saving work in comp details

Manuscript/CBD.tex

@@ -310,38 +310,65 @@ First, we consider the autoisomerization barrier (Subsection \ref{sec:auto}) and
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 \subsection{Selected configuration interaction calculations}
 \label{sec:SCI}
-States energies and excitations energies calculations in the SCI framework are performed using QUANTUM PACKAGE \cite{Garniron_2019} where the CIPSI algorithm is implemented. The CIPSI algorithm allows to avoid the exponential increase of the CI expansion. To treat electronic states in the same way we use a state-averaged formalism meaning that the ground and excited states are represented with the same number and same set of determinants but using different CI coefficients. Then the SCI energy is the sum of two terms, the variational energy obtained by diagonalization of the CI matrix in the reference space and a second-order perturbative correction which estimates the contribution of the determinants not included in the CI space (estimate error in the truncation). It is possible to estimate the FCI limit for the total energies and compute the corresponding transition energies by extrapolating this second-order correction to zero. Extrapolation brings error and we can estimate this one by energy difference between excitation energies obtained with the largest SCI wave function and the FCI extrapolated value. These errors provide a rough idea of the quality of the FCI extrapolation and cannot be seen as true bar error, they are reported in the following tables.
+For the SCI calculations, we rely on the CIPSI algorithm which is implemented in QUANTUM PACKAGE. \cite{Garniron_2019} 
+To treat electronic states on equal footing, we use a state-averaged formalism where the ground and excited states are expanded in the same number and same set of determinants but with different CI coefficients. 
+Note that the determinant selection for these states are performed simultaneously via the protocol described in Refs.~\onlinecite{Scemama_2019,Garniron_2019}.
+For a given size of the variational wave function, the CIPSI energy is the sum of two terms: the variational energy obtained by diagonalization of the CI matrix in the reference space and a second-order perturbative correction which estimates the contribution of the determinants not included in the variational space (estimate error in the truncation). 
+It is possible to estimate the FCI limit for the total energies and compute the corresponding transition energies by extrapolating this second-order correction to zero. 
+Extrapolation brings error and we can estimate this one by energy difference between excitation energies obtained with the largest SCI wave function and the FCI extrapolated value. 
+These errors provide a rough idea of the quality of the FCI extrapolation and cannot be seen as true bar error, they are reported in the following tables.
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 \subsection{Coupled-Cluster calculations}
 \label{sec:CC}
-Different flavours of coupled-cluster (CC) calculations are performed using different codes. Indeed, CC theory provides a hierarchy of methods that provide increasingly accurate energies via the increase of the maximum excitation degree of the cluster operator. Without any truncation of the cluster operator one has the full CC (FCC) that is equivalent to the full configuration interaction (FCI) giving the exact energy and wave function of the system for a fixed atomic basis set. However, due to the computational exponential scaling with system size we have to  use truncated CC methods. The CC with singles and doubles (CCSD), CC with singles, doubles and triples (CCSDT) calculations are achieved with \textcolor{red}{CFOUR}. The calculations in the context of CC response theory or ``approximate'' series (CC3,CC4) are performed with \textcolor{red}{DALTON}.\cite{Aidas_2014} The CC with singles, doubles, triples and quadruples (CCSDTQ) are done with the \textcolor{red}{CFOUR} code. The CC2, \cite{Christiansen_1995,Hattig_2000} CC3 \cite{Christiansen_1995,Koch_1995} and CC4 \cite{Kallay_2005,Matthews_2020} methods can be seen as cheaper approximations of CCSD,\cite{Purvis_1982} CCSDT \cite{Noga_1987a} and CCSDTQ \cite{Kucharski_1991a} by skipping the most expensive terms and avoiding the storage of higher-excitations amplitudes.
+Different flavours of coupled-cluster (CC) calculations are performed using different codes. 
+Indeed, CC theory provides a hierarchy of methods that provide increasingly accurate energies via the increase of the maximum excitation degree of the cluster operator. 
+Without any truncation of the cluster operator one has the full CC (FCC) that is equivalent to the full configuration interaction (FCI) giving the exact energy and wave function of the system for a fixed atomic basis set. 
+However, due to the computational exponential scaling with system size we have to  use truncated CC methods. 
+The CC with singles and doubles (CCSD), CC with singles, doubles and triples (CCSDT) calculations are achieved with \textcolor{red}{CFOUR}. 
+The calculations in the context of CC response theory or ``approximate'' series (CC3,CC4) are performed with \textcolor{red}{DALTON}.\cite{Aidas_2014} 
+The CC with singles, doubles, triples and quadruples (CCSDTQ) are done with the \textcolor{red}{CFOUR} code. 
+The CC2, \cite{Christiansen_1995,Hattig_2000} CC3 \cite{Christiansen_1995,Koch_1995} and CC4 \cite{Kallay_2005,Matthews_2020} methods can be seen as cheaper approximations of CCSD, \cite{Purvis_1982} CCSDT \cite{Noga_1987a} and CCSDTQ \cite{Kucharski_1991a} by skipping the most expensive terms and avoiding the storage of higher-excitations amplitudes.
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 \subsection{Multi-configurational calculations}
 \label{sec:Multi}
-State-averaged complete-active-space self-consistent field (SA-CASSCF) calculations are performed with \textcolor{red}{MOLPRO}.\cite{Werner_2012} On top of those, NEVPT2 calculations, both partially contracted (PC) and strongly contracted (SC) scheme are considered. The PC-NEVPT2 is theoretically more accurate to the strongly contracted version due to the larger number of perturbers and greater flexibility. CASPT2 is performed and extended multistate (XMS) CASPT2 for strong mixing between states with same spin and spatial symmetries is also performed.
+State-averaged complete-active-space self-consistent field (SA-CASSCF) calculations are performed with \textcolor{red}{MOLPRO}.\cite{Werner_2012} 
+On top of those, NEVPT2 calculations, both partially contracted (PC) and strongly contracted (SC) scheme are considered. 
+The PC-NEVPT2 is theoretically more accurate to the strongly contracted version due to the larger number of perturbers and greater flexibility. 
+CASPT2 is performed and extended multistate (XMS) CASPT2 for strong mixing between states with same spin and spatial symmetries is also performed.
 
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 \subsection{Spin-flip calculations}
 \label{sec:sf}
-In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Spin-flip techniques are broadly accessible and here, among them, we explore algebraic-diagrammatic construction \cite{Schirmer_1982} (ADC) using standard ADC(2)-s \cite{Trofimov_1997,Dreuw_2015} and extended ADC(2)-x \cite{Dreuw_2015} schemes as well as the ADC(3) \cite{Dreuw_2015,Trofimov_2002,Harbach_2014} scheme. We also use spin-flip within the TD-DFT \cite{Casida_1995} framework. The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1. \cite{Shao_2015} Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The B3LYP,\cite{Becke_1988b,Lee_1988a,Becke_1993b} PBE0 \cite{Adamo_1999a,Ernzerhof_1999} and BH\&HLYP hybrid GGA functionals are considered, they contain 20\%, 25\%, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We also have done spin-flip TD-DFT calculations using range-separated hybrid (RSH) functionals as: CAM-B3LYP,\cite{Yanai_2004a} LC-$\omega$PBE08 \cite{Weintraub_2009a} and $\omega$B97X-V. \cite{Mardirossian_2014}The main difference here between these RSH functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. To complete the use of spin-flip TD-DFT we also considered the hybrid meta-GGA functional M06-2X \cite{Zhao_2008} and the RSH meta-GGA functional M11.\cite{Peverati_2011} Note that all SF-TD-DFT calculations are done within the TDA approximation.
+In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. 
+Spin-flip techniques are broadly accessible and here, among them, we explore algebraic-diagrammatic construction \cite{Schirmer_1982} (ADC) using standard ADC(2)-s \cite{Trofimov_1997,Dreuw_2015} and extended ADC(2)-x \cite{Dreuw_2015} schemes as well as the ADC(3) \cite{Dreuw_2015,Trofimov_2002,Harbach_2014} scheme. 
+We also use spin-flip within the TD-DFT \cite{Casida_1995} framework. 
+The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1. \cite{Shao_2015} 
+Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The B3LYP,\cite{Becke_1988b,Lee_1988a,Becke_1993b} PBE0 \cite{Adamo_1999a,Ernzerhof_1999} and BH\&HLYP hybrid GGA functionals are considered, they contain 20\%, 25\%, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. 
+We also have done spin-flip TD-DFT calculations using range-separated hybrid (RSH) functionals as: CAM-B3LYP,\cite{Yanai_2004a} LC-$\omega$PBE08 \cite{Weintraub_2009a} and $\omega$B97X-V. \cite{Mardirossian_2014}
+The main difference here between these RSH functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. 
+To complete the use of spin-flip TD-DFT we also considered the hybrid meta-GGA functional M06-2X \cite{Zhao_2008} and the RSH meta-GGA functional M11.\cite{Peverati_2011} 
+Note that all SF-TD-DFT calculations are done within the TDA approximation.
 %EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1. 
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 \subsection{Theoretical best estimates}
-All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X $=$ D, T, Q.\cite{dunning_1989} For each studied quantity, i.e., the autoisomerisation barrier and the vertical excitations, we provide a theoretical best estimate (TBE). These TBEs are provided using extrapolated CCSDTQ/aug-cc-pVTZ values when possible and using NEVPT2(12,12) otherwise. The extrapolation of the CCSDTQ/aug-cc-pVTZ values is done using two schemes. The first one uses CC4 values for the extrapolation and proceed as follows
+All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X $=$ D, T, Q.\cite{dunning_1989} 
+For each studied quantity, i.e., the autoisomerisation barrier and the vertical excitations, we provide a theoretical best estimate (TBE). 
+These TBEs are provided using extrapolated CCSDTQ/aug-cc-pVTZ values when possible and using NEVPT2(12,12) otherwise. 
+The extrapolation of the CCSDTQ/aug-cc-pVTZ values is done using two schemes. 
+The first one uses CC4 values for the extrapolation and proceed as follows
 
 \begin{equation}
 \label{eq:aug-cc-pVTZ}
 \Delta E^{\text{CCSDTQ}}_{\text{aug-cc-pVTZ}} = \Delta E^{\text{CCSDTQ}}_{\text{aug-cc-pVDZ}} + \left[ \Delta E^{\text{CC4}}_{\text{aug-cc-pVTZ}} - \Delta E^{\text{CC4}}_{\text{aug-cc-pVDZ}} \right]
 \end{equation}
-
 and we evaluate the CCSDTQ/aug-cc-pVDZ values as 
 
 \begin{equation}
@@ -356,7 +383,6 @@ when CC4/aug-cc-pVTZ values have been obtained. If it is not the case we extrapo
 \end{equation}
 Then if the CC4 values have not been obtained then we use the second scheme which is the same as the first one but instead of the CC4 values we use CCSDT to extrapolate CCSDTQ. If none of the two schemes is possible then we use the NEVPT2(12,12) values. Note that a NEVPT2(12,12) value is used only once for one vertical excitation of the \Dfour structure.
 
-
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