

To prepare the sequence of DFT input files for a scan,
we first optimize the geometry of each monomer.
Next we prepare a {\tt .com} file (Gaussian input file)
in which the two monomer centers of mass
are placed in a given initial geometry.
We then generate a sequence of {\tt .com} files
by applying scripts that transform the initial {\tt .com} file
by moving one of the two monomers.
The resulting {\tt .com} files are executed by Gaussian
to produce {\tt .log} and {\tt .chk} files,
which provide the necessary information to compute $t$,
as described further below.

To test our new method, we first compare to previous results
for simple scans of pairs consisting of two identical molecules.
In the first example, the two molecules are symmetrically placed,
so that the ESD method suffices.
Fig.\ \ref{fig:TetraceneScan} presents results of Coropceanu et al.,
who performed a translation scan for
two tetracene molecules in a parallel arrangement,
and computed $t$ for hybridization of the monomer HOMOs and LUMOs
\cite{Coropceanu2007}.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{TetraceneScan.pdf}
\caption{$t$ value for hopping between HOMO (red) and LUMO (blue) of each tetracene,
from our results (solid lines) and Ref.\ \citenum{Coropceanu2007} (dashed lines).}
\label{fig:TetraceneScan}
\end{center}
\end{figure}

Evidently, our results and those of Ref.\ \citenum{Coropceanu2007} are quite comparable,
differing in only minor respects:
1) we find $t$ for hopping between tetracene HOMOs and LUMOs are essentially equal,
while Ref.\  \citenum{Coropceanu2007} finds that the HOMO $t$ values are slightly higher;
and 2) we find a slightly larger range for the hopping,
which may reflect a more generous basis set in our DFT calculations.

In the second example,
Valeev et al.\ calculated $t$ for hopping between HOMOs
of two ethylene molecules at a separation of 5 \AA,
in which one ethylene was rotated around its double bond\cite{Valeev2006}.
This rotation breaks the mirror symmetry,
so that the ESD method cannot be used\cite{Valeev2006}.
(Valeev et al.\ is not explicit about how their $t$ values were computed,
but presumably this was done analytically,
by computing Fock operator matrix elements
in the basis set used for the SCF calculations.)
Fig.\ \ref{fig:EthyleneRotation} presents their results,
compared to our results for the same scan.

Kirkpatrick also calculated $t$ for the very same scan\cite{Kirkpatrick2008},
using two different approaches.
In the first approach, Ref.\ \citenum{Kirkpatrick2008}
analytically computed matrix elements of the Fock operator and hence $t$.
The second approach, which is limited by the ZINDO approximation,
quantum calculations are required only of individual molecules and not of a pair,
constructs hybrid bonding and anti-bonding orbitals
from the orbitals of the isolated molecules.
Results from both approaches appear in Fig.\ \ref{fig:EthyleneRotation}.

Our Frontier Orbital Numerical Projection method
can likewise calculate $t$ for this ethylene pair rotation scan.
To proceed, we use the Gaussian utility {\tt cubegen}
to generate cube files for the frontier orbitals of the pair
as well as the constituent frontier orbitals of the two monomers,
for each pair geometry along the scan.
The cube files are generated with the same origin, axes, and mesh size,
to facilitate their use in computing the necessary inner products
to project the pair orbital onto the constituent monomer orbitals.
Information about our scripts that automate these overlap calculations
can be found in Supplemental Information.

As an example, for the ethylene pair rotation scan at a rotation angle of 10 degrees,
calculating as described above the overlaps of each monomer HOMO
with the pair HOMO and HOMO-1,
generates eigenvector expansion coefficients
\begin{equation}
\left\lbrack
\begin{array}{ccc}
  e^+_1 & e^-_1\\
  e^+_2 & e^-_2 \\
\end{array}
\right\rbrack = \left\lbrack
\begin{array}{ccc}
  0.721 & 0.693 \\
  -0.695 & 0.719 \\
\end{array}
\right\rbrack
\label{eqn:EthyleneMatrix}
\end{equation}

The coefficient matrix Eqn.\ \ref{eqn:EthyleneMatrix} is almost perfectly antisymmetric,
as expected from the analytical form Eqn.\ \ref{eqn:HamiltonianEigenvectors}
for an interacting $2 \times 2$ system.
Inevitably, the coefficient values do not quite satisfy the expected relations
$e^+_1 = e^-_2$ and $e^+_2 = -e^-_1$,
so that $\alpha$ obtained from $\alpha = e^-_1/e^-_2$
does not quite equal $\alpha = -e^+_2/e^+_1$.
Consequently, we average the two results, to obtain
 \begin{equation}
	\alpha=(1/2)\left(\left|e^-_1/e^-_2\right|
	+\left|e^+_2/e^+_1\right|\right)
	\label{eqn:AlphaFromMatrix}
\end{equation}

The hopping matrix element $t$ versus rotation angle $\phi$ can then be calculated
from $\alpha(\phi)$, the pair HOMO and HOMO-1 energies, and Eqn.\ \ref{eqn:Finalt}.
Fig.\ \ref{fig:EthyleneRotation} shows that results from our method (black)
are in good agreement with both methods of Ref.\ \citenum{Kirkpatrick2008} (green and orange),
while results from Ref.\ \citenum{Valeev2006} (blue) are systematically about two times larger.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{EthyleneRotation.pdf}
\caption{HOMO $t$ value for ethylene pair versus rotation angle $\phi$ at separation 5 \AA,
from Ref.\ \citenum{Valeev2006} (blue), present work (black),
Ref.\ \citenum{Kirkpatrick2008} MOO method (green) and projective method (orange).}
\label{fig:EthyleneRotation}
\end{center}
\end{figure}

Having tested our Frontier Orbital Numerical Projection method in this way,
we now use it to investigate hopping matrix elements
for moieties that appear in organic semiconductors
under development for photovoltaic materials.
In what follows, we select pairs of molecules to highlight the importance
of the energy, symmetry, and relative placement of the interacting orbitals.

\section{Thiophene translation scan}

For our first example scans, we investigate a pair of thiophene molecules,
thiophene being a well-studied constituent of many organic semiconductors.
Intuitively, we expect large $t$ values for thiophenes placed face to face,
as in Fig.\ \ref{fig:ThThTransScan}.

We first carry out a scan with respect to the separation between the thiophenes.
Throughout this scan, the monomer HOMOs hybridize to form the pair HOMO and HOMO-1,
while the monomer LUMOs hybridize to form the pair LUMO and LUMO+1.
For this scan, the two molecules remain symmetrically placed,
so $\alpha$ is equal to unity throughout the scan,
and $t$ can be computed from the splitting alone as $t = \Delta E/2$.

Fig.\ \ref{fig:ThThTransScan} shows the scan geometry,
the pair HOMO and HOMO-1 energies versus distance,
and the resulting values of $t$.
Qualitatively similar results with slightly higher $t$ values are found for hopping between the LUMOs.

\begin{figure*}
\begin{center}
\includegraphics[width=0.9 \textwidth]{ThThTransScan}
\caption{(a): Schematic of thiophene translation scan.
(b): Pair HOMO (blue) and HOMO-1 (orange) energies and average of the two (green) versus separation.
Red asymptote is HOMO of isolated monomer. (c): Resulting $t$ value versus separation.}
\label{fig:ThThTransScan}
\end{center}
\end{figure*}

As Fig.\ \ref{fig:ThThTransScan}(c) shows,
$t$ decreases approximately exponentially with distance,
reflecting the approximately exponential tails of the interacting monomer orbitals.
This behavior is consistent with distance scans for other moieties
\cite{Kwon:tt,Valeev2006}.

 Fig.\ \ref{fig:ThThTransScan}(b) shows that the pair HOMO and HOMO-1 energies
 are essentially degenerate beyond 6.5 \AA\ separation.
However, at this separation the HOMO and HOMO-1 remain significantly higher
than the energy of the isolated monomer HOMO
(red line in Fig.\ \ref{fig:ThThTransScan}(b)).
The HOMO and HOMO-1 pair energies
continue decreasing with distance until roughly 30 \AA.
This slow approach to truly isolated molecules does not arise from hybridization,
but long-range electrostatic interactions between the molecules,
each of which perturbs the HOMO of the other.

At long distances, the dominant interactions between neutral molecules
should be dipole-dipole interactions, as remarked by Valeev et al.\cite{Valeev2006}.
We can investigate this by analyzing the onsite energy shift
of the pair orbitals with respect to the isolated limit.

To calculate the onsite energy shift,
we average the pair HOMO and HOMO-1 energies,
and subtract the HOMO energy of an isolated thiophene.
Because the pair consists of identical molecules symmetrically placed,
the average of the pair HOMO and HOMO-1
must equal the onsite energy of each of the two monomers,
which are by symmetry equal.

Calculating this average against distance
gives a relationship fit by
Equation \ref{eqn:GreenGraphFittedEquation}.
Beyond a separation of 10 \AA,
the correction is less than 25 percent of the leading $1/R^3$ dependence,
consistent with the interaction energy between two dipoles at a distance $R$.

\begin{equation}
	U(R) = -\frac{51.1004}{R^4}+\frac{21.7046}{R^3}
	\label{eqn:GreenGraphFittedEquation}
\end{equation}

\section{Thiophene rotation scan}

On physical grounds, we expect the value of $t$ to depend
on the relative orientation of the two interacting monomers,
which governs how the lobes of the frontier orbitals overlap.
We explore the dependence of $t$ on orientation
by rotating one of a pair of thiophenes,
at a constant separation distance of 4.2 \AA.

Throughout the scan, the monomer HOMOs hybridize to form the pair HOMO and HOMO-1,
while the monomer LUMOs hybridize to form the LUMO and LUMO+1.
Fig.\ \ref{fig:ThThRotScanHOMO} shows the energy of the HOMO and HOMO-1 pair orbitals
and their corresponding value of $t$ throughout the rotation.
Because the two thiophenes are related throughout the scan
by a two-fold rotational symmetry,
the ESD method again suffices to determine the value of $t$ versus $\phi$.

\begin{figure*}
\begin{center}
\includegraphics[width=0.9\textwidth]{ThThRotScanHOMO.pdf}
\caption{(a): Schematic of thiophene rotation scan at 4.2 \AA\ separation.
(b): Pair HOMO (blue) and HOMO-1 (orange) energies and their average (green) versus $\phi$.
(c): Resulting t value versus $\phi$.}
\label{fig:ThThRotScanHOMO}
\end{center}
\end{figure*}

Fig.\ \ref{fig:ThThHomoOverlaps} displays images
of how the HOMOs of the two monomers in the pair overlap
at various rotations throughout the scan.
Evidently, at rotations of zero and 180 degrees,
the proximate lobes on the monomer HOMOs line up consistently,
so that symmetric and antisymmetric linear combinations of the two HOMOs
lead to bonding and antibonding pair orbitals.
Whereas, at 90 and 270 degrees,
the proximate lobes are orthogonally oriented,
so that regardless of the choice of sign
for the amplitudes of the two monomer HOMOs,
no consistent pattern of nodes or ``joins''
between the two HOMOs can be established.

This state of affairs is reflected
in the periodic dependence of $t$ on $\phi$.
At 0, 180, and 360 degrees
the interacting lobes directly face each other,
maximizing hybridization and thus $t$.
At 90 and 270 degrees, hybridization hardly lowers the energy of the pair HOMO-1.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{ThThHomoOverlaps.pdf}
\caption{Images of overlaying thiophene HOMOs at 0, 90, 180, and 270 degrees.}
\label{fig:ThThHomoOverlaps}
\end{center}
\end{figure}

The thiophene LUMO has a different pattern of lobes than the HOMO,
resulting in a different variation of the energy shifts and $t$ values versus $\phi$,
as shown in Fig.\ \ref{fig:ThThRotScanLUMO}.

\begin{figure}
     \centering
     \begin{subfigure}[b]{0.4\textwidth}
         \centering
         \includegraphics[width=\textwidth]{ThThRotScanLUMOEnerg.pdf}
         \caption{}
         \label{fig:ThRotScanLUMOEnerg}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.4\textwidth}
         \centering
         \includegraphics[width=\textwidth]{ThThRotScanLUMOt.pdf}
         \caption{}
         \label{fig:ThRotScanLUMOt}
     \end{subfigure}
       \caption{a): Pair LUMO (blue) and LUMO+1 (orange) energies
			for thiophene and thiophene scan at 4.2 \AA\ separation
			and their average (green) versus $\phi$. (b): Resulting t value versus $\phi$.}
        \label{fig:ThThRotScanLUMO}
\end{figure}

The periodicity of energy and $t$ versus rotation is determined
by the arrangement of lobes on the interacting frontier orbitals.
The schematics in Fig.\ \ref{fig:ThThLumoOverlaps} illustrate
the four opportunities for the frontier orbitals to line up for maximum hybridization,
which results in four maxima in $t(\phi)$.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{ThThLumoOverlaps.pdf}
\caption{Images of overlaying thiophene LUMOs at 0, 90, 180, 270 degrees.}
\label{fig:ThThLumoOverlaps}
\end{center}
\end{figure}

\section{Benzene pairs}

Because of its six-fold rotational symmetry,
both the HOMO and LUMO of benzene are doubly degenerate,
which has interesting consequences for hybridization
between two benzene moieties in close proximity.
For example, symmetrically placed benzene pairs
also have doubly degenerate frontier orbitals.
Fig.\ \ref{fig:BenzeneOrbitals} shows the frontier orbitals
for a pair of face-on benzene molecules;
two different bonding orbitals have the same HOMO-1 energy,
and two different antibonding orbitals have the same HOMO energy.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{BenzeneOrbitals.pdf}
\caption{Benzene pair orbitals with the HOMO-1 and HOMO energy at 4.2 \AA\ separation.}
\label{fig:BenzeneOrbitals}
\end{center}
\end{figure}

Fig.\ \ref{fig:BenzTransScan} shows results for a translation scan of two benzenes,
performed as for thiophene in Section V.
Because the molecules are symmetrically placed,
the ESD method suffices to compute $t$.
Throughout the scan, the pair HOMO and HOMO-1 are doubly degenerate.

\begin{figure}
     \centering
     \begin{subfigure}[b]{0.425\textwidth}
         \centering
         \includegraphics[width=\textwidth]{BenzTransScanEnerg.pdf}
         \caption{}
         \label{fig:BenzEnergScanTrans}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.4\textwidth}
         \centering
         \includegraphics[width=\textwidth]{BenzTransScant.pdf}
         \caption{}
         \label{fig:BenztScanTrans}
     \end{subfigure}
       \caption{(a): Pair HOMO (blue) and HOMO-1 (orange) energies for benzene and benzene scan and their average (green) versus separation. Red asymptote is HOMO of isolated monomer. (b): Resulting $t$ value versus separation.}
        \label{fig:BenzTransScan}
\end{figure}

The graph of $t$ versus separation in Fig.\ \ref{fig:BenzTransScan}
is strikingly similar to the results for thiophene.
As for thiophene, the benzene pair HOMO and HOMO-1
approach one another much faster
than they approach the isolated benzene monomer HOMO,
suggesting the presence of long-range interactions
that shift the energy of pair orbitals.

The sixfold symmetry of benzene and resulting degenerate frontier orbitals
has a surprising consequence for $t(\phi)$.
The two degenerate HOMOs on one benzene can be combined to produce an orbital
that aligns optimally with the other benzene throughout the entire scan,
minimizing the energy of the bonding orbital.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{BenzOrbitalsRot.pdf}
\caption{Benzene pair orbitals with the HOMO-1 and HOMO energy
at 4.2 \AA\  separation and 30 degrees rotation.}
\label{fig:BenzOrbitalsRot}
\end{center}
\end{figure}

Fig.\ \ref{fig:BenzOrbitalsRot} shows bonding and antibonding orbitals
for a benzene pair rotated by 30 degrees
--- which are identical to the orbitals of the unrotated pair depicted in Fig.\ \ref{fig:BenzeneOrbitals}.
As a result, for a benzene pair
the HOMO-1, HOMO, LUMO, and LUMO+1 energies,
as well as the corresponding $t$ values,
are completely independent of rotation.

\section{Thiophene-pyrrole pairs}

The ESD method does not work when the two interacting monomers are different.
Our new approach works for such cases,
which we illustrate here for thiophene and pyrrole.
The HOMO and LUMO of thiophene and pyrrole
have similar shapes but rather different energies,
which leads to asymmetric bonding and antibonding pair wavefunctions.

Although Fig.\ \ref{fig:ThPyrOrbitals} shows the HOMOs
of thiophene and pyrrole forming the HOMO and HOMO-2 of the pair,
this is only true at separations closer than 4.2 \AA,
when the hybridization between the monomer HOMOs is strong enough to
lower the bonding orbital energy to the HOMO-2 position.
Throughout the scan at larger separations (beyond 4.2 \AA),
the monomer HOMOs hybridize to form the pair HOMO and HOMO-1.

Fig.\ \ref{fig:ThioPyrTrans}(a) shows the energies of the pair orbitals
formed by the thiophene and pyrrole HOMOs throughout the scan.
Fig.\ \ref{fig:ThioPyrTrans}(b) displays the results for $t$ versus separation
obtained using the Frontier Orbital Numerical Projection method.

\begin{figure}
     \centering
     \begin{subfigure}[b]{0.4\textwidth}
         \centering
         \includegraphics[width=\textwidth]{ThioPyrTransEnerg.pdf}
         \caption{}
         \label{fig:ThioPyrEnergTrans}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.4\textwidth}
         \centering
         \includegraphics[width=\textwidth]{ThioPyrTranst.pdf}
         \caption{}
         \label{fig:ThioPyrtTrans}
     \end{subfigure}
       \caption{(a): Pair HOMO (blue) and HOMO-1 (orange) energies for thiophene and pyrrole scan
and their average (green) versus separation.
Red asymptote is HOMO of isolated thiophene and purple asymptote is HOMO of isolated pyrrole.
(b): Resulting $t$ value versus separation.}
        \label{fig:ThioPyrTrans}
\end{figure}

In Fig.\ \ref{fig:ThioPyrTrans}(a), the pair orbital energies
approach the values for the isolated monomers as the separation distance increases.
The resulting $t$ versus distance is rather similar
to results for the thiophene-thiophene scan,
with similar magnitudes and characteristic exponential decay length.

Rotation scans of a thiophene-pyrrole pair exhibit an interesting feature,
which is hybridization of orbitals other than the HOMO of both moieties,
as a consequence of close energy matches between disparate orbitals.
The pyrrole HOMO-1 energy of -6.34 eV
is nearly degenerate with the thiophene HOMO energy of -6.35 eV.
As a result, these orbitals strongly hybridize
when the two monomers are correctly oriented,
so that the lobes on one monomer orbital
are adjacent to lobes on the other orbital
with a consistent sign difference between them.

Fig.\ \ref{fig:ThPyrOrbitals90}
shows the HOMO-3 through HOMO
of the thiophene-pyrrole pair at 4.2 \AA\ and 90 degrees rotation.
This rotation is optimally aligned
for the pyrrole HOMO-1 and thiophene HOMO to mix,
forming the bonding and antibonding HOMO-2 and HOMO-1 pair orbitals.
At 90 degrees rotation,
the HOMO of thiophene has its lobes directly across from the HOMO-1 of pyrrole.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{ThPyrOrbitals90.pdf}
\caption{HOMO-3 through the HOMO of a pyrrole-thiophene pair
at 4.2 \AA\ separation and 90 degrees rotation.}
\label{fig:ThPyrOrbitals90}
\end{center}
\end{figure}

Fig.\ \ref{fig:ThPyrRotScan} presents results
for the pair HOMO-2 and HOMO-1 energies,
from which the $t$ to hop from the pyrrole HOMO-1 to the thiophene HOMO
is computed using our new method.

\begin{figure}
     \centering
     \begin{subfigure}[b]{0.4\textwidth}
         \centering
         \includegraphics[width=\textwidth]{ThPyrRotScanEnerg.pdf}
         \caption{}
         \label{fig:ThPyrRotEnerg}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.4\textwidth}
         \centering
         \includegraphics[width=\textwidth]{ThPyrRotScant.pdf}
         \caption{}
         \label{fig:ThPyrRott}
     \end{subfigure}
	\caption{(a): Pair HOMO-1 (blue) and HOMO-2 (orange) energies for thiophene and pyrrole scan
	at 4.2 \AA\ separation and their average (green) versus $\phi$. (b): Resulting $t$ value versus $\phi$.}
	\label{fig:ThPyrRotScan}
\end{figure}

\section{Thiophene tilt scans}

We now return to the thiophene-thiophene pair
to explore the effect on $t$ of ``tilting'' one monomer,
i.e., rotating it about an axis other than the common normal direction
that connects the centers of mass of the two molecules in their initial configuration.
Although the monomers are identical, the ESD method fails for this scan
because the ``tilt'' rotation breaks the C2 symmetry of the configuration;
thus, the Frontier Orbital Numerical Projection method will be used to calculate $t$.

The first tilt scan rotates one of the two thiophenes
around the axis from the center of the ring to the sulfur,
as shown in Fig.\ \ref{fig:ThThTiltScan1}(a).
Fig.\ \ref{fig:ThThTiltScan1} shows the energy of the pair HOMO and HOMO-1,
and the corresponding value of $|t|$ throughout the tilt.
For this scan, $t$ changes sign as the rotation angle $\phi$ exceeds 57.5 degrees.
This reflects a change in the relative sign
of the lobes of the two monomer HOMOs that are in close proximity, described further below.
The results presented in Fig.\ \ref{fig:ThThTiltScan1} are for the absolute value of $t$,
which is why the graph of Fig.\ \ref{fig:ThThTiltScan1}(c)
decreases linearly to zero at around 57.5 degrees,
and abruptly rises again.

\begin{figure*}
\begin{center}
\includegraphics[width=0.9\textwidth]{ThThTiltScan1.pdf}
\caption{(a): Schematic of tilt scan 1, at 5.0 \AA\ separation.
(b): Pair HOMO (blue) and HOMO-1 (orange) energies and their average (green) versus $\phi$.
(c): Resulting $t$ value versus $\phi$.}
\label{fig:ThThTiltScan1}
\end{center}
\end{figure*}

As the molecule tilts, lobes that were positioned to hybridize
move away from their initial optimal position at $\phi=0$.
At about 57.5 degrees, the lobes on the tilted thiophene
are sandwiched between the lobes on the other thophene,
such that the pair is neither bonding nor antibonding.
Beyond 57.5 degrees, the lobes line up to favor hybridization in a new arrangement.
The sides of the two closest lobes on the rotated molecule
begin to align across from the fronts of the two closest lobes on the stagnant molecule,
again resulting in bonding and antibonding orbitals.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{ThThTilt1Orbitals.pdf}
\caption{HOMO-1 and HOMO of thiophene-thiophene pair of molecules
with 57.5 and 90 degrees tilt and 5.0 \AA\ separation.}
\label{fig:ThThTilt1Orbitals}
\end{center}
\end{figure}

Fig.\ \ref{fig:ThThTilt1Orbitals} demonstrates both the negligible hybridization at 57.5 degrees
and the hybridization between the sides of the lobes of one molecule and the fronts of the other
that begins at rotations past 57.5 degrees.

We can also tilt one thiophene about the axis in the plane of the ring
orthogonal to the previous tilt axis,
which tips its sulfur to point towards the other thiophene,
as shown in Fig.\ \ref{fig:ThThTiltScan2}(a).
$t$ now decreases throughout the entire scan (see Fig.\ \ref{fig:ThThTiltScan2}(c)).
Fig.\ \ref{fig:ThThTilt2Orbitals} shows that for this tilt scan,
the monomer orbitals never realign to a geometry consistent with hybridization.

\begin{figure*}
\begin{center}
\includegraphics[width=0.9\textwidth]{ThThTiltScan2.pdf}
\caption{(a): Schematic of thiophene tilt scan 2 at 5.0 \AA\ separation.
(b): Pair HOMO (blue) and HOMO-1 (orange) energies and their average (green) versus $\phi$.
(c): Resulting $t$ value versus $\phi$.}
\label{fig:ThThTiltScan2}
\end{center}
\end{figure*}

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{ThThTilt2Orbitals.pdf}
\caption{HOMO-1 and HOMO of thiophene-thiophene pair of molecules
with 60 and 90 degrees tilt and 5.0 \AA\ separation.}
\label{fig:ThThTilt2Orbitals}
\end{center}
\end{figure}

\section{Transferability}

Evidently, interactions between large molecules should not be analyzed
as if they could be projected down to a single frontier orbital on each.
Large molecules will have multiple low-lying orbitals which must be represented.
For example, all-trans thiophene oligomers will have a set of close-lying sinusoidal orbitals,
which in the limit of long oligomers becomes a 1d band.

As we have emphasized, our method is meant to be used in conjunction with tight-binding models.
In such models, one makes appropriate choices of ``sites'' as moieties of a reasonable size,
such that representing them by a single localized orbital is a good approximation.
Properly constructed tight-binding models exhibit good agreement with DFT calculations,
and reasonable transferability of their coefficients
(onsite energies and hopping matrix elements)
between molecules of different architecture built from the same moieties.
\cite{Tipirneni:2020hg}.

Therefore, an important application of our method
to compute hopping matrix elements between nearby moieties
is to supply coefficients for tight-binding models of larger molecules.
An important question that arises in such applications
is the extent to which hopping matrix elements are ``transferable'',
i.e., can be applied between the same two local elements
in different molecular structures.

To provide a simple test of transferability,
we perform ``tilt scan 1'' of Fig.\ \ref{fig:ThThTiltScan1} again,
but this time using thiophene dimers rather than monomers.
In the scan, the end monomers of each dimer
are positioned and rotated in the same way as before;
Fig.\ \ref{fig:dimerTiltGeom} shows an example of the resulting geometry,
for a tilt angle of 45 degrees.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.3\textwidth]{dimerTiltGeometry}
\caption{Two thiophene dimers, with one tilted with respect to the other by 45 degrees,
analogous to ``tilt scan 1'' of Fig.\ \ref{fig:ThThTiltScan1} for thiophene monomers.}
\label{fig:dimerTiltGeom}
\end{center}
\end{figure}

On physical grounds, we expect that hopping between the molecules
occurs between the two end monomers,
so that the hopping matrix element obtained from this scan
should be somehow related to the results of Fig.\ \ref{fig:ThThTiltScan1}.
Fig.\ \ref{fig:dimerTiltResults} shows $|t|$ versus tilt angle for the new scan;
the curve very much resembles the result of Fig.\ \ref{fig:ThThTiltScan1},
but weaker by about a factor of two.
As we will now show, that is precisely what we expect
based on a simple tight-binding model.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.5\textwidth]{dimerTiltResult}
\caption{Hopping matrix element $|t|$ versus tilt angle,
for a pair of thiophene dimers, one tilted with respect to the other,
in the same way as for the tilt scan results of Fig.\ \ref{fig:ThThTiltScan1}.}
\label{fig:dimerTiltResults}
\end{center}
\end{figure}

The pair of interacting dimer molecules
can be described by a tight-binding Hamiltonian of the form
\begin{equation}
H^{(4)} = \left(\begin{array}{cccc}
\epsilon_{1T} & -t & 0 & 0 \\
-t & \epsilon_{2T} & 0 & -t' \\
0 & 0 & \epsilon_{1B} & -t \\
0 & -t' & -t & \epsilon_{2B}
\end{array}\right)
\label{eq:intDimer}
\end{equation}
In writing Eqn.\ \ref{eq:intDimer}, we allow for the possibility
that the onside energies of sites 1 and 2
on the top (T) and bottom (B) two molecules
may be shifted from their values in isolation
by the proximity of the other molecule.
$t'$ is the hopping matrix element
between the two nearby moieties (site 2 on T and B);
the intramolecular hopping matrix elements $t$
are assumed unaffected and identical.

We can relate the 4-site Hamiltonian $H^{(4)}$
to a simpler one that describes only interactions
between the HOMO frontier orbitals of the two molecules,
by projecting onto the $2 \times 2$ subspace
spanned by the two isolated HOMO orbitals:
\begin{equation}
\psi_T = \left(\begin{array}{c} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \\ 0 \end{array}\right) , \quad
\psi_B = \left(\begin{array}{c} 0 \\ 0 \\ 1/\sqrt{2} \\ -1/\sqrt{2} \end{array}\right)
\end{equation}

The relevant matrix elements are
\begin{eqnarray}
\langle \psi_T | H^{(4)} | \psi_T \rangle &=& (1/2)(\epsilon_{1T} + \epsilon_{2T}) + t \equiv \bar \epsilon_T \nonumber \\
\langle \psi_B | H^{(4)} | \psi_B \rangle &=& (1/2)(\epsilon_{1B} + \epsilon_{2B}) + t \equiv \bar \epsilon_B \nonumber \\
\langle \psi_T | H^{(4)} | \psi_B \rangle &=& -t'/2
\end{eqnarray}
Thus the projected 2-site Hamiltonian $H^{(2)}$ takes the form
\begin{equation}
H^{(2)} = \left(\begin{array}{cc} \bar \epsilon_T & -t'/2 \\ -t'/2 & \bar \epsilon_B \end{array}\right)
\end{equation}
This is exactly what we wrote for analyzing the hopping between two nearby moieties,
 with the hopping matrix element is identified as $t'/2$,
 half of the local value acting between site 2 on the top and bottom molecules.
 So by applying the Frontier Orbital Numerical Projection method
 to the pair of dimer molecules in a tilt scan,
 we should expect to obtain a hopping matrix element
 that couples the HOMOs of the two molecules,
 with a value about half that obtained
 in the corresponding scan for a pair of thiophene monomers.

\section{Conclusions}

Computing hopping matrix elements for moieties in close proximity
is an important part of building tractable models
for electronic interactions between such moieties,
with applications in modeling carrier transport
as well as exciton energetics and polarization
in organic semiconductor materials.
Hopping matrix elements can be inferred
from the energy level splittings
of hybridized frontier orbitals for the interacting pair
only in very special cases,
for which the molecules are chemically identical
and symmetrically placed,
leading to bonding and antibonding orbitals
that are symmetric and antisymmetric combinations
of the constituent monomer orbitals.

To treat the vast preponderance of cases
in which this symmetry is not present,
a more versatile method is required.
In this work, we present a simple and convenient method
to compute hopping matrix elements
between any pair of nearby small molecules.
The method relies on computing overlap integrals
between the frontier orbitals of the pair
and the frontier orbitals of the two interacting molecules
that hybridize to form the pair orbitals.

Such overlap integrals can in principle be computed analytically
from the set of basis function expansion coefficients for the orbitals.
However, commonly available DFT platforms such as Gaussian
do not provide utilities for such calculations;
code to compute such overlaps is tedious to write and validate,
and not readily available.
Instead, we compute such overlap integrals numerically using ``cube files'',
or spatially discretized representations of the pair and monomer orbitals.
Such cube files can be readily obtained
from utilities supplied with Gaussian and other DFT platforms.
Following this approach, we have created a set of Python and bash shell scripts
to compute hopping matrix elements between nearby molecules,
and to carry out scans in which one constituent molecule
is progressively translated or rotated with respect to the other
(see Supplemental Information for details).

We have validated this Frontier Orbital Numerical Projection method
by repeating published results for scans of $t$ versus separation
between two parallel tetracene molecules
(for which energy splitting is sufficient to determine $t$),
and as well for $t$ versus rotation between two initially parallel ethylene molecules
(for which orbital overlaps must be computed to determine $t$);
we find good agreement with previous results.
Then, we demonstrate how the method can be used
to explore how hopping matrix elements vary
with the chemical identity and relative placement
of two molecules in close proximity.
We select for our examples moieties that occur in the structure
of organic semiconducting polymers and non-fullerene acceptors
currently under study for photovoltaic material applications.

In forthcoming work, we apply our method to explore
the dependence of hopping matrix elements on relative placement of moieties
extracted from large configurations of semiconducting polymers
generated by atomistic molecular dynamics simulations.
Such studies will give insight into the heterogeniety
of electronic coupling within these disordered molecular solids,
and help us identify those configurations that lead
to particularly large or small values of $t$.

\section{Acknowledgements}

Funding support from the Office of Naval Research through Award N00014-19-1-2453 is gratefully acknowledged.

\section{Appendix:  non-orthogonal basis}

In our simple analysis of frontier orbitals on a pair of nearby moieties
interacting through a hopping matrix element,
we have implicitly assumed the orbitals $ \psi_1$ and $\psi_2 $
are far enough apart that they may be regarded as orthogonal.
If they are, then the expansion coefficients of a dimer frontier orbital $\psi $,
written as
\begin{equation}
\psi  = c_1 \psi_1+ c_2 \psi_2
\end{equation}
can be computed straightforwardly as
\begin{equation}
c_i = \langle \psi_i | \psi \rangle
\end{equation}
As emphasized by Valeev et al., this approach should be modified
if the localized states on the two moieties
have significant direct overlap\cite{Valeev2006}.

If $\psi_1$ and $\psi_2$ are not quite orthogonal,
we can still compute $c_1$ and $c_2$,
by introducing a ``dual basis'' of wavefunctions
$\tilde \psi_1$ and $\tilde \psi_2$, with the properties
\begin{equation}
\langle \tilde \psi_i | \psi_j \rangle = \delta_{ij}
\end{equation}
We can use the dual wavefunctions $\tilde \psi_i$
to compute the expansion coefficients $c_i$ as
\begin{equation}
c_i = \langle \tilde \psi_i | \psi \rangle
\end{equation}

To compute the dual basis in terms of the overlap integral
$\langle \psi_1 | \psi_2 \rangle = \gamma$,
we expand the dual wavefunctions in terms of the original set as
\begin{eqnarray}
\tilde \psi_1 &=& \alpha_1 \psi_1 + \beta_1 \psi_2 \nonumber \\
\tilde \psi_2 &=& \beta_2 \psi_2 + \alpha_2 \psi_2
\end{eqnarray}
The dual basis conditions lead to a matrix equation
for the coefficients $\alpha_i$ and $\beta_i$:
\begin{equation}
\left(\begin{array}{cc}\alpha_1 & \beta_1 \\ \beta_2 & \alpha_2 \end{array}\right)
\left(\begin{array}{cc}1 & \gamma \\ \gamma & 1 \end{array}\right)
= \left(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right)
\end{equation}
That is, the matrix of expansion coefficients
is the inverse of the matrix of overlap integrals $\langle \psi_i | \psi_j \rangle$.

Evidently for the present $2 \times 2$ case,
we can take $\beta_1 = \beta_2 = \beta$, and $\alpha_1 = \alpha_2 = \alpha$.
Explicitly computing the inverse, we find
\begin{eqnarray}
\alpha &=& 1/(1-\gamma^2) \nonumber \\
\beta &=& -\gamma/(1-\gamma^2)
\end{eqnarray}

If $\psi_1$ and $\psi_2$ are nearly orthogonal, $\gamma$ is small,
and we have $\alpha \approx 1$, $\beta \approx 0$
so that $\tilde \psi_1 \approx \psi_1$.
More generally, the expansion coefficients can be given as
\begin{eqnarray}
c_1 &=& \frac{\langle \psi_1 | \psi \rangle - \gamma \langle \psi_2 | \psi \rangle}{1 - \gamma^2} \nonumber \\
c_2 &=& \frac{\langle \psi_2 | \psi \rangle - \gamma \langle \psi_1 | \psi \rangle}{1 - \gamma^2}
\end{eqnarray}

Because we consider only pairs of moieties that are not too close to each other,
the overlap integrals in all the scans we report here are quite small.
For example, in the ``tilt scan 1'' leading to the results of Fig.\ \ref{fig:ThThTiltScan1},
the value of $\gamma$ is everywhere less than 0.005 in magnitude.
Accordingly, we neglect the corresponding small correction in our reported results.

redpajama_set_name: RedPajamaArXiv


Democratic congressional candidate Randy Bryce scheduled a fundraising event to be headlined by actors Sean Penn and Mark Ruffalo.
When asked where he stood on the actors' controversial statements, a spokeswoman for the campaign said the event has since been canceled.
The Daily Caller News Foundation obtained a copy of the fundraising invitation.
A picture of Randy Bryce's now-cancelled fundraiser. Image by TheDCNF.
The actor's comments regarding Chavez's successor, Nicolas Maduro, have also not aged well: "Venezuela and its revolution will endure under the proven leadership of vice president Maduro," Penn said in 2013.
Under Maduro, nearly 90 percent of Venezuela's citizens live in poverty, according to a university study cited by CNN.
Mark Ruffalo — another actor listed on Bryce's invitation — has espoused his fair share of controversial comments.
Bryan Steil is the Republican nominee in Wisconsin's 1st Congressional District race. His campaign hit Bryce hard for the now-canceled fundraiser.
"Over 90 percent of Randy Bryce's campaign has been funded by out of state liberals, so it's no surprise that he planned to jet to California and rub elbows with out-of-touch celebrities. Randy Bryce continues to show that his far-left policies are too extreme for Southeast Wisconsin," Steil spokesman Andrew Iverson stated to TheDCNF.
The nixed fundraiser comes after what has been a rocky road for the Wisconsin Democrat.
At the launch of his congressional bid in June 2017, Bryce was widely lauded by national Democrats as a candidate who had the potential to knock Ryan out of his long-held seat — Ryan has since announced his plans to retire from Congress and has endorsed Steil.
This excitement among progressives, however, has faded as parts of Bryce's private life have come into the public eye.
It was revealed in November 2017 that Bryce had been delinquent on his child support payments for nearly two years — and did not meet his payments until two months after launching his campaign.
Upon hearing that story, a former girlfriend of Bryce's came forward to reveal she had been trying to get Bryce to pay back a $1,776 debt he allegedly owed her for nearly 15 years. The woman had taken numerous steps — even obtaining a court order — to force Bryce to pay her back. He finally did after she approached the media in November 2017.
A much bigger part of Bryce's past came back to haunt him several months later.
Follow Jason and Evie on Twitter.


text:
If you have an issue logging into your Twilio SendGrid account, please read this [document](https://sendgrid.com/docs/ui/account-and-settings/troubleshooting-login/). For any questions regarding login issues, please contact our [support team](https://support.sendgrid.com).

If you have a non-library SendGrid issue, please contact our [support team](https://support.sendgrid.com).

If you can't find a solution below, please open an [issue](https://github.com/sendgrid/sendgrid-java/issues).

## Table of Contents

- [Table of Contents](#table-of-contents)
- [Migrating from v2 to v3](#migrating-from-v2-to-v3)
- [Continue Using v2](#continue-using-v2)
  - [via Maven w/ Gradle](#via-maven-w-gradle)
  - [via jar file](#via-jar-file)
- [Testing v3 /mail/send Calls Directly](#testing-v3-mailsend-calls-directly)
- [Versions](#versions)
- [Environment Variables and Your Twilio SendGrid API Key](#environment-variables-and-your-twilio-sendgrid-api-key)
- [Using the Package Manager](#using-the-package-manager)
- [Android Compatibility](#android-compatibility)
- [Viewing the Request Body](#viewing-the-request-body)
- [Verifying Event Webhooks](#signed-webhooks)

## Migrating from v2 to v3

Please review [our guide](https://sendgrid.com/docs/Classroom/Send/v3_Mail_Send/how_to_migrate_from_v2_to_v3_mail_send.html) on how to migrate from v2 to v3.

## Continue Using v2

[Here](https://github.com/sendgrid/sendgrid-java/tree/b64988f85474e04e9d75e17860d64ffacda1cdff) is the last working version with v2 support.

### via Maven w/ Gradle

Add the following to your build.gradle file in the root of your project.

```groovy
...
dependencies {
  ...
  compile 'com.sendgrid:sendgrid-java:2.2.2'
}

repositories {
  mavenCentral()
}
...
```

### via jar file

You can just drop the jar file in. It's a fat jar - it has all the dependencies built in.

[sendgrid-java.jar](http://repo1.maven.org/maven2/com/sendgrid/sendgrid-java/2.2.2/sendgrid-java-2.2.2-jar.jar)

## Testing v3 /mail/send Calls Directly

[Here](https://sendgrid.com/docs/for-developers/sending-email/curl-examples/) are some cURL examples for common use cases.

## Versions

We follow the MAJOR.MINOR.PATCH versioning scheme as described by [SemVer.org](http://semver.org). Therefore, we recommend that you always pin (or vendor) the particular version you are working with  your code and never auto-update to the latest version. Especially when there is a MAJOR point release since that is guaranteed to be a breaking change. Changes are documented in the [CHANGELOG](CHANGELOG.md) and [releases](https://github.com/sendgrid/sendgrid-java/releases) section.

## Environment Variables and Your Twilio SendGrid API Key

All of our examples assume you are using [environment variables](https://github.com/sendgrid/sendgrid-java#setup-environment-variables) to hold your Twilio SendGrid API key.

If you choose to add your Twilio SendGrid API key directly (not recommended):

`System.getenv("SENDGRID_API_KEY")`

becomes

`"SENDGRID_API_KEY"`

In the first case, SENDGRID_API_KEY is in reference to the name of the environment variable, while the second case references the actual Twilio SendGrid API Key.

## Using the Package Manager

We upload this library to [Maven](http://repo1.maven.org/maven2/com/sendgrid/sendgrid-java/) whenever we make a release. This allows you to use [maven and gradle](https://maven.apache.org/) for easy installation.

In most cases we recommend you download the latest version of the library, but if you need a different version, please use:

```groovy
...
dependencies {
  ...
  compile 'com.sendgrid:sendgrid-java:X.X.X'
}

repositories {
  mavenCentral()
}
...
```

## Android Compatibility

Since Android SDK 23, HttpClient is no longer supported. Some workarounds can be found [here](http://stackoverflow.com/questions/32153318/httpclient-wont-import-in-android-studio).

We have an issue to remove that dependency [here](https://github.com/sendgrid/java-http-client/issues/2), please upvote to move it up the queue.

## Viewing the Request Body

When debugging or testing, it may be useful to examine the raw request body to compare against the [documented format](https://sendgrid.com/docs/API_Reference/api_v3.html).

You can do this right before you call `request.setBody(mail.build())` like so:

```java
System.out.println(mail.build());
```

## Signed Webhook Verification

Twilio SendGrid's Event Webhook will notify a URL via HTTP POST with information about events that occur as your mail is processed. [This](https://docs.sendgrid.com/for-developers/tracking-events/getting-started-event-webhook-security-features) article covers all you need to know to secure the Event Webhook, allowing you to verify that incoming requests originate from Twilio SendGrid. The sendgrid-java library can help you verify these Signed Event Webhooks.

You can find the end-to-end usage example [here](examples/helpers/eventwebhook/Example.java) and the tests [here](/src/test/java/com/sendgrid/helpers/eventwebhook/EventWebhookTest.java).

If you are still having trouble getting the validation to work, follow the following instructions:
- Be sure to use the *raw* payload for validation
- Be sure to include a trailing carriage return and newline in your payload
- In case of multi-event webhooks, make sure you include the trailing newline and carriage return after *each* event

redpajama_set_name: RedPajamaGithub


On Thursday 1st October, Grant brought his team from WSM into school to lead a day based around the Rugby World Cup.
The children started the day with an assembly to explain the day, with its overarching theme of courage, ending with a Mexican wave in their countries.
They then participated in four different activities around the school: a Games session, a Discovery session, a Creative session and a Sports session.
During each session they could earn points, for example, for working as a team, or as a kind or motivational individual. The team with the most points would then be awarded medals at the closing ceremony. Our winners were Japan. The children ended the day with a whole school rendition of Swing Low, Sweet Chariot.
Hopefully we all had fun, and learnt something new during the day, either about rugby, the country we represented, or ourselves.


text:
My St. Richard's
Worship Home
Spiritual Expansion
2023 Pledge Drive
Flower Donations and Dedications
St Richard's Legacy Society
5151 Lake Howell Rd. Winter Park, FL 32792
New Feeding Ministry
Daily Morning Prayer | Evening Prayer | The Prayer Tree
Fourth Sunday after the Epiphany
Micah 6:1-8, 1 Corinthians 1:18-31, Matthew 5:1-12, Psalm 15
8:00 a.m. Rite I Holy Communion (in-person inside church)
10:30 a.m. Rite II Holy Communion (in-person inside church and live-streamed on YouTube)
5:00 p.m. Evening Worship (in-person inside church)
5:00 p.m. Evening Prayer (live-streamed online via Facebook Live)
Annual Meeting and Vestry Elections
Annual Meeting and Vestry Elections will take place on Sunday, January 29, immediately following the 10:30 am service. We will be offering voting both online and in person this year. Come and participate in this one meeting of the members of St. Richard's
Movie on the Lawn
Join us as we watch Kung Fu Panda as our Movie on the Lawn! Sunday, January 29, 2023, 5:30 pm. All are welcome and there will be free popcorn! Read more
Divine Diners
Sunday, January 29, 2022, at 6:00 p.m.
Come and join us at Miller's Ale House, 101 University Park Dr, Winter Park, FL 32792
R.S.V.P. with Ms. Charlie Wilson 321-279-1089.
Coalition for the Homeless Feeding Ministry
February: Pasta Casserole
Pans and recipes will be available Sunday, January 29 at 8:00 am and 10:30 am services. Please bring your pan to the kitchen at St Richard's no later than 3:00 pm Friday. You may put them in the refrigerator starting Wednesday. JOIN St Richard's parishioners by cooking and then serving at the Coalition for the Homeless, 18 N. Terry Avenue, Orlando 32801, on the first Friday of the month, 4:30-6:30 pm.
Help Fill the New Pantry
Sunday, February 5, 2023 between the 8:00 am and 10:30 am service
Love Bites!
Parish Wide Brunch
Sunday, February 12, 2023, after the 10:30 a.m. service
Come for bite-sized snacks and a valentine-good time! Bring your love or just yourself, all are welcome.
Godly Conversations about prayer
God is always inviting us into connection. Prayer is our response to that invitation! We will explore methods and approaches to prayer... Read more
Sunday, March 26, 2023, 9:00 a.m. - Coffee Hour
St. Richard's 2023 Lent Wednesday Series
High on the Hog
March 1, 8, 15, 22, 29, 2023
Time: 6:30 p.m. with an end time at 7:45 p.m. with Compline
Brought to you by the Beloved Community Committee of St. Richard's and the Sacred Ground study group.
This Lenten series will be a series of eating, watching, reflecting and discussing events in which you will experience some of the pains as well as the joys of African American people and their cuisine brought here on slave ships from West Africa. But we will experience it through food! We will eat together, watch the Netflix series together, pray and discuss. Each Wednesday evening, there will be a new entrée and a new experience. Read more
St. Richard's Wins Grant for National Clergy Program
St. Richard's has received a grant of almost $40,000 to enable its minister, The Rev. Alison P. Harrity, to participate in the 2022 National Clergy Renewal Program. St. Richard's is one of 168 congregations across the United States selected to participate in this competitive grant program, which is funded by Lilly Endowment, Inc., and administered by Christian Theological Seminary in Indianapolis. Established by the Endowment in 2000, the program's grants allow Christian congregations to support their pastors with the gift of extended time away from their ministerial duties and responsibilities.
National Clergy Renewal Program
Sue Brown, Judy Bowerman, Brenda Lutter, Jackie Jackson, Bonnie Danner, Jacky Rodriguez, Ray Pini, Ruth Vaisey, Bill Platt, Kathy F., Barb, Alice, Bob B., Seamone, Gina Varan, Betsy Zaorski, Priscilla Pini, Linda Young, Val Suarez, Meredith Knapp, Hazel Will, and Stan Zarolinski.
For our members who are unable to attend in-person worship: Hazel Will, Sheila Fountain, Ruth Vaisey, Sandra Barrett
And family and friends, Daniel Bostaph, Ruthie Dunlad, Bette Maurer, Judy Hernandez and family, Shamika, A.J., Lucia and Family, Dan, Joyce G., Bert Zug, Mariann Bruno, Jan Beck, June Sjoberg, Diana Beatty, Cindy W., Jim and family, Sarah, Rachel, and Emma. Also, teachers, first responders, our military personnel and healthcare workers.
May we who are merely inconvenienced, remember those whose lives are at stake.
May we who have no risk factors remember those most vulnerable. May those who have the luxury of working from home remember those who must choose between preserving their health or making their rent. May those who have the flexibility to care for our children when schools close remember those who have no options. May we who have to cancel a trip remember those who have no safe place to go. May we who are losing our margin money in the tumult of the economic market remember those who have no margin at all. May those who settle for quarantine at home remember those who have no home.
As fear grips our country, let us choose love during this time when we cannot physically wrap our arms around each other, let us find ways to be the loving embrace to God and our neighbor. Amen.
Prayer by Cameron Wiggins Bellm
Welcome to St. Richard's Episcopal Church!
All are welcome at the table of God
Every man woman and child.
For Christ brings peace to all,
Tearing down every hostile wall.
So that the many may become one,
One heart, one family, one new humanity.
For God who is love, and Christ who is all and in all
Show no partiality and make no distinction.
So neither race nor class, gender nor sexuality,
Politics nor religion, personality nor nationality,
Count for us, or against us.
The light of Christ enlightens all:
Christ the prisoner and the naked,
Christ the hungry and the sick,
Christ the thirsty and the stranger,
Christ the other.
May God's spirit hover over our chaos,
Our hatred and our indifference.
Descend in our hearts with love and pleasure.
Blow us out into the world to listen and serve.
And set us ablaze to forgive and reconcile.
For all are welcome at the table of God,
Every man, woman and child.
Welcome to St. Richard's Episcopal Church!
Sunday services are in person and live-streamed on YouTube.
Sunday Worship, 8:00 & 10:30 a.m.
Evening Worship, 5:00 p.m. (in person and Facebook Live)
Morning Prayer, Monday-Friday at 9 a.m. on Facebook Live only.
Join us on Facebook Live or subscribe to our Youtube channel.
5151 Lake Howell Rd, Winter Park, FL 32792
Holy Eucharist, Sundays 8am/10:30am
Sunday Evening Worship, 5pm
Home Service Times News and Events Community My St. Richard's


It has helped to free me from the rat race and I get to do work that I absolutely love. I've been blogging and earning a consistent income online for about two years now and there are some things that I've learned along the way.
The following are some important things you need to know before starting a blog for earning income online. I hope these tips help you to create an awesome blog of your own to begin earning a passive income.
I've made mistakes with blogging in the past that had to do with niche selection. The first mistake was that I didn't choose a niche.
Years ago, I had a health and fitness blog that didn't focus on any one niche. For the most part, I wrote about anything on the health and fitness topic.
It was difficult to earn any income with that blog because a majority of visitors would land on a post and immediately click away making it impossible to sell anything.
Since the blog lacked focus, I know that when people landed on a page, they thought they'd find information related to their search query and didn't.
The second mistake that I made was choosing a niche (which was better than going broad), based on income potential rather than my genuine interest.
The niche that I chose was golf. I've never played golf so I know nothing about it. It made it almost impossible to create good content because I wasn't familiar, nor interested in the topic.
I always recommend choosing a niche that you have a genuine interest in. Otherwise, it will be a struggle to write blog posts on an ongoing basis.
It is easy to get caught up in the money-making aspect of creating a blog for profit. It is natural to want to sell, sell, sell.
When money is put first, your blog will show it with a lack of helpful content and tons of affiliate links.
Blog readers are smart and they can tell when someone is not genuinely trying to help with their content.
If you take a look at some of the most successful bloggers online, a majority of them serve their niche.
They put out super helpful and actionable content that people love. In return, they are able to earn commissions from affiliate products they recommend or even sell their own products.
Serve your niche by producing valuable content and the income will come.
In order to retain full ownership of your blog content, I highly recommend registering your own domain name and using a self-hosted WordPress website.
The problem with free blogging services is that you risk the chance of having your account closed which means losing all of the content you've worked so hard on.
Besides that, free services are often limiting in terms of storage space as well as how you can earn income.
There are plenty of web hosting providers to choose from and a majority of them are extremely economical.
You can get a free domain name and WordPress automatically installed for you with any Optimized WordPress Plan by HostPapa.
WordPress is easy to use and learn. It is also free! It really is the way to go for starting a blog.
Content creation is your primary job when managing a niche blog. Posting one or two blog posts per month isn't going to cut it.
Most successful bloggers that I follow post several times per week if not daily. Don't let that intimidate you.
Setting up a schedule for yourself will help. You also don't need to post daily. If you can only post once per week, then do that but stick to it.
Part of the reason for blogging often is that each time you post, it signals to the search engines that you post fresh content on a regular basis.
Another reason is that the more content that you have posted, the more free organic traffic you can receive.
Think of each new blog post as a way to attract new visitors who are interested in your niche.
The search engine robots will crawl your website more often and your content has a higher chance of ranking well in the search results.
Writer's block is no fun. It happens to all of us and it can eat into your productivity time when it occurs.
One of the ways I combat writer's block is by creating a month's worth of blog ideas. It is easy to do using a free keyword tool called Keyword.io.
By coming up with 30-days of blog ideas, you will no longer waste time figuring out what to write about when you sit down to create a new blog post.
All you will have to do is choose one from your list and get going. It is an efficient way to generate content on a regular basis.
Social media plays a key role in helping to get traffic to your blog. This is especially true in the early stages when you have no traffic at all.
Rather than trying to become an expert on every social media platform, I recommend focusing on one and becoming proficient in it.
My favorite is YouTube. The reason is that it is another search engine. People in your niche are likely searching on YouTube for help.
You can create video tutorials and then place a link to your blog in the video description. I use screen capture software to create video tutorials.
Another social media platform that many bloggers use is Pinterest. Regardless of which social media channel you prefer, focus on one and do it well.
As I briefly mentioned earlier, you cannot post a few blog posts and sit back. Getting a blog to the point of earning passive income requires consistent effort.
This is especially true when starting out. You can expect to spend a lot of hours working on your blog. Months will go by with no signs of progress.
I recall being 8 months into working on my blog with barely any visits. However, I knew that when I started it would take time.
Therefore I stayed consistent and posted content on a regular basis. It paid off about a year and a half in.
If I had given up at the 8th month mark, I would be kicking myself today. Commit to at least a year. All businesses need time to grow. A blog is no different.
When I had my health and fitness blog, it would receive decent traffic. At one point I was getting 1,200+ visitors a day.
That traffic disappeared after Google's major algorithm updates. One of the reasons is that I created thin content.
I offered very little value in what I wrote and my blog posts were quite short ranging from 3 to 5 paragraphs long.
I've had the best success creating content over 1,000 words. You can do a search about the benefits of long-form content.
Most articles will agree that longer content helps with ranking well. Of course, it isn't solely about the length of an article.
Your content should be relevant as well. When you focus on serving your niche, your blog posts will be long. It happens naturally.
One of the ways you can earn passive income with a blog is by promoting affiliate products. Don't make the mistake of promoting products you've never used.
I used to do that in the past and never made a sale. It is difficult to sell something when you are not familiar with it.
I've had the best results when I've promoted products that I currently sue or have used in the past.
When you write about affiliate products that you can stand behind, your writing will be genuine. It builds trust with your readers and they are more likely to take you up on the recommendation by buying using your affiliate link.
Finally, blogging truly is one of the best ways to earn income online. It is low-maintenance, fun, and has unlimited earning potential.
It is also duplicable. Once you learn how to create passive income with a blog, you can repeat the process over and over again.
It isn't uncommon to have several blogs across multiple niches all earning income. I hope these tips have been helpful.
The best time to start a blog is now. If you're ready to get started, get a self-hosted WordPress blog and start creating awesome content.