****************************************** * 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 0.95000000 2 0.05000000 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 0.001704 seconds 1 2 3 6 9 10 11 12 15 Computed ERIs in 0.024170 seconds Scaling integrals by 1.0000000000000000 Total CPU time for reading integrals = 0.017 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 | 4.9796953024 | -0.9052441027 | -0.1074176568 | 0.108413 | 2.000010 | | 2 | -1.0539100159 | -0.4556861286 | -0.0812134436 | 0.128950 | 2.000000 | | 3 | -1.0791916095 | -0.4865145121 | -0.0837974112 | 0.086362 | 2.000001 | | 4 | -1.0984519790 | -0.5438221251 | -0.0883471570 | 0.002098 | 2.000001 | | 5 | -1.0984694975 | -0.5457012374 | -0.0885007153 | 0.000152 | 2.000001 | | 6 | -1.0984695395 | -0.5456163662 | -0.0884944331 | 0.000002 | 2.000001 | ------------------------------------------------------------------------------------------ ------------------------------------------------- Summary ------------------------------------------------- One-electron energy: -2.4164284676 au Kinetic energy: 1.0636104254 au Potential energy: -3.4800388930 au ------------------------------------------------- Two-electron energy: 0.6036732138 au Coulomb energy: 1.2377840131 au Exchange energy: -0.5456163662 au Correlation energy: -0.0884944331 au ------------------------------------------------- Electronic energy: -1.8127552538 au Nuclear repulsion: 0.7142857143 au Kohn-Sham energy: -1.0984695395 au ------------------------------------------------- KS HOMO energy: -11.008721 eV KS LUMO energy: -0.279096 eV KS HOMO-LUMO gap: 10.729625 eV ------------------------------------------------- ----------------------------------------- Kohn-Sham orbital coefficients ----------------------------------------- 1 2 3 4 5 1 -0.70125910 0.24287826 0.20471020 -0.39588279 0.00000000 2 -0.16233994 -0.47585486 0.25222286 -6.89696304 0.00000000 3 -0.01192629 3.29316907 -0.64569892 4.22667578 0.00000000 4 0.00000000 0.00000000 0.00000000 0.00000000 0.01933609 5 0.00000000 0.00000000 0.00000000 0.00000000 0.00150683 6 -0.01903356 -0.01975064 0.01401485 0.05330334 0.00000000 7 0.00000000 0.00000000 0.00000000 0.00000000 0.50651522 8 0.00000000 0.00000000 0.00000000 0.00000000 0.03947182 9 0.00907599 -0.26665529 -0.00645721 -1.26330504 0.00000000 10 -0.70125910 -0.24287826 0.20471020 0.39588279 0.00000000 11 -0.16233994 0.47585486 0.25222286 6.89696304 0.00000000 12 -0.01192629 -3.29316907 -0.64569892 -4.22667578 0.00000000 13 0.00000000 0.00000000 0.00000000 0.00000000 0.01933609 14 0.00000000 0.00000000 0.00000000 0.00000000 0.00150683 15 0.01903356 -0.01975064 -0.01401485 0.05330334 0.00000000 16 0.00000000 0.00000000 0.00000000 0.00000000 0.50651522 17 0.00000000 0.00000000 0.00000000 0.00000000 0.03947182 18 -0.00907599 -0.26665529 0.00645721 -1.26330504 0.00000000 6 7 8 9 10 1 0.00000000 0.37004286 0.00000000 0.00000000 0.53739890 2 0.00000000 -0.88112148 0.00000000 0.00000000 -30.04228471 3 0.00000000 0.44134012 0.00000000 0.00000000 2.89236848 4 0.00150683 0.00000000 0.01623076 -0.00410407 0.00000000 5 -0.01933609 0.00000000 -0.00410407 -0.01623076 0.00000000 6 0.00000000 0.00718338 0.00000000 0.00000000 0.02396139 7 0.03947182 0.00000000 -1.92015928 0.48552676 0.00000000 8 -0.50651522 0.00000000 0.48552676 1.92015928 0.00000000 9 0.00000000 1.22307027 0.00000000 0.00000000 -7.56907509 10 0.00000000 0.37004286 0.00000000 0.00000000 -0.53739890 11 0.00000000 -0.88112148 0.00000000 0.00000000 30.04228471 12 0.00000000 0.44134012 0.00000000 0.00000000 -2.89236848 13 0.00150683 0.00000000 -0.01623076 0.00410407 0.00000000 14 -0.01933609 0.00000000 0.00410407 0.01623076 0.00000000 15 0.00000000 -0.00718338 0.00000000 0.00000000 0.02396139 16 0.03947182 0.00000000 1.92015928 -0.48552676 0.00000000 17 -0.50651522 0.00000000 -0.48552676 -1.92015928 0.00000000 18 0.00000000 -1.22307027 0.00000000 0.00000000 -7.56907509 11 12 13 14 15 1 -1.36401859 -1.58284822 0.00000000 0.00000000 0.69301439 2 0.64065149 -24.68858624 0.00000000 0.00000000 -0.41206171 3 -0.21508422 0.71079961 0.00000000 0.00000000 0.14448419 4 0.00000000 0.00000000 -0.17818090 -0.64526564 0.00000000 5 0.00000000 0.00000000 -0.64526564 0.17818090 0.00000000 6 -0.01402768 0.45889973 0.00000000 0.00000000 -0.76350210 7 0.00000000 0.00000000 0.08381900 0.30354275 0.00000000 8 0.00000000 0.00000000 0.30354275 -0.08381900 0.00000000 9 0.97603268 -6.99578272 0.00000000 0.00000000 0.47234437 10 -1.36401859 1.58284822 0.00000000 0.00000000 0.69301439 11 0.64065149 24.68858624 0.00000000 0.00000000 -0.41206171 12 -0.21508422 -0.71079961 0.00000000 0.00000000 0.14448419 13 0.00000000 0.00000000 -0.17818090 -0.64526564 0.00000000 14 0.00000000 0.00000000 -0.64526564 0.17818090 0.00000000 15 0.01402768 0.45889973 0.00000000 0.00000000 0.76350210 16 0.00000000 0.00000000 0.08381900 0.30354275 0.00000000 17 0.00000000 0.00000000 0.30354275 -0.08381900 0.00000000 18 -0.97603268 -6.99578272 0.00000000 0.00000000 -0.47234437 16 17 18 1 0.00000000 0.00000000 -4.42368715 2 0.00000000 0.00000000 8.01797268 3 0.00000000 0.00000000 -0.45144709 4 1.06691994 0.06953043 0.00000000 5 -0.06953043 1.06691994 0.00000000 6 0.00000000 0.00000000 -2.16193235 7 -0.76772237 -0.05003193 0.00000000 8 0.05003193 -0.76772237 0.00000000 9 0.00000000 0.00000000 2.17431700 10 0.00000000 0.00000000 4.42368715 11 0.00000000 0.00000000 -8.01797268 12 0.00000000 0.00000000 0.45144709 13 -1.06691994 -0.06953043 0.00000000 14 0.06953043 -1.06691994 0.00000000 15 0.00000000 0.00000000 -2.16193235 16 0.76772237 0.05003193 0.00000000 17 -0.05003193 0.76772237 0.00000000 18 0.00000000 0.00000000 2.17431700 --------------------------------------- Kohn-Sham orbital energies --------------------------------------- 1 1 -0.40456303 2 -0.01025658 3 0.00991243 4 0.09817183 5 0.13615499 6 0.13615499 7 0.28584302 8 0.33132517 9 0.33132517 10 0.41904722 11 0.51293450 12 0.96925361 13 1.27982757 14 1.27982757 15 1.72550671 16 1.89496148 17 1.89496148 18 3.28594306 ------------------------------------------------- ENSEMBLE ENERGIES ------------------------------------------------- Ensemble energy: -1.0984695395 au GIC Ensemble energy: -1.0669345695 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL KINETIC ENERGIES ------------------------------------------------- Kinetic energy state 1: 1.1026207443 au Kinetic energy state 2: 0.3224143668 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL POTENTIAL ENERGIES ------------------------------------------------- Potential energy state 1: -3.6031035252 au Potential energy state 2: -1.1418108827 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL HARTREE ENERGIES ------------------------------------------------- Hartree energy state 1: 1.3154344166 au Hartree energy state 2: 0.3933338477 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL EXCHANGE ENERGIES ------------------------------------------------- Exchange energy state 1: -0.5741281892 au Exchange energy state 2: -0.0038917300 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL CORRELATION ENERGIES ------------------------------------------------- Correlation energy state 1: -0.0913523731 au Correlation energy state 2: -0.0344016734 au ------------------------------------------------- ------------------------------------------------- ENSEMBLE DERIVATIVE CONTRIBUTIONS ------------------------------------------------- x ensemble derivative state 1: 0.0085121658 au c ensemble derivative state 1: -0.0004319983 au xc ensemble derivative state 1: 0.0080801675 au x ensemble derivative state 2: -0.1617311498 au c ensemble derivative state 2: 0.0082079682 au xc ensemble derivative state 2: -0.1535231816 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL AND EXCITATION ENERGIES ------------------------------------------------- Individual energy state 1: -1.1281630448 au Individual energy state 2: 0.0964064611 au ------------------------------------------------- Excitation energy 1 -> 2: 1.2245695059 au x energy contribution : 0.5702364592 au c energy contribution : 0.0569506997 au xc energy contribution : 0.6271871589 au x ensemble derivative : -0.1702433156 au c ensemble derivative : 0.0086399666 au xc ensemble derivative : -0.1616033490 au ------------------------------------------------- Excitation energy 1 -> 2: 33.3222335326 eV x energy contribution : 15.5169244128 eV c energy contribution : 1.5497074738 eV xc energy contribution : 17.0666318866 eV x ensemble derivative : -4.6325565783 eV c ensemble derivative : 0.2351054657 eV xc ensemble derivative : -4.3974511126 eV ------------------------------------------------- Total CPU time for GOC-RKS = 8.179 seconds