excited states D4h
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@ -414,10 +414,10 @@ All the calculations are performed using four basis set, the 6-31+G(d) basis and
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\subsubsection{D2h geometry}
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Table \ref{tab:sf_tddft_D2h} shows the results obtained for the vertical transition energies using spin-flip methods and Table \ref{tab:D2h} shows the results obtained with the standard methods. We discuss first the SF-TD-DFT values with hybrid functionals. For the B3LYP functional we can see that the energy differences for each state and throughout all bases are small with the largest one for the $1\,{}^3B_{1g}$ state with 0.012 eV. The same observation can be done for the PBE0 and BH\&HLYP functionals, we can also oberve that adding exact exchange to the functional (20\% of exact exchange for B3LYP, 25\% for PBE0 and 50\% for BH\&HLYP increase the energy difference between the $1\,{}^1B_{1g}$ and the $1\,{}^3B_{1g}$ states. Put another way, increasing the amount of exact exchange in the functional reduces the energy difference between the $1\,{}^3B_{1g}$ and the $\text{X}\,{}^1A_{g}$ states. We can also notice that the vertical energies of the different states do not vary in the same way when adding exact exchange, for instance the energy variation for the $1\,{}^3B_{1g}$ state from PBE0 to BH\&HLYP is around 0.1 eV whereas for the $1\,{}^1B_{1g}$ and the $1\,{}^1A_{1g}$ states this energy variation is about 0.4-0.5 eV and 0.34 eV respectively. For the RSH functionals we can not make the same observation, indeed we can see that for the CAM-B3LYP functional we have that the energy difference between the $1\,{}^1B_{1g}$ and the $1\,{}^3B_{1g}$ states is larger than for the $\omega$B97X-V and LC-$\omega $PBE08 functionals despite the fact that the latter ones have a bigger amount of exact exchange. However we can observe that we have a small energy difference for each state throughout the bases and for each RSH functional. The M06-2X functional is an Hybrid meta-GGA functional and contains 54\% of Hartree-Fock exchange, we can compare the energies with the BH\&HLYP functional and we can see that the energy differences are small with around 0.03-0.08 eV. We can notice that the upper bound of 0.08 eV in the energy differences is due to the $1\,{}^3B_{1g}$ state.
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Then we discuss the various ADC scheme (ADC(2)-s, ADC(2)-x and ADC(3)) results. For ADC(2) we have vertical energy differencies of about 0.03 eV for the $1\,{}^3B_{1g}$ state and around 0.06 eV for $1\,{}^1A_{1g}$ state throughout all bases. However for the $1\,{}^1B_{1g}$ state we have an energy difference of about 0.2 eV. For the ADC(2)-x and ADC(3) schemes the calculations with the AVQZ basis are not feasible with our resources. With ADC(2)-x we have similar vertical energies for the triplet and the $1\,{}^1B_{1g}$ states but for the $1\,{}^1A_{1g}$ state the energy difference between the ADC(2) and ADC(2)-x schemes is about 0.4-0.5 eV. The ADC(3) values are closer from the ADC(2) than the ADC(2)-x except for the triplet state for which we have a energy difference of about 0.09-0.14 eV. Now, we look at Table \ref{tab:D2h} to discuss the results of standard methods. First we discuss the CC values, we have computed the vertical energies at the CCSDT and CCSDTQ level as well as their approximation the CC3 and CC4 methods, respectively. We can notice that for the $1\,{}^3B_{1g}$ and the $1\,{}^1B_{1g}$ states the CCSDT and the CC3 values are close with an energy difference of 0.009-0.02 eV for all bases. The energy difference is larger for the $1\,{}^1A_{1g}$ state with around 0.35-0.38 eV. The same observation can be done for CCSDTQ and CC4 with similar vertical energies for all bases. Note that the $1\,{}^1B_{1g}$ state can not be described with this methods.
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Then we discuss the various ADC scheme (ADC(2)-s, ADC(2)-x and ADC(3)) results. For ADC(2) we have vertical energy differencies of about 0.03 eV for the $1\,{}^3B_{1g}$ state and around 0.06 eV for $1\,{}^1A_{1g}$ state throughout all bases. However for the $1\,{}^1B_{1g}$ state we have an energy difference of about 0.2 eV. For the ADC(2)-x and ADC(3) schemes the calculations with the AVQZ basis are not feasible with our resources. With ADC(2)-x we have similar vertical energies for the triplet and the $1\,{}^1B_{1g}$ states but for the $1\,{}^1A_{1g}$ state the energy difference between the ADC(2) and ADC(2)-x schemes is about 0.4-0.5 eV. The ADC(3) values are closer from the ADC(2) than the ADC(2)-x except for the triplet state for which we have a energy difference of about 0.09-0.14 eV. Now, we look at Table \ref{tab:D2h} to discuss the results of standard methods. First we discuss the CC values, we have computed the vertical energies at the CCSDT and CCSDTQ level as well as their approximation the CC3 and CC4 methods, respectively. We can notice that for the $1\,{}^3B_{1g}$ and the $1\,{}^1B_{1g}$ states the CCSDT and the CC3 values are close with an energy difference of 0.009-0.02 eV for all bases. The energy difference is larger for the $1\,{}^1A_{1g}$ state with around 0.35-0.38 eV. The same observation can be done for CCSDTQ and CC4 with similar vertical energies for all bases. Note that the $1\,{}^3B_{1g}$ state can not be described with these methods.
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Then we review the vertical energies obtained with multireference methods. The smallest active space considered is four electrons in four orbitals, for CASSCF(4,4) we have small energy variations throughout bases for the $1\,{}^3B_{1g}$ and the $1\,{}^1A_{1g}$ states but a larger variation for the $1\,{}^1B_{1g}$ state with around 0.1 eV. We can observe that we have the inversion of the states compared to all methods discussed so far between the $1\,{}^1A_{1g}$ and $1\,{}^1B_{1g}$ states with $1\,{}^1B_{1g}$ higher than $1\,{}^1A_{1g}$ due to the lack of dynamical correlation in the CASSCF methods. The $1\,{}^1B_{1g}$ state values in CASSCF(4,4) is much higher than for any of the other methods discussed so far. With CASPT2(4,4) we retrieve the right ordering between the states and we see large energy differences with the CASSCF values. Indeed, we have approximatively 0.22-0.25 eV of energy difference for the triplet state for all bases and 0.32-0.36 eV for the $1\,{}^1A_{1g}$ state, the largest energy difference is for the $1\,{}^1B_{1g}$ state with 1.5-1.6 eV.
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For the XMS-CASPT2(4,4) only the $1\,{}^1A_{1g}$ state is described with values similar than for the CAPST2(4,4) method. For the NEVPT2(4,4) methods (SC-NEVPT2 and PC-NEVPT2) the vertical energies are similar for the $1\,{}^1B_{1g}$ and the $1\,{}^1A_{1g}$ states with approximatively 0.002-0.003 eV and 0.02-0.03 eV of energy difference for all bases,respectively. The energy difference for the $1\,{}^1B_{1g}$ state is slightly larger with 0.05 eV for all bases. Note that for this state the vertical energy varies of 0.23 eV from the 6-31+G(d) basis to the AVDZ one. Then we use a larger active space with twelve electrons in twelve orbitals, the CASSF(12,12) values are close to the the CASSCF(4,4) for the triplet state with 0.01-0.02 eV of energy differences. For the $1\,{}^1A_{1g}$ state we have an energy difference of about 0.2 eV between the CASSCF(4,4) and the CASSCF(12,12) values. We can notice that increasing the size of the active space gives the right ordering for the states and we have an energy difference of around 0.7 eV for the $1\,{}^1B_{1g}$ state between CASSCF(4,4) and the CASSCF(12,12) values. The CASPT2(12,12) method decreases the energy of all states compared to the CASSCF(12,12) method, again the decrease is not the same for all states. We have a diminution from CASSCF to CASPT2 of about 0.17 to 0.2 eV for the $1\,{}^3B_{1g}$ and the $1\,{}^1A_{1g}$ states and for the different bases. Again, the energy difference for the $1\,{}^1A_{1g}$ state is larger with 0.5-0.7 eV depending on the basis. In a similar way than with XMS-CASPT2(4,4), the XMS-CASPT(12,12) only describes the $1\,{}^1A_{1g}$ state and the vertical energies for this state are close to the CASPT(12,12) values. For the NEVPT2(12,12) schemes we see that for the triplet and the $1\,{}^1A_{1g}$ states the energies are similar with an energy difference between the SC-NEVPT2(12,12) and the PC-NEVPT2(12,12) values of about 0.03-0.04 eV and 0.02-0.03 eV respectively.
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For the XMS-CASPT2(4,4) only the $1\,{}^1A_{1g}$ state is described with values similar than for the CAPST2(4,4) method. For the NEVPT2(4,4) methods (SC-NEVPT2 and PC-NEVPT2) the vertical energies are similar for the $1\,{}^1B_{1g}$ and the $1\,{}^1A_{1g}$ states with approximatively 0.002-0.003 eV and 0.02-0.03 eV of energy difference for all bases, respectively. The energy difference for the $1\,{}^1B_{1g}$ state is slightly larger with 0.05 eV for all bases. Note that for this state the vertical energy varies of 0.23 eV from the 6-31+G(d) basis to the AVDZ one. Then we use a larger active space with twelve electrons in twelve orbitals, the CASSF(12,12) values are close to the the CASSCF(4,4) for the triplet state with 0.01-0.02 eV of energy differences. For the $1\,{}^1A_{1g}$ state we have an energy difference of about 0.2 eV between the CASSCF(4,4) and the CASSCF(12,12) values. We can notice that increasing the size of the active space gives the right ordering for the states and we have an energy difference of around 0.7 eV for the $1\,{}^1B_{1g}$ state between CASSCF(4,4) and the CASSCF(12,12) values. The CASPT2(12,12) method decreases the energy of all states compared to the CASSCF(12,12) method, again the decrease is not the same for all states. We have a diminution from CASSCF to CASPT2 of about 0.17 to 0.2 eV for the $1\,{}^3B_{1g}$ and the $1\,{}^1A_{1g}$ states and for the different bases. Again, the energy difference for the $1\,{}^1A_{1g}$ state is larger with 0.5-0.7 eV depending on the basis. In a similar way than with XMS-CASPT2(4,4), the XMS-CASPT(12,12) only describes the $1\,{}^1A_{1g}$ state and the vertical energies for this state are close to the CASPT(12,12) values. For the NEVPT2(12,12) schemes we see that for the triplet and the $1\,{}^1A_{1g}$ states the energies are similar with an energy difference between the SC-NEVPT2(12,12) and the PC-NEVPT2(12,12) values of about 0.03-0.04 eV and 0.02-0.03 eV respectively.
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%%% TABLE II %%%
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\begin{squeezetable}
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@ -661,8 +661,79 @@ CIPSI & & & & \\
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\subsubsection{D4h geometry}
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Table \ref{tab:sf_D4h} shows vertical energies obtained with spin-flip methods and Table \ref{tab:D4h} vertical energies obtained with standard methods. As for the previous geometry we start with the SF-TD-DFT results with hybrid functionals. We can first notice that for the B3LYP and the PBE0 functionals we have a wrong ordering of the first triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. We retrieve the good ordering with the BH\&HLYP functional, so adding exact exchange to the functional allows us to have the right ordering between these two states. For the B3LYP and the PBE0 functionals we have that the energy differences for each states and for all bases are small with 0.004-0.007 eV for the triplet state $1\,{}^3A_{2g}$. We have 0.015-0.021 eV of energy difference for the $2\,{}^1A_{1g}$ state through all bases, we can notice that this state is around 0.13 eV (considering all bases) higher with the PBE0 functional. We can make the same observation for the $1\,{}^1B_{2g}$ state for the B3LYP and the PBE0 functionals, indeed we have small energy differences for all bases and the state is around 0.14-0.15 eV for the PBE0 functional. For the BH\&HLYP functional the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states are higher in energy than for the two other hybrid functionals with about 0.65-0.69 eV higher for the $2\,{}^1A_{1g}$ state and 0.75-0.77 eV for the $1\,{}^1B_{2g}$ state compared to the PBE0 functional. Then, we have the RSH functionals CAM-B3LYP, $\omega$B97X-V and LC-$\omega$PBE08. For these functionals the vertical energies are similar for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states with a maximum energy difference of 0.01-0.02 eV for the $2\,{}^1A_{1g}$ state and 0.005-0.009 eV for the $1\,{}^1B_{2g}$ state considering all bases. The maximum energy difference for the triplet state is larger with 0.047-0.057 eV for all bases. Note that the vertical energies obtained with the RSH functionals are close to the PBE0 ones except that we have the right ordering between the triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. The M06-2X results are closer to the BH\&HLYP ones but the M06-2X vertical energies are always higher than the BH\&HLYP ones. We can notice that the M06-2X energies for the $2\,{}^1A_{1g}$ state are close to the BH\&HLYP energies for the $1\,{}^1B_{2g}$ state. For these two states, when we compared the results obtained with the M06-2X and the BH\&HLYP functionals, we have an energy difference of 0.16-0.17 eV for the $2\,{}^1A_{1g}$ state and 0.17-0.18 eV for the $1\,{}^1B_{2g}$ state considering all bases. For the triplet state $1\,{}^3A_{2g}$ the energy differences are smaller with 0.03-0.04 eV for all bases. The M11 vertical energies are very close to the M06-2X ones for the triplet state with a maximum energy difference of 0.003 eV considering all bases, and are closer to the BH\&HLYP results for the two other states with 0.06-0.07 eV and 0.07-0.08 eV of energy difference for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively. Then we discuss the various ADC scheme results, note that we were not able to obtain the vertical energies with the AVQZ basis due to computational resources. For the ADC(2)-s scheme we can see that the energy difference for the triplet state are smaller than for the two other states, indeed we have an energy difference of 0.09 eV for the triplet state whereas we have 0.15 eV and 0.25 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, again when considering all bases. The energy difference for each state and through the bases are similar for the two other ADC schemes. We can notice a large variation of the vertical energies for the $2\,{}^1A_{1g}$ state between ADC(2)-s and ADC(2)-x with around 0.52-0.58 eV through all bases. The ADC(3) vertical energies are very similar to the ADC(2) ones for the $1\,{}^1B_{2g}$ state with an energy difference of 0.01-0.02 eV for all bases, whereas we have an energy difference of 0.04-0.11 eV and 0.17-0.22 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively.
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%%% TABLE V %%%
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Now we look at Table \ref{tab:D4h} for vertical energies obtained with standard methods, we have first the various CC methods, for all the CC methods we were only able to reach the AVTZ basis.
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%For the CCSD method we cannot obtain the vertical energy for the $1\,{}^1B_{2g}$ state, we can notice a small energy variation through the bases for the triplet state with around 0.06 eV. The energy variation is larger for the $2\,{}^1A_{1g}$ state with 0.20 eV.
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Again, we have computed the vertical energies at the CCSDT and CCSDTQ level as well as their approximation the CC3 and CC4 methods, respectively. For the CC3 method we do not have the vertical energies for the triplet state $1\,{}^3A_{2g}$. Considering all bases for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states we have an energy difference of about 0.15 eV and 0.12 eV, respectively. The CCSDT energies are close to the CC3 ones for the $2\,{}^1A_{1g}$ state with an energy difference of around 0.03-0.06 eV considering all bases. For the $1\,{}^1B_{2g}$ state the energy difference between the CC3 and the CCSDT values is larger with 0.18-0.27 eV. We can make a similar observation between the CC4 and the CCSDTQ values, for the $2\,{}^1A_{1g}$ state we have an energy difference of about 0.01 eV and this time we have smaller energy difference for the $1\,{}^1B_{2g}$ with 0.01 eV. Then we discuss the multireference results and this time we were able to reach the AVQZ basis. Again we consider two different active spaces, four electrons in four orbitals and twelve electrons in twelve orbitals. If we compare the CASSCF(4,4) and CASPT2(4,4) values we can see large energy differences for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, for the $2\,{}^1A_{1g}$ state we have an energy difference of about 0.67-0.74 eV and 1.65-1.81 eV for the $1\,{}^1B_{2g}$ state. The energy difference is smaller for the triplet state with 0.27-0.31 eV, we can notice that all the CASSCF(4,4) vertical energies are higher than the CASPT2(4,4) ones. Then we have the NEVPT2(4,4) methods (SC-NEVPT2(4,4) and PC-NEVPT2(4,4)) for which the vertical energies are quite similar, however we can notice that we have a different ordering of the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states with $1\,{}^1B_{2g}$ higher in energy than $2\,{}^1A_{1g}$ for the two NEVPT2(4,4) methods. Then we have the results for the same methods but with a larger active space. For the CASSCF(12,12) we have similar values for the triplet state with energy difference of about 0.06 eV for all bases but larger energy difference for the $2\,{}^1A_{1g}$ state with around 0.28-0.29 eV and 0.79-0.81 eV for the $1\,{}^1B_{2g}$ state. Note that from CASSCF(4,4) to CASSCF(12,12) every vertical energy is smaller. We can make the contrary observation for the CASPT2 method where from CASPT2(4,4) to CASPT2(12,12) every vertical energy is larger. For the CASPT2(12,12) method we have similar values for the triplet state and for the $2\,{}^1A_{1g}$ state, considering all bases, with an energy difference of around 0.05-0.06 eV and 0.02-0.05 eV respectively. The energy difference is larger for the $1\,{}^1B_{2g}$ state with about 0.27-0.29 eV. Next we have the NEVPT2 methods, the first observation that we can make is that by increasing the size of the active space we retrieve the right ordering of the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states. Again, every vertical energy is higher in the NEVPT2(12,12) case than for the NEVPT2(4,4) one.
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%%% TABLE VI %%%
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\begin{squeezetable}
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\begin{table}
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\caption{
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Standard vertical excitation energies (with respect to the singlet $\text{X}\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states of CBD at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3A_{2g}$ state.
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\label{tab:sf_D4h}}
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\begin{ruledtabular}
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\begin{tabular}{llrrr}
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& \mc{4}{r}{Excitation energies (eV)} \hspace{0.5cm}\\
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\cline{3-5}
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Method & Basis & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\
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\hline
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%SF-CIS & 6-31+G(d) & $0.355$ & $2.742$ & $3.101$ \\
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%& AVDZ & $0.318$ & $2.593$ & $3.052$ \\
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%& AVTZ & $0.305$ & $2.576$ & $3.053$ \\
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%& AVQZ & $0.306$ & $2.577$ & $3.056$ \\[0.1cm]
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SF-TD-B3LYP & 6-31+G(d) & $-0.016$ & $0.487$ & $0.542$ \\
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& AVDZ & $-0.019$ & $0.477$ & $0.536$ \\
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& AVTZ & $-0.020$ & $0.472$ & $0.533$ \\
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& AVQZ & $-0.020$ & $0.473$ & $0.533$ \\[0.1cm]
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SF-TD-PBE0 & 6-31+G(d) & $-0.012$ & $0.618$ & $0.689$ \\
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& AVDZ & $-0.016$ & $0.602$ & $0.680$ \\
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& AVTZ & $-0.019$ & $0.597$ & $0.677$ \\
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& AVQZ & $-0.018$ & $0.597$ & $0.677$ \\[0.1cm]
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SF-TD-BH\&HLYP& 6-31+G(d) & $0.064$ & $1.305$ & $1.458$ \\
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& AVDZ & $0.051$ & $1.260$ & $1.437$ \\
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& AVTZ & $0.045$ & $1.249$ & $1.431$ \\
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& AVQZ & $0.046$ & $1.250$ & $1.432$ \\[0.1cm]
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SF-TD-M06-2X & 6-31+G(d) & $0.102$ & $1.476$ & $1.640$ \\
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& AVDZ & $0.086$ & $1.419$ & $1.611$ \\
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& AVTZ & $0.078$ & $1.403$ & $1.602$ \\
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& AVQZ & $0.079$ & $1.408$ & $1.607$ \\[0.1cm]
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SF-TD-CAM-B3LYP & 6-31+G(d) & $0.021$ & $0.603$ & $0.672$ \\
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& AVDZ & $0.012$ & $0.585$ & $0.666$ \\
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& AVTZ & $0.010$ & $0.580$ & $0.664$ \\
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& AVQZ & $0.010$ & $0.580$ & $0.664$ \\[0.1cm]
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SF-TD-$\omega $B97X-V & 6-31+G(d) & $0.040$ & $0.600$ & $0.670$ \\
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& AVDZ & $0.029$ & $0.576$ & $0.664$ \\
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& AVTZ & $0.026$ & $0.572$ & $0.662$ \\
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& AVQZ & $0.026$ & $0.572$ & $0.662$ \\[0.1cm]
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SF-TD-LC-$\omega $PBE08 & 6-31+G(d) & $0.078$ & $0.593$ & $0.663$ \\
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& AVDZ & $0.060$ & $0.563$ & $0.659$ \\
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& AVTZ & $0.058$ & $0.561$ & $0.658$ \\
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& AVQZ & $0.058$ & $0.561$ & $0.659$ \\[0.1cm]
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SF-TD-M11 & 6-31+G(d) & $0.102$ & $1.236$ & $1.374$ \\
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& AVDZ & $0.087$ & $1.196$ & $1.362$ \\
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& AVTZ & $0.081$ & $1.188$ & $1.359$ \\
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& AVQZ & $0.080$ & $1.185$ & $1.357$ \\[0.1cm]
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SF-ADC(2)-s & 6-31+G(d) & $0.345$ & $1.760$ & $2.096$ \\
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& AVDZ & $0.269$ & $1.656$ & $1.894$ \\
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& AVTZ & $0.256$ & $1.612$ & $1.844$ \\[0.1cm]
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SF-ADC(2)-x & 6-31+G(d) & $0.264$ & $1.181$ & $1.972$ \\
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& AVDZ & $0.216$ & $1.107$ & $1.760$ \\
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& AVTZ & $0.212$ & $1.091$ & $1.731$ \\[0.1cm]
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SF-ADC(3) & 6-31+G(d) & $0.123$ & $1.650$ & $2.078$ \\
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& AVDZ & $0.088$ & $1.571$ & $1.878$ \\
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& AVTZ & $0.079$ & $1.575$ & $1.853$ \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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\end{squeezetable}
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%%% %%% %%% %%%
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%%% TABLE V %%%
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\begin{squeezetable}
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\begin{table*}
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\caption{
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@ -674,10 +745,10 @@ CIPSI & & & & \\
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\cline{3-5}
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Method & Basis & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\
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\hline
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CCSD & 6-31+G(d) & $0.148$ & $1.788$ & \\
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& AVDZ & $0.100$ & $1.650$ & \\
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& AVTZ & $0.085$ & $1.600$ & \\
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& AVQZ & $0.084$ & $1.588$ & \\[0.1cm]
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% CCSD & 6-31+G(d) & $0.148$ & $1.788$ & \\
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% & AVDZ & $0.100$ & $1.650$ & \\
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% & AVTZ & $0.085$ & $1.600$ & \\
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% & AVQZ & $0.084$ & $1.588$ & \\[0.1cm]
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CC3 & 6-31+G(d) & & $1.809$ & $2.836$ \\
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||||
& AVDZ & & $1.695$ & $2.646$ \\
|
||||
& AVTZ & & $1.662$ & $2.720$ \\[0.1cm]
|
||||
@ -738,69 +809,7 @@ CIPSI & 6-31+G(d) & $0.2010\pm 0.0030$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\
|
||||
\end{squeezetable}
|
||||
%%% %%% %%% %%%
|
||||
|
||||
%%% TABLE VI %%%
|
||||
\begin{squeezetable}
|
||||
\begin{table}
|
||||
\caption{
|
||||
Standard vertical excitation energies (with respect to the singlet $\text{X}\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states of CBD at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3A_{2g}$ state.
|
||||
\label{tab:sf_D4h}}
|
||||
\begin{ruledtabular}
|
||||
\begin{tabular}{llrrr}
|
||||
& \mc{4}{r}{Excitation energies (eV)} \hspace{0.5cm}\\
|
||||
\cline{3-5}
|
||||
Method & Basis & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\
|
||||
\hline
|
||||
%SF-CIS & 6-31+G(d) & $0.355$ & $2.742$ & $3.101$ \\
|
||||
%& AVDZ & $0.318$ & $2.593$ & $3.052$ \\
|
||||
%& AVTZ & $0.305$ & $2.576$ & $3.053$ \\
|
||||
%& AVQZ & $0.306$ & $2.577$ & $3.056$ \\[0.1cm]
|
||||
SF-TD-B3LYP & 6-31+G(d) & $-0.016$ & $0.487$ & $0.542$ \\
|
||||
& AVDZ & $-0.019$ & $0.477$ & $0.536$ \\
|
||||
& AVTZ & $-0.020$ & $0.472$ & $0.533$ \\
|
||||
& AVQZ & $-0.020$ & $0.473$ & $0.533$ \\[0.1cm]
|
||||
SF-TD-PBE0 & 6-31+G(d) & $-0.012$ & $0.618$ & $0.689$ \\
|
||||
& AVDZ & $-0.016$ & $0.602$ & $0.680$ \\
|
||||
& AVTZ & $-0.019$ & $0.597$ & $0.677$ \\
|
||||
& AVQZ & $-0.018$ & $0.597$ & $0.677$ \\[0.1cm]
|
||||
SF-TD-BH\&HLYP& 6-31+G(d) & $0.064$ & $1.305$ & $1.458$ \\
|
||||
& AVDZ & $0.051$ & $1.260$ & $1.437$ \\
|
||||
& AVTZ & $0.045$ & $1.249$ & $1.431$ \\
|
||||
& AVQZ & $0.046$ & $1.250$ & $1.432$ \\[0.1cm]
|
||||
SF-TD-M06-2X & 6-31+G(d) & $0.102$ & $1.476$ & $1.640$ \\
|
||||
& AVDZ & $0.086$ & $1.419$ & $1.611$ \\
|
||||
& AVTZ & $0.078$ & $1.403$ & $1.602$ \\
|
||||
& AVQZ & $0.079$ & $1.408$ & $1.607$ \\[0.1cm]
|
||||
SF-TD-CAM-B3LYP & 6-31+G(d) & $0.021$ & $0.603$ & $0.672$ \\
|
||||
& AVDZ & $0.012$ & $0.585$ & $0.666$ \\
|
||||
& AVTZ & $0.010$ & $0.580$ & $0.664$ \\
|
||||
& AVQZ & $0.010$ & $0.580$ & $0.664$ \\[0.1cm]
|
||||
SF-TD-$\omega $B97X-V & 6-31+G(d) & $0.040$ & $0.600$ & $0.670$ \\
|
||||
& AVDZ & $0.029$ & $0.576$ & $0.664$ \\
|
||||
& AVTZ & $0.026$ & $0.572$ & $0.662$ \\
|
||||
& AVQZ & $0.026$ & $0.572$ & $0.662$ \\[0.1cm]
|
||||
SF-TD-M11 & 6-31+G(d) & $0.102$ & $1.236$ & $1.374$ \\
|
||||
& AVDZ & $0.087$ & $1.196$ & $1.362$ \\
|
||||
& AVTZ & $0.081$ & $1.188$ & $1.359$ \\
|
||||
& AVQZ & $0.080$ & $1.185$ & $1.357$ \\[0.1cm]
|
||||
SF-TD-LC-$\omega $PBE08 & 6-31+G(d) & $0.078$ & $0.593$ & $0.663$ \\
|
||||
& AVDZ & $0.060$ & $0.563$ & $0.659$ \\
|
||||
& AVTZ & $0.058$ & $0.561$ & $0.658$ \\
|
||||
& AVQZ & $0.058$ & $0.561$ & $0.659$ \\[0.1cm]
|
||||
SF-ADC(2)-s & 6-31+G(d) & $0.345$ & $1.760$ & $2.096$ \\
|
||||
& AVDZ & $0.269$ & $1.656$ & $1.894$ \\
|
||||
& AVTZ & $0.256$ & $1.612$ & $1.844$ \\[0.1cm]
|
||||
SF-ADC(2)-x & 6-31+G(d) & $0.264$ & $1.181$ & $1.972$ \\
|
||||
& AVDZ & $0.216$ & $1.107$ & $1.760$ \\
|
||||
& AVTZ & $0.212$ & $1.091$ & $1.731$ \\[0.1cm]
|
||||
SF-ADC(3) & 6-31+G(d) & $0.123$ & $1.650$ & $2.078$ \\
|
||||
& AVDZ & $0.088$ & $1.571$ & $1.878$ \\
|
||||
& AVTZ & $0.079$ & $1.575$ & $1.853$ \\
|
||||
\end{tabular}
|
||||
\end{ruledtabular}
|
||||
|
||||
\end{table}
|
||||
\end{squeezetable}
|
||||
%%% %%% %%% %%%
|
||||
|
||||
|
||||
%%% TABLE I %%%
|
||||
\begin{squeezetable}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user