****************************************** * eDFT: density-functional for ensembles * ****************************************** ---------------------- Number of atoms 2 ---------------------- ---------------------- Number of spin-up electron 1 Number of spin-down electron 1 Total number of electron 2 ---------------------- ---------------------- Number of core electron 0 Number of Rydberg electron 0 ---------------------- ------------------ Molecular geometry ------------------ Atom n. 1 Z = 1.0000000000 Atom coordinates: 0.0000000000 0.0000000000 0.0000000000 Atom n. 2 Z = 1.0000000000 Atom coordinates: 0.0000000000 0.0000000000 1.4000000000 ------------------ Nuclear repulsion energy = 0.7142857143 ------------------ Gaussian basis set ------------------ Atom n. 1 number of shells 5 ------------------ s-type shell with K = 3 Exponents Contraction 13.0100000000 0.0196850000 1.9620000000 0.1379770000 0.4446000000 0.4781480000 s-type shell with K = 1 Exponents Contraction 0.1220000000 1.0000000000 s-type shell with K = 1 Exponents Contraction 0.0297400000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.7270000000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.1410000000 1.0000000000 ------------------ Atom n. 2 number of shells 5 ------------------ s-type shell with K = 3 Exponents Contraction 13.0100000000 0.0196850000 1.9620000000 0.1379770000 0.4446000000 0.4781480000 s-type shell with K = 1 Exponents Contraction 0.1220000000 1.0000000000 s-type shell with K = 1 Exponents Contraction 0.0297400000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.7270000000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.1410000000 1.0000000000 ------------------ Number of shells 10 ------------------ ------------------ Number of basis functions 18 ------------------ ---------------------------------------------------------- Number of states in ensemble = 2 ---------------------------------------------------------- ---------------------------------------------------------- Ensemble weights ---------------------------------------------------------- 1 1 0.52500000 2 0.47500000 Nuclear Coordinates (Angstrom) ------------------------------ ----------------------------------------------------------------------- Center Atomic Element Coordinates (Angstroms) Number X Y Z ----------------------------------------------------------------------- 1 1 H 0.000000 0.000000 0.000000 2 1 H 0.000000 0.000000 0.740848 ----------------------------------------------------------------------- Nuclear repulsion : 0.714285662548 Atomic Basis set ---------------- ----------------------------------------------------------------------- # Angular Coordinates (Bohr) Exponents Coefficients Momentum X Y Z ----------------------------------------------------------------------- 1-3 S 0.0000 0.0000 0.0000 1.30100000e+01 1.96850000e-02 1.96200000e+00 1.37977000e-01 4.44600000e-01 4.78148000e-01 1.22000000e-01 1.00000000e+00 2.97400000e-02 1.00000000e+00 ----------------------------------------------------------------------- 4-9 P 0.0000 0.0000 0.0000 7.27000000e-01 1.00000000e+00 1.41000000e-01 1.00000000e+00 ----------------------------------------------------------------------- 10-12 S 0.0000 0.0000 1.4000 1.30100000e+01 1.96850000e-02 1.96200000e+00 1.37977000e-01 4.44600000e-01 4.78148000e-01 1.22000000e-01 1.00000000e+00 2.97400000e-02 1.00000000e+00 ----------------------------------------------------------------------- 13-18 P 0.0000 0.0000 1.4000 7.27000000e-01 1.00000000e+00 1.41000000e-01 1.00000000e+00 ----------------------------------------------------------------------- 55 significant shell pairs computed in 0.001166 seconds 1 2 3 6 9 10 11 12 15 Computed ERIs in 0.025577 seconds Scaling integrals by 1.0000000000000000 Total CPU time for reading integrals = 0.012 seconds Lowdin orthogonalization ---------------------------------------------------------- Quadrature grid: SG-1 ---------------------------------------------------------- Radial precision = 0.1E-06 Number of radial points = 74 Number of angular points = 194 Total number of points = 14356 ************************************************ * Restricted Kohn-Sham calculation * * *** for ensembles *** * ************************************************ ******************************************************************* * EXCHANGE RUNG * ******************************************************************* * 1st rung of Jacob's ladder: local-density approximation (LDA) * * You have selected the following functional: RMFL20 * ******************************************************************* ******************************************************************* * CORRELATION RUNG * ******************************************************************* * 1st rung of Jacob's ladder: local-density approximation (LDA) * * You have selected the following functional: RMFL20 * ******************************************************************* ------------------------------------------------------------------------------------------ | # | E(KS) | Ex(KS) | Ec(KS) | Conv | nEl | ------------------------------------------------------------------------------------------ | 1 | 2.7771679351 | -0.6072232123 | -0.0585261396 | 0.085221 | 2.000006 | | 2 | -0.7417607085 | -0.4509353600 | -0.0537470748 | 0.030318 | 2.000000 | | 3 | -0.7454073099 | -0.4888936071 | -0.0556531748 | 0.004898 | 2.000001 | | 4 | -0.7457260874 | -0.4774748785 | -0.0550028219 | 0.001246 | 2.000001 | | 5 | -0.7457394148 | -0.4792859159 | -0.0550993053 | 0.000064 | 2.000001 | | 6 | -0.7457394580 | -0.4793817301 | -0.0551040580 | 0.000002 | 2.000001 | ------------------------------------------------------------------------------------------ ------------------------------------------------- Summary ------------------------------------------------- One-electron energy: -1.8473658364 au Kinetic energy: 1.0340842049 au Potential energy: -2.8814500413 au ------------------------------------------------- Two-electron energy: 0.3873406640 au Coulomb energy: 0.9218264521 au Exchange energy: -0.4793817301 au Correlation energy: -0.0551040580 au ------------------------------------------------- Electronic energy: -1.4600251723 au Nuclear repulsion: 0.7142857143 au Kohn-Sham energy: -0.7457394580 au ------------------------------------------------- KS HOMO energy: -16.265960 eV KS LUMO energy: -2.215450 eV KS HOMO-LUMO gap: 14.050511 eV ------------------------------------------------- ----------------------------------------- Kohn-Sham orbital coefficients ----------------------------------------- 1 2 3 4 5 1 -0.78855732 0.49057462 0.24804846 0.40464539 0.00000000 2 -0.10850575 0.84181128 0.12958804 4.43472193 0.00000000 3 -0.00407695 1.65050026 -0.59034269 -4.87333410 0.00000000 4 0.00000000 0.00000000 0.00000000 0.00000000 0.04571996 5 0.00000000 0.00000000 0.00000000 0.00000000 0.00298263 6 -0.03181204 -0.04203849 0.01854480 -0.04644085 0.00000000 7 0.00000000 0.00000000 0.00000000 0.00000000 0.49416518 8 0.00000000 0.00000000 0.00000000 0.00000000 0.03223779 9 0.01221495 -0.07316510 0.06878046 0.76568051 0.00000000 10 -0.78855913 -0.49057236 0.24805281 -0.40464361 0.00000000 11 -0.10850413 -0.84181171 0.12960076 -4.43472281 0.00000000 12 -0.00407698 -1.65050250 -0.59034656 4.87333322 0.00000000 13 0.00000000 0.00000000 0.00000000 0.00000000 0.04572020 14 0.00000000 0.00000000 0.00000000 0.00000000 0.00298264 15 0.03181186 -0.04203889 -0.01854438 -0.04644116 0.00000000 16 0.00000000 0.00000000 0.00000000 0.00000000 0.49416958 17 0.00000000 0.00000000 0.00000000 0.00000000 0.03223808 18 -0.01221570 -0.07316766 -0.06878152 0.76567898 0.00000000 6 7 8 9 10 1 0.00000000 0.39763764 0.00000000 0.00000000 -0.63556236 2 0.00000000 -0.94281403 0.00000000 0.00000000 28.48188807 3 0.00000000 0.51550411 0.00000000 0.00000000 -3.21963806 4 -0.00298263 0.00000000 -0.00261088 0.00064085 0.00000000 5 0.04571996 0.00000000 0.00064085 0.00261088 0.00000000 6 0.00000000 0.02312194 0.00000000 0.00000000 -0.00484336 7 -0.03223779 0.00000000 1.91351139 -0.46968098 0.00000000 8 0.49416518 0.00000000 -0.46968098 -1.91351139 0.00000000 9 0.00000000 1.13215602 0.00000000 0.00000000 7.04863016 10 0.00000000 0.39764115 0.00000000 0.00000000 0.63556530 11 0.00000000 -0.94279260 0.00000000 0.00000000 -28.48188950 12 0.00000000 0.51550039 0.00000000 0.00000000 3.21963868 13 -0.00298264 0.00000000 0.00261095 -0.00064087 0.00000000 14 0.04572020 0.00000000 -0.00064087 -0.00261095 0.00000000 15 0.00000000 -0.02312161 0.00000000 0.00000000 -0.00484303 16 -0.03223808 0.00000000 -1.91351026 0.46968070 0.00000000 17 0.49416958 0.00000000 0.46968070 1.91351026 0.00000000 18 0.00000000 -1.13216119 0.00000000 0.00000000 7.04863308 11 12 13 14 15 1 -1.28190545 1.60131936 0.00000000 0.00000000 0.72572061 2 0.58228713 26.85452088 0.00000000 0.00000000 -0.43602695 3 -0.20219431 -0.85387590 0.00000000 0.00000000 0.15440490 4 0.00000000 0.00000000 0.11598635 -0.65798125 0.00000000 5 0.00000000 0.00000000 0.65798125 0.11598635 0.00000000 6 -0.01827337 -0.41012647 0.00000000 0.00000000 -0.76257283 7 0.00000000 0.00000000 -0.05810749 0.32963914 0.00000000 8 0.00000000 0.00000000 -0.32963914 -0.05810749 0.00000000 9 1.07027172 7.55466969 0.00000000 0.00000000 0.48954260 10 -1.28190440 -1.60131855 0.00000000 0.00000000 0.72571655 11 0.58220342 -26.85452168 0.00000000 0.00000000 -0.43602624 12 -0.20218452 0.85387622 0.00000000 0.00000000 0.15440448 13 0.00000000 0.00000000 0.11598660 -0.65798266 0.00000000 14 0.00000000 0.00000000 0.65798266 0.11598660 0.00000000 15 0.01827320 -0.41012696 0.00000000 0.00000000 0.76257385 16 0.00000000 0.00000000 -0.05810769 0.32964027 0.00000000 17 0.00000000 0.00000000 -0.32964027 -0.05810769 0.00000000 18 -1.07025053 7.55466938 0.00000000 0.00000000 -0.48954254 16 17 18 1 0.00000000 0.00000000 -4.38250638 2 0.00000000 0.00000000 8.44919356 3 0.00000000 0.00000000 -0.46462382 4 -1.06344790 0.11182668 0.00000000 5 0.11182668 1.06344790 0.00000000 6 0.00000000 0.00000000 -2.17168034 7 0.79095359 -0.08317259 0.00000000 8 -0.08317259 -0.79095359 0.00000000 9 0.00000000 0.00000000 2.29754542 10 0.00000000 0.00000000 4.38250675 11 0.00000000 0.00000000 -8.44919374 12 0.00000000 0.00000000 0.46462388 13 1.06344701 -0.11182659 0.00000000 14 -0.11182659 -1.06344701 0.00000000 15 0.00000000 0.00000000 -2.17167989 16 -0.79095326 0.08317255 0.00000000 17 0.08317255 0.79095326 0.00000000 18 0.00000000 0.00000000 2.29754523 --------------------------------------- Kohn-Sham orbital energies --------------------------------------- 1 1 -0.59776302 2 -0.08141628 3 -0.02731527 4 0.04104005 5 0.06047363 6 0.06047363 7 0.21437472 8 0.26489940 9 0.26489940 10 0.34397272 11 0.41917012 12 0.83854365 13 1.11556050 14 1.11556050 15 1.55789132 16 1.74194941 17 1.74194941 18 3.10557702 ------------------------------------------------- ENSEMBLE ENERGIES ------------------------------------------------- Ensemble energy: -0.7457394580 au GIC Ensemble energy: -0.6253491449 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL KINETIC ENERGIES ------------------------------------------------- Kinetic energy state 1: 1.2960194064 au Kinetic energy state 2: 0.7445768771 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL POTENTIAL ENERGIES ------------------------------------------------- Potential energy state 1: -3.8412682143 au Potential energy state 2: -1.8205983764 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL HARTREE ENERGIES ------------------------------------------------- Hartree energy state 1: 1.4341473802 au Hartree energy state 2: 0.6093529250 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL EXCHANGE ENERGIES ------------------------------------------------- Exchange energy state 1: -0.6670384301 au Exchange energy state 2: -0.2719716934 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL CORRELATION ENERGIES ------------------------------------------------- Correlation energy state 1: -0.0635449565 au Correlation energy state 2: -0.0460972727 au ------------------------------------------------- ------------------------------------------------- ENSEMBLE DERIVATIVE CONTRIBUTIONS ------------------------------------------------- x ensemble derivative state 1: 0.0627303806 au c ensemble derivative state 1: -0.0032393465 au xc ensemble derivative state 1: 0.0594910341 au x ensemble derivative state 2: -0.0693335786 au c ensemble derivative state 2: 0.0035803303 au xc ensemble derivative state 2: -0.0657532482 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL AND EXCITATION ENERGIES ------------------------------------------------- Individual energy state 1: -1.0679080659 au Individual energy state 2: -0.1362050743 au ------------------------------------------------- Excitation energy 1 -> 2: 0.9317029916 au x energy contribution : 0.3950667367 au c energy contribution : 0.0174476838 au xc energy contribution : 0.4125144205 au x ensemble derivative : -0.1320639592 au c ensemble derivative : 0.0068196769 au xc ensemble derivative : -0.1252442823 au ------------------------------------------------- Excitation energy 1 -> 2: 25.3529297608 eV x energy contribution : 10.7503134759 eV c energy contribution : 0.4747756590 eV xc energy contribution : 11.2250891350 eV x ensemble derivative : -3.5936433722 eV c ensemble derivative : 0.1855728595 eV xc ensemble derivative : -3.4080705127 eV ------------------------------------------------- Total CPU time for GOC-RKS = 7.425 seconds