533 lines
24 KiB
TeX
533 lines
24 KiB
TeX
\documentclass[aip,jcp,reprint,onecolumn,noshowkeys,superscriptaddress]{revtex4-1}
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% addresses
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\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
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\begin{document}
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\title{Supporting Information for ``Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism''}
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\author{Enzo \surname{Monino}}
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\affiliation{\LCPQ}
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\author{Pierre-Fran\c{c}ois \surname{Loos}}
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\email{loos@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\maketitle
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\begin{table*}
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\caption{Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$ and $\text{E}\,{}^1\Sigma_g^+$ states of \ce{H2} obtained with the cc-pVQZ basis at the CIS, TD-BH\&HLYP, BSE@{\GOWO}, and EOM-CCSD levels of theory.}
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\begin{ruledtabular}
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\begin{tabular}{lrrrrrrrr}
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&\mc{2}{c}{CIS} & \mc{2}{c}{BH\&HLYP} & \mc{2}{c}{BSE@{\GOWO}} & \mc{2}{c}{EOM-CCSD} \\
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\cline{2-3} \cline{4-5} \cline{6-7} \cline{8-9}
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$R(\ce{H-H})$ (\AA) & $\text{B}\, ^1 \Sigma_u^+$& $\text{E}\, ^1 \Sigma_g^+$ & $\text{B}\, ^1 \Sigma_u^+$& $\text{E}\, ^1 \Sigma_g^+$ & $\text{B}\, ^1 \Sigma_u^+$& $\text{E}\, ^1 \Sigma_g^+$ & $\text{B}\, ^1 \Sigma_u^+$& $\text{E}\, ^1 \Sigma_g^+$ \\
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\hline
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$0 .5$ & $15 .942$ & $17 .398$ & $15 .253$ & $16 .896$ & $15 .535$ & \
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$16 .135$ & $15 .703$ & $16 .737$ \\
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$0 .6$ & $14 .791$ & $16 .579$ & $14 .18$ & $16 .199$ & $14 .767$ & \
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$15 .073$ & $14 .61$ & $16 .056$ \\
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$0 .7$ & $13 .745$ & $15 .891$ & $13 .339$ & $15 .614$ & $14 .108$ & \
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$14 .12$ & $13 .621$ & $15 .491$ \\
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$0 .8$ & $12 .8$ & $15 .311$ & $12 .514$ & $15 .122$ & $13 .236$ & \
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$13 .591$ & $12 .735$ & $15 .017$ \\
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$0 .9$ & $11 .943$ & $14 .815$ & $11 .766$ & $14 .699$ & $12 .444$ & \
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$13 .126$ & $11 .938$ & $14 .615$ \\
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$1.$ & $11 .163$ & $14 .389$ & $11 .088$ & $14 .334$ & $11 .722$ & \
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$12 .733$ & $11 .224$ & $14 .27$ \\
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$1 .1$ & $10 .454$ & $14 .025$ & $10 .474$ & $14 .02$ & $11 .068$ & \
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$12 .41$ & $10 .587$ & $13 .962$ \\
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$1 .2$ & $9 .8096$ & $13 .712$ & $9 .919$ & $13 .75$ & $10 .477$ & \
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$12 .132$ & $10 .023$ & $13 .648$ \\
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$1 .3$ & $9 .3685$ & $13 .401$ & $9 .421$ & $13 .515$ & $9 .4696$ & \
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$12 .139$ & $9 .5306$ & $13 .201$ \\
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$1 .4$ & $9 .1278$ & $13 .262$ & $8 .9771$ & $13 .309$ & $8 .7427$ & \
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$12 .211$ & $9 .1076$ & $14 .241$ \\
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$1 .5$ & $8 .9859$ & $13 .18$ & $8 .5848$ & $13 .127$ & $8 .2988$ & \
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$12 .3$ & $8 .7525$ & $13 .814$ \\
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$1 .6$ & $8 .9106$ & $13 .125$ & $8 .2413$ & $12 .966$ & $8 .0543$ & \
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$12 .395$ & $8 .4631$ & $13 .606$ \\
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$1 .7$ & $8 .8839$ & $13 .085$ & $7 .9431$ & $12 .824$ & $7 .9457$ & \
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$12 .482$ & $8 .2361$ & $13 .475$ \\
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$1 .8$ & $8 .8936$ & $13 .058$ & $7 .6866$ & $12 .699$ & $7 .9282$ & \
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$12 .563$ & $8 .0669$ & $13 .383$ \\
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$1 .9$ & $8 .9307$ & $13 .041$ & $7 .4677$ & $12 .593$ & $7 .9697$ & \
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$12 .641$ & $7 .9505$ & $13 .317$ \\
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$2.$ & $8 .9888$ & $13 .033$ & $7 .2827$ & $12 .502$ & $8 .0486$ & \
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$12 .714$ & $7 .881$ & $13 .272$ \\
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$2 .1$ & $9 .0627$ & $13 .031$ & $7 .1279$ & $12 .421$ & $8 .1508$ & \
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$12 .783$ & $7 .8523$ & $13 .239$ \\
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$2 .2$ & $9 .1485$ & $13 .031$ & $6 .9996$ & $12 .343$ & $8 .2671$ & \
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$12 .845$ & $7 .8581$ & $13 .212$ \\
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$2 .3$ & $9 .2429$ & $13 .031$ & $6 .8947$ & $12 .265$ & $8 .3914$ & \
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$12 .901$ & $7 .8923$ & $13 .187$ \\
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$2 .4$ & $9 .3435$ & $13 .031$ & $6 .81$ & $12 .186$ & $8 .5197$ & \
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$12 .951$ & $7 .9492$ & $13 .164$ \\
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$2 .5$ & $9 .4484$ & $13 .032$ & $6 .7427$ & $12 .109$ & $8 .6495$ & \
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$12 .997$ & $8 .0239$ & $13 .145$ \\
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$2 .6$ & $9 .5561$ & $13 .037$ & $6 .6902$ & $12 .03$ & $8 .7792$ & \
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$13 .042$ & $8 .1122$ & $13 .133$ \\
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$2 .7$ & $9 .6657$ & $13 .043$ & $6 .6501$ & $11 .946$ & $8 .908$ & \
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$13 .084$ & $8 .2105$ & $13 .125$ \\
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$2 .8$ & $9 .7763$ & $13 .05$ & $6 .6205$ & $11 .851$ & $9 .0353$ & \
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$13 .123$ & $8 .3162$ & $13 .12$ \\
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$2 .9$ & $9 .8874$ & $13 .056$ & $6 .5996$ & $11 .744$ & $9 .1605$ & \
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$13 .154$ & $8 .4269$ & $13 .115$ \\
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$3.$ & $9 .9984$ & $13 .057$ & $6 .5857$ & $11 .627$ & $9 .283$ & $13 \
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.174$ & $8 .5408$ & $13 .106$ \\
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$3 .1$ & $10 .109$ & $13 .053$ & $6 .5778$ & $11 .505$ & $9 .4032$ & \
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$13 .183$ & $8 .6564$ & $13 .091$ \\
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$3 .2$ & $10 .219$ & $13 .043$ & $6 .5746$ & $11 .383$ & $9 .5211$ & \
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$13 .181$ & $8 .7726$ & $13 .069$ \\
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$3 .3$ & $10 .328$ & $13 .027$ & $6 .5754$ & $11 .266$ & $9 .6369$ & \
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$13 .169$ & $8 .8884$ & $13 .041$ \\
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$3 .4$ & $10 .435$ & $13 .006$ & $6 .5792$ & $11 .158$ & $9 .7506$ & \
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$13 .15$ & $9 .003$ & $13 .008$ \\
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$3 .5$ & $10 .541$ & $12 .983$ & $6 .5856$ & $11 .062$ & $9 .862$ & \
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$13 .126$ & $9 .1159$ & $12 .972$ \\
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$3 .6$ & $10 .645$ & $12 .958$ & $6 .5939$ & $10 .977$ & $9 .971$ & \
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$13 .1$ & $9 .2265$ & $12 .935$ \\
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$3 .7$ & $10 .748$ & $12 .933$ & $6 .6037$ & $10 .905$ & $10 .077$ & \
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$13 .073$ & $9 .3347$ & $12 .899$ \\
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$3 .8$ & $10 .848$ & $12 .908$ & $6 .6145$ & $10 .846$ & $10 .181$ & \
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$13 .047$ & $9 .4401$ & $12 .863$ \\
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$3 .9$ & $10 .947$ & $12 .884$ & $6 .626$ & $10 .798$ & $10 .282$ & \
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$13 .023$ & $9 .5424$ & $12 .83$ \\
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$4.$ & $11 .043$ & $12 .861$ & $6 .6381$ & $10 .761$ & $10 .38$ & \
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$13.$ & $9 .6415$ & $12 .8$ \\
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\end{tabular}
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\end{ruledtabular}
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\end{table*}
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\begin{table*}
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\caption{Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$, $\text{E}\,{}^1\Sigma_g^+$, and $\text{F}\,{}^1\Sigma_g^+$ states of \ce{H2} obtained with the cc-pVQZ basis at the SF-CIS, SF-TD-BH\&HLYP, SF-BSE@{\GOWO}, and EOM-CCSD levels of theory.
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All the spin-conserved and spin-flip calculations have been performed with an unrestricted reference.}
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\begin{ruledtabular}
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\begin{tabular}{lrrrrrrrrrrrrrrrrrrrrr}
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&\mc{3}{c}{SF-CIS} & \mc{3}{c}{SF-BH\&HLYP} & \mc{3}{c}{SF-BSE@{\GOWO}}& \mc{3}{c}{EOM-CCSD}\\
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\cline{2-4} \cline{5-7} \cline{8-10} \cline{11-13}
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$R(\ce{H-H})$ (\AA) & $\text{B}\, ^1 \Sigma_u^+$& $\text{E}\, ^1 \Sigma_g^+$ & $ \text{F}\,^1 \Sigma_g^+$& $\text{B}\, ^1 \Sigma_u^+$ & $\text{E}\, ^1 \Sigma_g^+$ & $ \text{F}\,^1 \Sigma_g^+$& $\text{B}\, ^1 \Sigma_u^+$ & $\text{E}\, ^1 \Sigma_g^+$ & $ \text{F}\,^1 \Sigma_g^+$& $\text{B}\, ^1 \Sigma_u^+$ & $\text{E}\, ^1 \Sigma_g^+$ & $ \text{F}\,^1 \Sigma_g^+$\\
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\hline
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$0 .5$ & $14 .829$ & $15 .279$ & $28 .726$ & $17 .276$ & $13 .506$ & \
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$27 .846$ & $16 .208$ & $16 .026$ & $29 .398$ & $15 .703$ & $17 .126$ \
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& $29 .997$ \\
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$0 .6$ & $14 .057$ & $14 .694$ & $27 .528$ & $15 .523$ & $12 .674$ & \
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$26 .696$ & $14 .953$ & $15 .206$ & $28 .044$ & $14 .61$ & $16 .38$ & \
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$28 .608$ \\
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$0 .7$ & $13 .385$ & $14 .227$ & $26 .27$ & $13 .916$ & $11 .978$ & \
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$25 .396$ & $13 .759$ & $14 .469$ & $26 .668$ & $13 .621$ & $15 .76$ \
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& $27 .011$ \\
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$0 .8$ & $12 .784$ & $13 .849$ & $24 .801$ & $12 .469$ & $11 .414$ & \
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$23 .715$ & $12 .92$ & $13 .824$ & $25 .101$ & $12 .735$ & $15 .244$ \
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& $25 .114$ \\
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$0 .9$ & $12 .228$ & $13 .535$ & $22 .906$ & $11 .191$ & $10 .965$ & \
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$21 .235$ & $12 .141$ & $13 .284$ & $23 .004$ & $11 .938$ & $14 .808$ \
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& $22 .869$ \\
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$1.$ & $11 .71$ & $13 .273$ & $20 .834$ & $10 .086$ & $10 .617$ & $18 \
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.824$ & $11 .434$ & $12 .849$ & $20 .725$ & $11 .224$ & $14 .437$ & \
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$20 .591$ \\
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$1 .1$ & $11 .233$ & $13 .054$ & $18 .885$ & $9 .1444$ & $10 .353$ & \
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$16 .693$ & $10 .803$ & $12 .507$ & $18 .643$ & $10 .587$ & $14 .114$ \
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& $18 .502$ \\
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$1 .2$ & $10 .804$ & $12 .869$ & $17 .164$ & $8 .3499$ & $10 .155$ & \
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$14 .838$ & $10 .246$ & $12 .241$ & $16 .776$ & $10 .023$ & $13 .811$ \
|
|
& $16 .68$ \\
|
|
$1 .3$ & $10 .427$ & $12 .704$ & $15 .7$ & $7 .6792$ & $10 .003$ & \
|
|
$13 .233$ & $9 .7563$ & $12 .023$ & $15 .185$ & $9 .5306$ & $13 .456$ \
|
|
& $15 .2$ \\
|
|
$1 .4$ & $10 .106$ & $12 .526$ & $14 .516$ & $7 .1116$ & $9 .8732$ & \
|
|
$11 .863$ & $9 .3359$ & $11 .821$ & $13 .884$ & $9 .1076$ & $14 .241$ \
|
|
& $12 .853$ \\
|
|
$1 .5$ & $9 .8431$ & $12 .262$ & $13 .663$ & $6 .6301$ & $9 .7087$ & \
|
|
$10 .751$ & $8 .9836$ & $11 .554$ & $12 .889$ & $8 .7525$ & $13 .814$ \
|
|
& $11 .971$ \\
|
|
$1 .6$ & $9 .6364$ & $13 .198$ & $11 .831$ & $6 .2217$ & $10 .108$ & \
|
|
$9 .2661$ & $8 .6957$ & $12 .31$ & $11 .105$ & $8 .4631$ & $13 .606$ \
|
|
& $11 .096$ \\
|
|
$1 .7$ & $9 .4831$ & $13 .006$ & $11 .32$ & $5 .8767$ & $9 .9322$ & \
|
|
$8 .5243$ & $8 .4675$ & $12 .066$ & $10 .52$ & $8 .2361$ & $13 .475$ \
|
|
& $10 .347$ \\
|
|
$1 .8$ & $9 .3786$ & $12 .933$ & $10 .855$ & $5 .5871$ & $9 .8777$ & \
|
|
$7 .8097$ & $8 .2964$ & $11 .962$ & $9 .9678$ & $8 .0669$ & $13 .383$ \
|
|
& $9 .7387$ \\
|
|
$1 .9$ & $9 .3173$ & $12 .913$ & $10 .481$ & $5 .3465$ & $9 .862$ & \
|
|
$7 .1894$ & $8 .1749$ & $11 .916$ & $9 .5101$ & $7 .9505$ & $13 .317$ \
|
|
& $9 .2619$ \\
|
|
$2.$ & $9 .2934$ & $12 .922$ & $10 .197$ & $5 .1495$ & $9 .8671$ & $6 \
|
|
.6653$ & $8 .0991$ & $11 .902$ & $9 .152$ & $7 .881$ & $13 .272$ & $8 \
|
|
.9019$ \\
|
|
$2 .1$ & $9 .3009$ & $12 .943$ & $9 .9949$ & $4 .991$ & $9 .8815$ & \
|
|
$6 .2297$ & $8 .0645$ & $11 .903$ & $8 .8854$ & $7 .8523$ & $13 .239$ \
|
|
& $8 .642$ \\
|
|
$2 .2$ & $9 .3342$ & $12 .968$ & $9 .8615$ & $4 .8667$ & $9 .8946$ & \
|
|
$5 .8728$ & $8 .0632$ & $11 .908$ & $8 .6977$ & $7 .8581$ & $13 .212$ \
|
|
& $8 .4659$ \\
|
|
$2 .3$ & $9 .3878$ & $12 .988$ & $9 .7841$ & $4 .7722$ & $9 .9011$ & \
|
|
$5 .585$ & $8 .0893$ & $11 .911$ & $8 .5761$ & $7 .8923$ & $13 .187$ \
|
|
& $8 .3583$ \\
|
|
$2 .4$ & $9 .4572$ & $13 .005$ & $9 .7515$ & $4 .7034$ & $9 .9021$ & \
|
|
$5 .357$ & $8 .1373$ & $11 .915$ & $8 .5077$ & $7 .9492$ & $13 .164$ \
|
|
& $8 .3054$ \\
|
|
$2 .5$ & $9 .5384$ & $12 .987$ & $9 .7538$ & $4 .6565$ & $9 .9014$ & \
|
|
$5 .1798$ & $8 .2035$ & $11 .919$ & $8 .4827$ & $8 .0239$ & $13 .145$ \
|
|
& $8 .2956$ \\
|
|
$2 .6$ & $9 .6283$ & $12 .971$ & $9 .783$ & $4 .6277$ & $9 .9008$ & \
|
|
$5 .0451$ & $8 .2838$ & $11 .924$ & $8 .4919$ & $8 .1122$ & $13 .133$ \
|
|
& $8 .319$ \\
|
|
$2 .7$ & $9 .7245$ & $12 .968$ & $9 .8329$ & $4 .6139$ & $9 .8999$ & \
|
|
$4 .9458$ & $8 .3743$ & $11 .93$ & $8 .5274$ & $8 .2105$ & $13 .125$ \
|
|
& $8 .3677$ \\
|
|
$2 .8$ & $9 .825$ & $12 .972$ & $9 .8983$ & $4 .6124$ & $9 .8959$ & \
|
|
$4 .8758$ & $8 .473$ & $11 .933$ & $8 .5834$ & $8 .3162$ & $13 .12$ & \
|
|
$8 .4355$ \\
|
|
$2 .9$ & $9 .9281$ & $12 .979$ & $9 .9751$ & $4 .6208$ & $9 .8857$ & \
|
|
$4 .8292$ & $8 .5762$ & $11 .934$ & $8 .6537$ & $8 .4269$ & $13 .115$ \
|
|
& $8 .5173$ \\
|
|
$3.$ & $10 .033$ & $12 .986$ & $10 .06$ & $4 .6369$ & $9 .8666$ & $4 \
|
|
.8016$ & $8 .6819$ & $11 .93$ & $8 .7342$ & $8 .5408$ & $13 .106$ & \
|
|
$8 .6091$ \\
|
|
$3 .1$ & $10 .139$ & $12 .989$ & $10 .152$ & $4 .6592$ & $9 .8385$ & \
|
|
$4 .7891$ & $8 .7879$ & $11 .921$ & $8 .8214$ & $8 .6564$ & $13 .091$ \
|
|
& $8 .7079$ \\
|
|
$3 .2$ & $10 .244$ & $12 .987$ & $10 .247$ & $4 .6864$ & $9 .803$ & \
|
|
$4 .7887$ & $8 .8935$ & $11 .905$ & $8 .9133$ & $8 .7726$ & $13 .069$ \
|
|
& $8 .8112$ \\
|
|
$3 .3$ & $10 .345$ & $12 .979$ & $10 .35$ & $4 .7174$ & $9 .7627$ & \
|
|
$4 .7978$ & $8 .9983$ & $11 .884$ & $9 .0085$ & $8 .8884$ & $13 .041$ \
|
|
& $8 .9172$ \\
|
|
$3 .4$ & $10 .445$ & $12 .966$ & $10 .454$ & $4 .7512$ & $9 .7205$ & \
|
|
$4 .8144$ & $9 .1033$ & $11 .857$ & $9 .1066$ & $9 .003$ & $13 .008$ \
|
|
& $9 .0243$ \\
|
|
$3 .5$ & $10 .546$ & $12 .949$ & $10 .558$ & $4 .7873$ & $9 .679$ & \
|
|
$4 .8368$ & $9 .2059$ & $11 .829$ & $9 .2071$ & $9 .1159$ & $12 .972$ \
|
|
& $9 .1315$ \\
|
|
$3 .6$ & $10 .646$ & $12 .93$ & $10 .66$ & $4 .8249$ & $9 .64$ & $4 \
|
|
.8636$ & $9 .3055$ & $11 .8$ & $9 .3098$ & $9 .2265$ & $12 .935$ & $9 \
|
|
.2378$ \\
|
|
$3 .7$ & $10 .746$ & $12 .91$ & $10 .76$ & $4 .8635$ & $9 .6045$ & $4 \
|
|
.8937$ & $9 .4048$ & $11 .771$ & $9 .4109$ & $9 .3347$ & $12 .899$ & \
|
|
$9 .3427$ \\
|
|
$3 .8$ & $10 .845$ & $12 .889$ & $10 .859$ & $4 .9029$ & $9 .5734$ & \
|
|
$4 .9265$ & $9 .5033$ & $11 .743$ & $9 .5104$ & $9 .4401$ & $12 .863$ \
|
|
& $9 .4455$ \\
|
|
$3 .9$ & $10 .942$ & $12 .868$ & $10 .956$ & $4 .9425$ & $9 .5465$ & \
|
|
$4 .9609$ & $9 .6003$ & $11 .717$ & $9 .6078$ & $9 .5424$ & $12 .83$ \
|
|
& $9 .546$ \\
|
|
$4.$ & $11 .038$ & $12 .848$ & $11 .051$ & $4 .9822$ & $9 .5238$ & $4 \
|
|
.9964$ & $9 .6956$ & $11 .693$ & $9 .7031$ & $9 .6415$ & $12 .8$ & $9 \
|
|
.6437$ \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table*}
|
|
|
|
\begin{table*}
|
|
\caption{Expectation value of the spin operator $\expval{\hat{S}^2}$ of the $\text{B}\,{}^1\Sigma_u^+$, $\text{E}\,{}^1\Sigma_g^+$, and $\text{F}\,{}^1\Sigma_g^+$ states of \ce{H2} obtained with the cc-pVQZ basis at the SF-CIS, SF-TD-BH\&HLYP, SF-BSE@{\GOWO}, and EOM-CCSD levels of theory.
|
|
All the spin-conserved and spin-flip calculations have been performed with an unrestricted reference.}
|
|
\begin{ruledtabular}
|
|
\begin{tabular}{lrrrrrrrrrrrr}
|
|
&\mc{3}{c}{SF-CIS} & \mc{3}{c}{SF-BH\&HLYP} & \mc{3}{c}{SF-BSE@{\GOWO}}\\
|
|
\cline{2-4} \cline{5-7} \cline{8-10} \cline{11-13}
|
|
$R(\ce{H-H})$ (\AA) & $\text{B}\, ^1 \Sigma_u^+$& $\text{E}\, ^1 \Sigma_g^+$ & $ \text{F}\,^1 \Sigma_g^+$& $\text{B}\, ^1 \Sigma_u^+$ & $\text{E}\, ^1 \Sigma_g^+$ & $ \text{F}\,^1 \Sigma_g^+$& $\text{B}\, ^1 \Sigma_u^+$ & $\text{E}\, ^1 \Sigma_g^+$ & $ \text{F}\,^1 \Sigma_g^+$\\
|
|
\hline
|
|
$0 .5$ & $0 .0472$ & $0 .9825$ & $0 .987$ & $0 .8926$ & $0 .9746$ & \
|
|
$1.$ & $0 .1904$ & $0 .9774$ & $0 .9936$ \\
|
|
$0 .6$ & $0 .0735$ & $0 .9849$ & $0 .9664$ & $0 .8418$ & $0 .9734$ & \
|
|
$1.$ & $0 .0716$ & $0 .9778$ & $0 .9827$ \\
|
|
$0 .7$ & $0 .1058$ & $0 .9875$ & $0 .9001$ & $0 .7782$ & $0 .972$ & \
|
|
$0 .9251$ & $0 .1123$ & $0 .9785$ & $0 .9262$ \\
|
|
$0 .8$ & $0 .1373$ & $0 .99$ & $0 .7033$ & $0 .694$ & $0 .9707$ & $0 \
|
|
.4824$ & $0 .1382$ & $0 .9796$ & $0 .7122$ \\
|
|
$0 .9$ & $0 .1623$ & $0 .992$ & $0 .4176$ & $0 .5923$ & $0 .9694$ & \
|
|
$0 .1771$ & $0 .1602$ & $0 .981$ & $0 .3645$ \\
|
|
$1.$ & $0 .178$ & $0 .9932$ & $0 .2486$ & $0 .4851$ & $0 .9681$ & $0 \
|
|
.143$ & $0 .1736$ & $0 .9822$ & $0 .2031$ \\
|
|
$1 .1$ & $0 .1849$ & $0 .9928$ & $0 .1776$ & $0 .3875$ & $0 .9666$ & \
|
|
$0 .1412$ & $0 .1799$ & $0 .9827$ & $0 .1488$ \\
|
|
$1 .2$ & $0 .1853$ & $0 .9886$ & $0 .1528$ & $0 .3103$ & $0 .9645$ & \
|
|
$0 .1447$ & $0 .1785$ & $0 .9805$ & $0 .1316$ \\
|
|
$1 .3$ & $0 .1817$ & $0 .9731$ & $0 .1576$ & $0 .2555$ & $0 .9598$ & \
|
|
$0 .1509$ & $0 .1744$ & $0 .9708$ & $0 .1395$ \\
|
|
$1 .4$ & $0 .1763$ & $0 .9202$ & $0 .2082$ & $0 .2192$ & $0 .9432$ & \
|
|
$0 .1682$ & $0 .1689$ & $0 .9342$ & $0 .1753$ \\
|
|
$1 .5$ & $0 .1706$ & $0 .7566$ & $0 .3737$ & $0 .196$ & $0 .8475$ & \
|
|
$0 .2642$ & $0 .1639$ & $0 .7966$ & $0 .3175$ \\
|
|
$1 .6$ & $0 .1658$ & $0 .6399$ & $0 .4945$ & $0 .1816$ & $0 .6784$ & \
|
|
$0 .4335$ & $0 .1597$ & $0 .6174$ & $0 .5018$ \\
|
|
$1 .7$ & $0 .1623$ & $0 .807$ & $0 .3334$ & $0 .173$ & $0 .8802$ & $0 \
|
|
.2321$ & $0 .1571$ & $0 .8172$ & $0 .3083$ \\
|
|
$1 .8$ & $0 .1607$ & $0 .8814$ & $0 .2662$ & $0 .1684$ & $0 .9249$ & \
|
|
$0 .1883$ & $0 .1561$ & $0 .8959$ & $0 .237$ \\
|
|
$1 .9$ & $0 .161$ & $0 .9174$ & $0 .2381$ & $0 .1664$ & $0 .9409$ & \
|
|
$0 .174$ & $0 .1568$ & $0 .931$ & $0 .2097$ \\
|
|
$2.$ & $0 .1631$ & $0 .9371$ & $0 .2268$ & $0 .1662$ & $0 .9488$ & $0 \
|
|
.1683$ & $0 .1589$ & $0 .9493$ & $0 .1996$ \\
|
|
$2 .1$ & $0 .1669$ & $0 .9488$ & $0 .2234$ & $0 .1674$ & $0 .9535$ & \
|
|
$0 .1663$ & $0 .1624$ & $0 .9596$ & $0 .1973$ \\
|
|
$2 .2$ & $0 .1722$ & $0 .9561$ & $0 .2245$ & $0 .1695$ & $0 .9567$ & \
|
|
$0 .1663$ & $0 .1672$ & $0 .9661$ & $0 .1989$ \\
|
|
$2 .3$ & $0 .1788$ & $0 .9606$ & $0 .2281$ & $0 .1723$ & $0 .9589$ & \
|
|
$0 .1677$ & $0 .1731$ & $0 .9704$ & $0 .2027$ \\
|
|
$2 .4$ & $0 .1866$ & $0 .9633$ & $0 .2333$ & $0 .1754$ & $0 .9604$ & \
|
|
$0 .1698$ & $0 .1797$ & $0 .9729$ & $0 .2078$ \\
|
|
$2 .5$ & $0 .1953$ & $0 .9645$ & $0 .2397$ & $0 .1789$ & $0 .9614$ & \
|
|
$0 .1726$ & $0 .187$ & $0 .9741$ & $0 .2138$ \\
|
|
$2 .6$ & $0 .2047$ & $0 .9643$ & $0 .2468$ & $0 .1826$ & $0 .9619$ & \
|
|
$0 .1758$ & $0 .1947$ & $0 .974$ & $0 .2205$ \\
|
|
$2 .7$ & $0 .2145$ & $0 .9627$ & $0 .2544$ & $0 .1864$ & $0 .9619$ & \
|
|
$0 .1793$ & $0 .2028$ & $0 .9727$ & $0 .2277$ \\
|
|
$2 .8$ & $0 .2247$ & $0 .9596$ & $0 .2623$ & $0 .1902$ & $0 .9614$ & \
|
|
$0 .183$ & $0 .2113$ & $0 .9699$ & $0 .2353$ \\
|
|
$2 .9$ & $0 .2349$ & $0 .9553$ & $0 .2704$ & $0 .1939$ & $0 .9605$ & \
|
|
$0 .1867$ & $0 .2201$ & $0 .9656$ & $0 .2435$ \\
|
|
$3.$ & $0 .2451$ & $0 .9497$ & $0 .2783$ & $0 .1975$ & $0 .9593$ & $0 \
|
|
.1905$ & $0 .2293$ & $0 .96$ & $0 .2519$ \\
|
|
$3 .1$ & $0 .255$ & $0 .9431$ & $0 .286$ & $0 .201$ & $0 .9578$ & $0 \
|
|
.1942$ & $0 .2385$ & $0 .9538$ & $0 .2602$ \\
|
|
$3 .2$ & $0 .2646$ & $0 .936$ & $0 .2934$ & $0 .2042$ & $0 .956$ & $0 \
|
|
.1977$ & $0 .2475$ & $0 .9473$ & $0 .268$ \\
|
|
$3 .3$ & $0 .2737$ & $0 .9286$ & $0 .3003$ & $0 .2072$ & $0 .9542$ & \
|
|
$0 .2009$ & $0 .2558$ & $0 .941$ & $0 .2749$ \\
|
|
$3 .4$ & $0 .2822$ & $0 .9213$ & $0 .3068$ & $0 .2097$ & $0 .9523$ & \
|
|
$0 .2039$ & $0 .2634$ & $0 .935$ & $0 .2811$ \\
|
|
$3 .5$ & $0 .2901$ & $0 .9142$ & $0 .3127$ & $0 .2119$ & $0 .9505$ & \
|
|
$0 .2064$ & $0 .2701$ & $0 .9295$ & $0 .2864$ \\
|
|
$3 .6$ & $0 .2974$ & $0 .9075$ & $0 .318$ & $0 .2138$ & $0 .9489$ & \
|
|
$0 .2086$ & $0 .276$ & $0 .9246$ & $0 .2908$ \\
|
|
$3 .7$ & $0 .3039$ & $0 .9013$ & $0 .3226$ & $0 .2152$ & $0 .9475$ & \
|
|
$0 .2104$ & $0 .281$ & $0 .9203$ & $0 .2945$ \\
|
|
$3 .8$ & $0 .3096$ & $0 .8957$ & $0 .3267$ & $0 .2162$ & $0 .9464$ & \
|
|
$0 .2118$ & $0 .2852$ & $0 .9167$ & $0 .2973$ \\
|
|
$3 .9$ & $0 .3147$ & $0 .8908$ & $0 .3301$ & $0 .2169$ & $0 .9457$ & \
|
|
$0 .2129$ & $0 .2885$ & $0 .9139$ & $0 .2994$ \\
|
|
$4.$ & $0 .3189$ & $0 .8867$ & $0 .3328$ & $0 .2172$ & $0 .9453$ & $0 \
|
|
.2136$ & $0 .291$ & $0 .9119$ & $0 .3007$ \\
|
|
\end{tabular}
|
|
\end{ruledtabular}
|
|
\end{table*}
|
|
|
|
%%% FIG 2 %%%
|
|
\begin{figure*}
|
|
|
|
\includegraphics[width=0.45\linewidth]{H2_BLYP}
|
|
\hspace{0.05\linewidth}
|
|
\includegraphics[width=0.45\linewidth]{H2_B3LYP}
|
|
\vspace{0.025\linewidth}
|
|
\\
|
|
\includegraphics[width=0.45\linewidth]{H2_CAM_B3LYP}
|
|
\hspace{0.05\linewidth}
|
|
\includegraphics[width=0.45\linewidth]{H2_WB97X_D}
|
|
\vspace{0.025\linewidth}
|
|
\\
|
|
\includegraphics[width=0.45\linewidth]{H2_LC_wPBE08}
|
|
\hspace{0.05\linewidth}
|
|
\includegraphics[width=0.45\linewidth]{H2_dBSE}
|
|
\caption{
|
|
Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$ (red), $\text{E}\,{}^1\Sigma_g^+$ (black), and $\text{F}\,{}^1\Sigma_g^+$ (blue) states of \ce{H2} obtained with the cc-pVQZ basis at various levels of theory.
|
|
The reference EOM-CCSD excitation energies are represented as solid lines, while the results obtained with and without spin-flip are represented as dashed and dotted lines, respectively.
|
|
All the spin-conserved and spin-flip calculations have been performed with an unrestricted reference.
|
|
\label{fig:H2}}
|
|
\end{figure*}
|
|
%%% %%% %%%
|
|
|
|
%%% FIG 3 %%%
|
|
\begin{figure}
|
|
\includegraphics[width=0.5\linewidth]{H2_BSE_RHF}
|
|
\caption{
|
|
Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$ (red), $\text{E}\,{}^1\Sigma_g^+$ (black), and $\text{F}\,{}^1\Sigma_g^+$ (blue) states of \ce{H2} obtained with the cc-pVQZ basis at the (SF-)BSE level of theory.
|
|
The reference EOM-CCSD excitation energies are represented as solid lines, while the results obtained with and without spin-flip are represented as dashed and dotted lines, respectively.
|
|
In this case, the spin-conserved calculations have been performed with a restricted reference while the spin-flip calculations have been performed with an unrestricted reference.
|
|
\label{fig:H2_RHF}}
|
|
\end{figure}
|
|
%%% %%% %%%
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\bibliography{sfBSE}
|
|
%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
\end{document}
|