15 significant shell pairs computed in 0.000024 seconds 0 Computed Electron repulsion integrals Integrals in parallel in 0.006196 seconds ****************************************************************************************** * QuAcK QuAcK QuAcK * * __ __ __ __ __ __ __ __ __ * * <(o )___ <(o )___ <(o )___ <(o )___ <(o )___ <(o )___ <(o )___ <(o )___ <(o )___ * * ( ._> / ( ._> / ( ._> / ( ._> / ( ._> / ( ._> / ( ._> / ( ._> / ( ._> / * *|--------------------------------------------------------------------------------------|* ****************************************************************************************** ---------------------- Number of atoms 1 ---------------------- ---------------------- Number of spin-up electron 3 Number of spin-down electron 1 Total number of electron 4 ---------------------- ---------------------- Number of core electron 0 Number of Rydberg electron 0 ---------------------- ------------------ Molecular geometry ------------------ Atom n. 1 Z = 4.0000000000 Atom coordinates: 0.0000000000 0.0000000000 0.0000000000 ------------------ Nuclear repulsion energy = 0.0000000000 ------------------ Gaussian basis set ------------------ Atom n. 1 number of shells 5 ------------------ s-type shell with K = 6 Exponents Contraction 1264.5856900000 0.0019447576 189.9368060000 0.0148350520 43.1590890000 0.0720905463 12.0986627000 0.2371541500 3.8063232200 0.4691986519 1.2728903000 0.3565202279 s-type shell with K = 3 Exponents Contraction 3.1964630980 -0.1126487285 0.7478133038 -0.2295064079 0.2199663302 1.1869167640 s-type shell with K = 1 Exponents Contraction 0.0823099007 1.0000000000 p-type shell with K = 3 Exponents Contraction 3.1964630980 0.0559801998 0.7478133038 0.2615506110 0.2199663302 0.7939723389 p-type shell with K = 1 Exponents Contraction 0.0823099007 1.0000000000 ------------------ Number of shells 5 ------------------ ------------------ Number of basis functions 9 ------------------ Scaling integrals by 1.0000000000000000 Total CPU time for reading integrals = 0.001 seconds Lowdin orthogonalization ************************************************ * Unrestricted Hartree-Fock calculation * ************************************************ ---------------------------------------------------------- | # | E(UHF) | Ex(UHF) | Conv | ---------------------------------------------------------- | 1 | -9.9721029045 | -2.0953566404 | 1.000000 | | 2 | -14.4210226712 | -2.8785772874 | 0.098608 | | 3 | -14.4953149355 | -2.7893548498 | 0.042250 | | 4 | -14.5050033288 | -2.7581278709 | 0.016759 | | 5 | -14.5063217114 | -2.7475342080 | 0.006660 | | 6 | -14.5065144688 | -2.7437993990 | 0.002675 | | 7 | -14.5065445914 | -2.7424416130 | 0.001086 | | 8 | -14.5065495355 | -2.7419354626 | 0.000444 | | 9 | -14.5065503733 | -2.7417426132 | 0.000183 | | 10 | -14.5065505181 | -2.7416677103 | 0.000076 | | 11 | -14.5065505434 | -2.7416381324 | 0.000032 | | 12 | -14.5065505478 | -2.7416262892 | 0.000013 | | 13 | -14.5065505486 | -2.7416214930 | 0.000006 | | 14 | -14.5065505487 | -2.7416195330 | 0.000002 | | 15 | -14.5065505488 | -2.7416187262 | 0.000001 | | 16 | -14.5065505488 | -2.7416183923 | 0.000000 | | 17 | -14.5065505488 | -2.7416182535 | 0.000000 | | 18 | -14.5065505488 | -2.7416181957 | 0.000000 | ---------------------------------------------------------- ------------------------------------------------- Summary ------------------------------------------------- One-electron energy: -18.9311389165 au One-electron a energy: -10.9912119933 au One-electron b energy: -7.9399269232 au Kinetic energy: 14.5581042628 au Kinetic a energy: 7.7845610378 au Kinetic b energy: 6.7735432250 au Potential energy: -33.4892431793 au Potential a energy: -18.7757730311 au Potential b energy: -14.7134701482 au ------------------------------------------------- Two-electron energy: 4.4245883678 au Two-electron aa energy: 1.1932336284 au Two-electron ab energy: 3.2313547394 au Two-electron bb energy: 0.0000000000 au Coulomb energy: 7.1662065635 au Coulomb aa energy: 2.7997526399 au Coulomb ab energy: 3.2313547394 au Coulomb bb energy: 1.1350991842 au Exchange energy: -2.7416181957 au Exchange a energy: -1.6065190115 au Exchange b energy: -1.1350991842 au ------------------------------------------------- Electronic energy: -14.5065505488 au Nuclear repulsion: 0.0000000000 au UHF energy: -14.5065505488 au ------------------------------------------------- UHF HOMO a energy: -6.448889 eV UHF LUMO a energy: 1.306653 eV UHF HOMOa-LUMOa gap: 7.755542 eV ------------------------------------------------- UHF HOMO b energy: -128.126772 eV UHF LUMO b energy: 0.905889 eV UHF HOMOb-LUMOb gap : 129.032661 eV ------------------------------------------------- S (exact) : 3.000000 S : 3.000000 (exact) : 2.000000 : 2.000000 ------------------------------------------------- Dipole moment (Debye) X Y Z Tot. 0.000000 0.000000 0.000000 0.000000 ------------------------------------------------- ----------------------------------------- UHF spin-up orbital coefficients ----------------------------------------- 1 2 3 4 5 1 0.99757840 0.22433488 0.00000000 0.00000000 0.00000000 2 0.01808137 -0.35232016 0.00000000 0.00000000 0.00000000 3 -0.00536995 -0.70063722 0.00000000 0.00000000 0.00000000 4 0.00000000 0.00000000 -0.53634002 -0.01964709 0.03642320 5 0.00000000 0.00000000 0.00000000 0.27808757 0.15000360 6 0.00000000 0.00000000 0.07085886 -0.14871138 0.27569194 7 0.00000000 0.00000000 -0.54886156 -0.04729676 0.08768216 8 0.00000000 0.00000000 0.00000000 0.66944480 0.36110615 9 0.00000000 0.00000000 0.07251316 -0.35799535 0.66367777 6 7 8 9 1 0.00000000 -0.00978671 0.00000000 0.00000000 2 0.00000000 -2.00710393 0.00000000 0.00000000 3 0.00000000 1.92140976 0.00000000 0.00000000 4 1.22142423 0.00000000 0.01122086 0.17094564 5 0.00000000 0.00000000 1.30515347 -0.08567021 6 -0.16136914 0.00000000 0.08493219 1.29391003 7 -1.21584899 0.00000000 -0.00952235 -0.14506949 8 0.00000000 0.00000000 -1.10759159 0.07270226 9 0.16063256 0.00000000 -0.07207595 -1.09805008 ----------------------------------------- UHF spin-down orbital coefficients ----------------------------------------- 1 2 3 4 5 1 0.99781793 -0.22129021 0.00000000 0.00000000 0.00000000 2 0.01770722 -0.02073430 0.00000000 0.00000000 0.00000000 3 -0.00612257 1.04026501 0.00000000 0.00000000 0.00000000 4 0.00000000 0.00000000 -0.01285725 0.02043569 0.14863214 5 0.00000000 0.00000000 0.15602453 0.09816389 0.00000000 6 0.00000000 0.00000000 -0.09731824 0.15468043 -0.01963662 7 0.00000000 0.00000000 -0.06048857 0.09614229 0.88576256 8 0.00000000 0.00000000 0.73403704 0.46182436 0.00000000 9 0.00000000 0.00000000 -0.45784591 0.72771357 -0.11702302 6 7 8 9 1 0.00000000 0.00000000 0.03121871 0.00000000 2 0.00000000 0.00000000 -2.03768966 0.00000000 3 0.00000000 0.00000000 1.76083731 0.00000000 4 -0.00959284 0.17431589 0.00000000 -1.32568709 5 -1.33088497 -0.07324037 0.00000000 0.00000000 6 -0.07260943 1.31941986 0.00000000 0.17514389 7 0.00740452 -0.13455091 0.00000000 0.99747805 8 1.02728315 0.05653276 0.00000000 0.00000000 9 0.05604575 -1.01843347 0.00000000 -0.13178237 --------------------------------------- UHF spin-up orbital energies --------------------------------------- 1 1 -4.74712616 2 -0.38927141 3 -0.23699229 4 0.04801863 5 0.04801863 6 0.39370428 7 0.40988920 8 0.43513796 9 0.43513796 --------------------------------------- UHF spin-down orbital energies --------------------------------------- 1 1 -4.70857207 2 0.03329080 3 0.12673661 4 0.12673661 5 0.15961124 6 0.47922281 7 0.47922281 8 0.49186357 9 0.51235955 Total CPU time for UHF = 0.001 seconds AO to MO transformation... Please be patient Total CPU time for AO to MO transformation = 0.001 seconds ************************************************ | One-shot G0W0 calculation | | *** Unrestricted version *** | ************************************************ Tamm-Dancoff approximation activated! ------------------------------------------------------------- RPA@UHF calculation: spin-conserved manifold ------------------------------------------------------------- | State | Excitation energy (au) | Excitation energy (eV) | ------------------------------------------------------------- | 1 | 0.301673 | 8.208931 | | 2 | 0.301673 | 8.208931 | | 3 | 0.495256 | 13.476595 | | 4 | 0.495256 | 13.476595 | | 5 | 0.664016 | 18.068786 | | 6 | 0.678515 | 18.463337 | | 7 | 0.681585 | 18.546884 | | 8 | 0.681585 | 18.546884 | | 9 | 0.806855 | 21.955648 | | 10 | 0.855869 | 23.289381 | | 11 | 0.856160 | 23.297299 | | 12 | 0.856160 | 23.297299 | | 13 | 4.760931 | 129.551529 | | 14 | 4.798555 | 130.575320 | | 15 | 4.798555 | 130.575320 | | 16 | 4.837455 | 131.633855 | | 17 | 4.837455 | 131.633855 | | 18 | 4.869807 | 132.514190 | | 19 | 5.156163 | 140.306330 | | 20 | 5.167652 | 140.618962 | ------------------------------------------------------------- *** Quasiparticle energies obtained by linearization *** -------------------------------------------------------------------------------------------------------------------------------- Unrestricted one-shot G0W0 calculation (eV) -------------------------------------------------------------------------------------------------------------------------------- | | e_HF | Sig_c | Z | e_QP | | #| up dw | up dw | up dw | up dw | -------------------------------------------------------------------------------------------------------------------------------- | 1| -129.175882 -128.126772| 2.972974 2.868076| 0.892301 0.897159| -126.523094 -125.553653| | 2| -10.592615 0.905889| 0.016891 -0.741062| 0.969734 0.965457| -10.576234 0.190425| | 3| -6.448889 3.448679| 0.168181 -0.447188| 0.979999 0.970408| -6.284072 3.014724| | 4| 1.306653 3.448679| -0.110841 -0.447188| 0.984833 0.970408| 1.197494 3.014724| | 5| 1.306653 4.343243| -0.110841 -0.262704| 0.984833 0.985031| 1.197494 4.084472| | 6| 10.713239 13.040317| -0.220768 -1.209004| 0.978456 0.791743| 10.497227 12.083096| | 7| 11.153653 13.040317| -0.418786 -1.209004| 0.966367 0.791743| 10.748952 12.083096| | 8| 11.840707 13.384290| -0.818342 -1.142127| 0.945109 0.916762| 11.067284 12.337231| | 9| 11.840707 13.942014| -0.818342 -1.085519| 0.945109 0.926119| 11.067284 12.936694| -------------------------------------------------------------------------------------------------------------------------------- G0W0 HOMO energy (eV): -6.284072 G0W0 LUMO energy (eV): 0.190425 G0W0 HOMO-LUMO gap (eV): 6.474497 -------------------------------------------------------------------------------------------------------------------------------- RPA@G0W0 total energy = -14.518568 RPA@G0W0 correlation energy = -0.012018 -------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------- BSE@UGW calculation: spin-flip manifold ------------------------------------------------------------- | State | Excitation energy (au) | Excitation energy (eV) | ------------------------------------------------------------- | 1 | -0.084532 | -2.300242 | | 2 | 0.003653 | 0.099402 | | 3 | 0.068619 | 1.867213 | | 4 | 0.068619 | 1.867213 | | 5 | 0.143001 | 3.891249 | | 6 | 0.201811 | 5.491558 | | 7 | 0.201811 | 5.491558 | | 8 | 0.259908 | 7.072443 | | 9 | 0.365209 | 9.937851 | | 10 | 0.377346 | 10.268119 | | 11 | 0.380302 | 10.348538 | | 12 | 0.380302 | 10.348538 | | 13 | 0.514626 | 14.003674 | | 14 | 0.514626 | 14.003674 | | 15 | 0.560391 | 15.249025 | | 16 | 0.564795 | 15.368849 | | 17 | 4.226223 | 115.001373 | | 18 | 4.242892 | 115.454980 | | 19 | 4.242892 | 115.454980 | | 20 | 4.367893 | 118.856432 | ------------------------------------------------------------- ------------------------------------------------------------- Excitation n. 1: -2.300242 eV f = 0.0000 = 0.0037 ------------------------------------------------------------- 2A -> 5B = 0.195866 3A -> 2B = 0.970045 3A -> 8B = -0.120588 ------------------------------------------------------------- Excitation n. 2: 0.099402 eV f = 0.0000 = 1.9985 ------------------------------------------------------------- 2A -> 2B = 0.707214 2A -> 8B = -0.106883 3A -> 5B = 0.674487 3A -> 9B = -0.183005 ------------------------------------------------------------- Excitation n. 3: 1.867213 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 3A -> 3B = 0.381148 3A -> 4B = -0.908506 3A -> 7B = -0.167192 ------------------------------------------------------------- Excitation n. 4: 1.867213 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 3A -> 3B = -0.908506 3A -> 4B = -0.381148 3A -> 6B = 0.167192 ------------------------------------------------------------- Excitation n. 5: 3.891249 eV f = 0.0000 = 0.0234 ------------------------------------------------------------- 2A -> 2B = -0.686629 3A -> 5B = 0.717296 ------------------------------------------------------------- Excitation n. 6: 5.491558 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 2A -> 3B = -0.976791 2A -> 6B = 0.163785 2A -> 7B = 0.128946 ------------------------------------------------------------- Excitation n. 7: 5.491558 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 2A -> 4B = -0.976791 2A -> 6B = 0.128946 2A -> 7B = -0.163785 ------------------------------------------------------------- Excitation n. 8: 7.072443 eV f = 0.0000 = 0.0133 ------------------------------------------------------------- 2A -> 5B = -0.958868 2A -> 9B = 0.190086 3A -> 2B = 0.210445 ------------------------------------------------------------- Excitation n. 9: 9.937851 eV f = 0.0000 = 0.9834 ------------------------------------------------------------- 2A -> 2B = 0.125265 2A -> 8B = 0.287586 3A -> 5B = 0.167806 3A -> 9B = 0.934578 ------------------------------------------------------------- Excitation n. 10: 10.268119 eV f = 0.0000 = 0.9972 ------------------------------------------------------------- 2A -> 9B = 0.305560 3A -> 2B = 0.121316 3A -> 8B = 0.939179 ------------------------------------------------------------- Excitation n. 11: 10.348538 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 3A -> 3B = -0.140210 3A -> 6B = -0.985209 ------------------------------------------------------------- Excitation n. 12: 10.348538 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 3A -> 4B = 0.140210 3A -> 7B = -0.985209 ------------------------------------------------------------- Excitation n. 13: 14.003674 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 2A -> 3B = 0.166773 2A -> 4B = 0.125060 2A -> 6B = 0.977677 ------------------------------------------------------------- Excitation n. 14: 14.003674 eV f = 0.0000 = 1.0000 ------------------------------------------------------------- 2A -> 3B = 0.125060 2A -> 4B = -0.166773 2A -> 7B = 0.977677 ------------------------------------------------------------- Excitation n. 15: 15.249025 eV f = 0.0000 = 0.9948 ------------------------------------------------------------- 2A -> 2B = -0.112678 2A -> 8B = -0.946739 3A -> 9B = 0.297646 ------------------------------------------------------------- Excitation n. 16: 15.368849 eV f = 0.0000 = 0.9857 ------------------------------------------------------------- 2A -> 5B = -0.179874 2A -> 9B = -0.929728 3A -> 8B = 0.321310 ------------------------------------------------------------- Excitation n. 17: 115.001373 eV f = 0.0000 = 1.0172 ------------------------------------------------------------- 1A -> 2B = -0.950651 1A -> 8B = 0.310233 ------------------------------------------------------------- Excitation n. 18: 115.454980 eV f = 0.0000 = 2.0000 ------------------------------------------------------------- 1A -> 4B = -0.679768 1A -> 5B = 0.568999 1A -> 8B = -0.142778 1A -> 9B = 0.440193 ------------------------------------------------------------- Excitation n. 19: 115.454980 eV f = 0.0000 = 2.0000 ------------------------------------------------------------- 1A -> 4B = -0.568999 1A -> 5B = -0.679768 1A -> 8B = -0.440193 1A -> 9B = -0.142778 ------------------------------------------------------------- Excitation n. 20: 118.856432 eV f = 0.0000 = 2.0000 ------------------------------------------------------------- 1A -> 3B = 0.621799 1A -> 4B = -0.570321 1A -> 6B = -0.112937 1A -> 7B = -0.524731 Thomas-Reiche-Kuhn sum rule = 0.000000 *** dynamical TDA activated *** --------------------------------------------------------------------------------------------------- First-order dynamical correction to static Bethe-Salpeter excitation energies --------------------------------------------------------------------------------------------------- BSE neutral excitation must be lower than the GW gap = 6.474497 eV --------------------------------------------------------------------------------------------------- # Static (eV) Dynamic (eV) Correction (eV) Renorm. (eV) --------------------------------------------------------------------------------------------------- 1 -2.300242 -2.514146 -0.213904 1.014404 2 0.099402 -0.151189 -0.250591 1.013468 3 1.867213 1.723326 -0.143887 1.011906 4 1.867213 1.723326 -0.143887 1.011906 5 3.891249 3.748669 -0.142581 1.013889 6 5.491558 5.310106 -0.181452 1.013155 7 5.491558 5.310106 -0.181452 1.013155 8 7.072443 6.910211 -0.162232 1.013494 9 9.937851 9.695362 -0.242489 1.014455 10 10.268119 10.083710 -0.184410 1.010499 --------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------- Tr@BSE@UG0W0 correlation energy (spin-conserved) = 0.0000000000 Tr@BSE@UG0W0 correlation energy (spin-flip) = 0.0000000000 Tr@BSE@UG0W0 correlation energy = 0.0000000000 Tr@BSE@UG0W0 total energy = -14.5065505488 ------------------------------------------------------------------------------- Total CPU time for G0W0 = 0.003 seconds Total CPU time for QuAcK = 0.006 seconds