# June 2022¶

## Wednesday 1st June¶

• State averaged (SA) CASSCF optimises the orbitals to be appropriate for a number of electronic states, rather than just for one. The averages of these states is NOT a part of the CI.

1. The determinants are generated and culled, and are optimised for the CI coefficients (CASCI)
2. The orbitals are optimised with the CI coefficients, either for a single state or for an average of multiple states (CASSCF/SA-CASSCF)
3. Apply a post CASSCF treatment to the wavefunction to incorporate dynamic correlation
• This could be through perturbation theory (CASPT2/NEVPT2), through further CI, or through a density based correction.
• Orbitals that are good for ground state static correlation and those that are good for electronic excitations tend to be mutually exclusive.
• Size intensivity is similar to size extensivity, except that rather than looking at the difference in the energy of multiple isolated systems, it considers whether the excitation energy of one system ($$A\to A^*$$) will be effected by a noninteracting system ($$B)$$.
\begin{align} \text{Where a method can be considered size extensive if:}\\ E(A) + E(B) &= E(A\cup B)\\ \text{A method can be considered size intensive if:}\\ E(A^*)-E(A)&=E(A^*\cup B)-E(A\cup B) \end{align}
• SA-CASSCF is not size intensive. This could theoretically be overcome if the state average coefficients were not equal, however this would not represent multiple excited states with the same accuracy
• This lack of size intensivity is a result of the inclusion of different states degrading the accuracy of each state individually.
• CASSCF often produces discontinuous PES, as the solution of both the CI coefficients and the MOs isa linear problem that has multiple local solutions.
• This is also a present issue because the static correlation that is modelled by these methods is limited to the active space, and can thus localise on a particular region of interest.
• This can be somewhat mitigated by using CASCI with MOs from a non-CAS correlated basis or by using naturalised orbitals.
• CAS selection is complicated, particularly in optimisations and PES exploration as orbitals may shift in and out of the active space, and root-flipping may occur. (The active space is very geometry dependent)
• One proposed solution is to use an unrestricted natural orbital (UNO) MO basis, and use an active space that consists of all orbitals with occupations of 0.02-1.98
• This is a contentious method though… some say that a lack of complete occupation does not inherently mean correlation in an excited state manner.
• Another strategy is to use the active space that’s the most appropriate for the most strongly correlated portion of the PES and use it to model all of the PES.
• Dynamic correlation is a cumulation of very small and subtle configuration interactions, where static correlation is usually focused on a few configurations with larger contributions, form specific orbitals.
• Static correlation typically requires the inclusion of excitations higher than those considered in post HF methods.
• DFT handles static correlation better than HF, but breaks down for strongly correlated systems.
• Dynamic correlation isn’t hugely important for nuclear gradients, but is for very important for energetics.

## Thursday 2nd June¶

• This paper is all about breaking down the UNO method for active space assignment.
• It proposes that UNO occupation numbers could also be used to define the RAS subspaces, e.g.:
• RAS1 = 1.99 - 1.90
• RAS2 = 1.90 - 0.1
• RAS3 = 0.1 - 0.01
• Typically the range is considered 0.02 - 0.98 as being in the active space, though this can lead to a huge number of orbitals being selected, so instead it might be useful to refine this down to 0.075 - 1.925.
• These higher thresholds are also justified by the use of subsequent correlated methods such ads NEVPT2 and MR-CC methods for less strongly correlated systems
• My final take is that I’m not really convinced, though this might be because I can’t seem to get a non-integer population form a UNO in ORCA…

## Tuesday 7th June¶

Graduate research conference is happening atm, so I’m not sure how much work I’ll get done (on top of other issues), but I’ll try to see.

#### To do:¶

• Test out CPPE vs explicit water vs EFP
• Find multireference lectures

These slides are pretty good for an overview, I wish I could find the lecture itself though…

• Always specify in the SI how you chose your active space

## Friday 10th June¶

• Need to make a table of comparisons of packages
• What packages do the big names use?

• Benedetta Mennucci - Gaussian
• Lars Goerigk - ORCA/turbomole
• Laura Gagliardi - (Open)Molcas/ORCA

## Sunday 12th June¶

I made that table of packages and capabilities, and it’s quite disparaging to see how sparse the solvent model support is. It’s interesting to note that many of the implementations don’t support excited states though, so I guess that narrows things down further?

I’ve also downloaded a whole bunch of papers about linear response and state specific continuum solvation models, which I think could be quite important to get my head around, and should be my next point of reading.

If my PhD is going to focus on excited state solvation, then perhaps that’s where I need to focus my reading, rather than in trying to pick apart all the electronic methods.

Solvent Model (Known to support ES) Packages
CPCM ORCA(A), Psi4(N), GAMESS(A), Gaussian(A), Molcas(A), QCHEM(A)
IEFPCM Psi4(N), GAMESS(A), Gaussian(A), Dalton(A)
SMD ORCA(A), GAMESS(A), Gaussian(A), QCcem(A-g)(N-e), NWChem
SCIPCM Gaussian(A)
DPCM GAMESS(A)
IPCM Gaussian(A)
PTE Gaussian(A-EOMCCSD), ORCA(A-CC)
COSMO PySCF(A), MolPro(A), ADF(A), QChem(A), NWChem(A), TURBOMOLE(A)
(D)COSMO-RS TURBOMOLE(A)
Polarisable Embedding Psi4(Static), PySCF(Static), Dalton(Static)
EFP Psi4(Static), GAMESS(A), QChem(A), OpenMolcas?
VEM NWChem(A)
SS(V)PE QChem(A-g)(N-e)
CMIRS QChem(N-g)
Langevin Dipoles QChem(N-g)
PBC QChem(N-g)
Kirkwood Molcas(A)
Polarisable Density Embedding Dalton(A)
Frozen Density Embedding ADF(A), TURBOMOLE(A), Dalton(A)

## Monday 13th June¶

Definition of the day

• SCRF: Solvation that acts within the SCF. It is converged as a part of the reaction field instead of being applied as a correction.
• State Specific solvation: When the SCRF procedure is performed, it has to be performed on the same electronic configuration as is being formed in the SCF procedure. This is usually the groun state. State specific solvation considers a specific state other than the ground state.
• Equilibrium solvation: When considering solvation of excited states, since the electronic excitation happens very quickly compared to the nuclear relaxation, the solvent is considered to be in a non-equilibrium if the ground state solvation is used for the excited states. Equilibrium solvation recomputes the solvent field for each root, as though the solvent has has time to relax around the excited state.

## Thursday 16th June¶

Last night I put in my application to move from full-time study to part-time. I also put in the application to switch my secondary supervisor from Andrea to Toby.

• In terms of solvation, Linear Response is a correction to the ground state density used for the SCRF procedure. It’s implemented by calculating the excited state dynamic polarisation response from the transition density. State Specific uses a slightly different approach, calculating the dynamic polarisation from the difference between the ground and exited state densities.

Definition of the day

• Nonequilibrium solvation: If equilibrium solvation is that in which the solvent has completely equilibrated with the change in the solute, nonequilibrium solvation is what happens when the fast dynamic polarisation process (electronic reorganisation) happens, but the slow polarisation (molecular reorganisation) does not.
Solvent Model Unknown Fast (LR) Fast (SS) Slow/eq PTE
CPCM GAMESS(A), Molcas(A) Psi4(N), ORCA(A), Gaussian(A), QCHEM(A-ptLR) Gaussian(A-cLR, N-VEM with VEMGAUSS[g09]), QCHEM(A-SS/ptSS) ORCA(A), Gaussian(A), QCHEM(A), QCHEM(A) Gaussian(A-EOMCCSD), ORCA(A-CC), QChem(A)
IEFPCM GAMESS(A) Psi4(N), Gaussian(A)), QCHEM(A-ptLR), Dalton(A) Gaussian(A-cLR)), QCHEM(A-SS/ptSS) Gaussian(A), QCHEM(A), Dalton(A) Gaussian(A-EOMCCSD), ORCA(A-CC), QChem(A)
SMD ORCA(A), GAMESS(A), Gaussian(A), QCcem(A-g)(N-e), NWChem
SCIPC Gaussian(A)
DPCM GAMESS(A)
IPCM Gaussian(A)
COSMO MolPro(A), ADF(A), QChem(A), TURBOMOLE(A) PySCF(A) NWChem(A-VEM) PySCF(A), NWChem(A)
(D)COSMO-RS TURBOMOLE(A)
EFP Psi4(Static), GAMESS(A), QChem(A), OpenMolcas?
SS(V)PE QChem(A-g)(N-e) GAMESS(A)(Does SS(V)PE use LR?) GAMESS(A)

## Friday 17th June¶

• The SS solvation approach comes in three forms:
• Vertical Excitation Method (VEM) - An iterative/self consistent approach
• Corrected-LR (cLR) - “can be seen as the first cycle of this iterative process.”
• Improta, Barone, Scalmani, and Frisch (IBSF) - Iterative like VEM, but the total excited state density is used instead of just the density difference.
• LR is good for systems where there is little electronic rearrangement between the GS and ES, otherwise an SS approach needs to be used.

## Tuesday 21st June¶

• Finished off that paper, the conclusions are ultimately that the correct solvation approach is method dependent, though this was also only a sample size of two solvents and two chromophores.

## Thursday 23rd June¶

• So as I keep reading, this tangled web of solvation models gets more complicated. It seems as though there’s a handful of approaches, all of which branch out with different corrections. From what I can tell, these are the main overarching categories:
• PCM
• Is broken down into:
• CPCM, DPCM, IPCM, IEFPCM, COSMO, ddCOSMO, SS(V)PE
• These are all different formalisms for how to consider the polarisable continuum. IEFPCM and SS(V)PE seem to be considered the most sophisticated implementations.
• With vertical excitation models:
• LR, VEM, SS
• I think ptSS and ptLR are just QChem implementations?
• and cLR seems to be an implementation of SS
• These seem to use an optical dielectric $$\varepsilon_\infty$$ (square of the refractive index @ 293K?)
• Density and perturbation methods
• EFP, CPPE, PDE, FPE
• These are solvent microstate methods that represent the solvent as either a responsive of frozen electrostatic mass, with differing amounts of dispersion contribution. They better represent solvent specific interactions, such as hydrogen bonding and pi stacking, but lack the generalised nature of continuum based methods.
• Parameterised models
• Usually take a PCM basis and apply a correction on top based on some sort of identification of sites or density of the solute
• nD-RISM, SMn, SMD, CMIRS
• These usually do not analytically support excited states
• The term SCRF seems to refer specifically to a solvent model that’s directly implemented in the SCF procedures and is thus self consistent with the electronic state, though since the SCF procedure is typically the ground state, the excitation model is used a correction, taking into account either the transition density or the density difference between the GS and ES.

## Thursday 30th June¶

• Formulations of PCM
• DPCM is the initial formulation of PCM and uses the electrostatic definition of charge forming at the surface of two dielectric media
• CPCM and COSMO are both methods that utilise a conductor as the bulk and scale the resulting surface charges as a function of the dielectric constant. The scaling factor takes the form $$f(\varepsilon)=\frac{\varepsilon-1}{\varepsilon+x}$$. CPCM takes the value of $$x=0$$ where in COSMO $$x=0.5$$
• The Integral Equation Formulation of PCM (IEFPCM) is a more generalised case from which DPCM and CPCM can be considered subcases. It is considered to be more mathematically exact
• IEFPCM fixes two big issues of DPCM
1. It correctly models the case in which the solute charge extends beyond the cavity
2. It can be extended to work with anisotropic dielectrics and complex environments
• Numerical Implementation
• Initially this was done by creating a vdW surface around the solute and treating each point as a specific charge.
• The vdW surface could be filled up to represent the Solvent Excluded Surface (SES)
• Modern implementations use a continuous charge by modelling these points with simple spherical Gaussian functions
• These use a Lebedev grid rather than a GEPOL surface, and the portion of the surface area represented by the gaussian element is used as an integration weight.
• The SES method does not work here, so instead a scaling factor is used to increase the vdW radii to recover the solvent excluded regions

• Comparison of Methods for Active Orbital Selection in Multiconfigurational Calculations
• CAS without SCF—Why to use CASCI and where to get the orbitals
• Combining Wave Function Methods with Density Functional Theory for Excited States