****************************************** * 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 0.55000000 2 0.45000000 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 0.001393 seconds 1 2 3 6 9 10 11 12 15 Computed ERIs in 0.025457 seconds Scaling integrals by 1.0000000000000000 Total CPU time for reading integrals = 0.011 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 | 2.9003385172 | -0.6233331725 | -0.0606934733 | 0.080595 | 2.000006 | | 2 | -0.7643714425 | -0.4487736245 | -0.0549786637 | 0.034566 | 2.000000 | | 3 | -0.7691046876 | -0.4906180090 | -0.0571931434 | 0.004867 | 2.000001 | | 4 | -0.7694277556 | -0.4793496864 | -0.0565148874 | 0.001296 | 2.000001 | | 5 | -0.7694411233 | -0.4811441006 | -0.0566147890 | 0.000065 | 2.000001 | | 6 | -0.7694411656 | -0.4812379645 | -0.0566196536 | 0.000002 | 2.000001 | ------------------------------------------------------------------------------------------ ------------------------------------------------- Summary ------------------------------------------------- One-electron energy: -1.8788135842 au Kinetic energy: 1.0319401741 au Potential energy: -2.9107537583 au ------------------------------------------------- Two-electron energy: 0.3950867043 au Coulomb energy: 0.9329443224 au Exchange energy: -0.4812379645 au Correlation energy: -0.0566196536 au ------------------------------------------------- Electronic energy: -1.4837268799 au Nuclear repulsion: 0.7142857143 au Kohn-Sham energy: -0.7694411656 au ------------------------------------------------- KS HOMO energy: -16.032617 eV KS LUMO energy: -2.128491 eV KS HOMO-LUMO gap: 13.904126 eV ------------------------------------------------- ----------------------------------------- Kohn-Sham orbital coefficients ----------------------------------------- 1 2 3 4 5 1 -0.78476786 0.47728480 0.24524915 0.40608508 0.00000000 2 -0.11104609 0.81370109 0.13548602 4.54635239 0.00000000 3 -0.00417339 1.72770601 -0.59314770 -4.85809110 0.00000000 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00253166 5 0.00000000 0.00000000 0.00000000 0.00000000 -0.04447136 6 -0.03124525 -0.04098333 0.01822807 -0.04689174 0.00000000 7 0.00000000 0.00000000 0.00000000 0.00000000 0.02818221 8 0.00000000 0.00000000 0.00000000 0.00000000 -0.49505110 9 0.01195208 -0.07571084 0.06627754 0.78666417 0.00000000 10 -0.78476984 -0.47728239 0.24525392 -0.40608312 0.00000000 11 -0.11104469 -0.81370136 0.13549793 -4.54635331 0.00000000 12 -0.00417341 -1.72770866 -0.59315153 4.85809006 0.00000000 13 0.00000000 0.00000000 0.00000000 0.00000000 0.00253167 14 0.00000000 0.00000000 0.00000000 0.00000000 -0.04447160 15 0.03124506 -0.04098376 -0.01822763 -0.04689208 0.00000000 16 0.00000000 0.00000000 0.00000000 0.00000000 0.02818248 17 0.00000000 0.00000000 0.00000000 0.00000000 -0.49505587 18 -0.01195280 -0.07571342 -0.06627809 0.78666245 0.00000000 6 7 8 9 10 1 0.00000000 0.39556483 0.00000000 0.00000000 -0.63087652 2 0.00000000 -0.93996422 0.00000000 0.00000000 28.57494944 3 0.00000000 0.51208358 0.00000000 0.00000000 -3.20430349 4 0.04447136 0.00000000 -0.00346307 0.00019174 0.00000000 5 0.00253166 0.00000000 0.00019174 0.00346307 0.00000000 6 0.00000000 0.02225434 0.00000000 0.00000000 -0.00573464 7 0.49505110 0.00000000 1.96787683 -0.10895578 0.00000000 8 0.02818221 0.00000000 -0.10895578 -1.96787683 0.00000000 9 0.00000000 1.13772039 0.00000000 0.00000000 7.07838418 10 0.00000000 0.39556842 0.00000000 0.00000000 0.63087994 11 0.00000000 -0.93994076 0.00000000 0.00000000 -28.57495116 12 0.00000000 0.51207916 0.00000000 0.00000000 3.20430426 13 0.04447160 0.00000000 0.00346315 -0.00019174 0.00000000 14 0.00253167 0.00000000 -0.00019174 -0.00346315 0.00000000 15 0.00000000 -0.02225401 0.00000000 0.00000000 -0.00573429 16 0.49505587 0.00000000 -1.96787557 0.10895571 0.00000000 17 0.02818248 0.00000000 0.10895571 1.96787557 0.00000000 18 0.00000000 -1.13772604 0.00000000 0.00000000 7.07838745 11 12 13 14 15 1 -1.28622741 1.60101954 0.00000000 0.00000000 0.72426388 2 0.58600272 26.74478610 0.00000000 0.00000000 -0.43477933 3 -0.20306426 -0.84604347 0.00000000 0.00000000 0.15389398 4 0.00000000 0.00000000 0.22157255 -0.63040685 0.00000000 5 0.00000000 0.00000000 0.63040685 0.22157255 0.00000000 6 -0.01822531 -0.41264165 0.00000000 0.00000000 -0.76263084 7 0.00000000 0.00000000 -0.11067710 0.31489282 0.00000000 8 0.00000000 0.00000000 -0.31489282 -0.11067710 0.00000000 9 1.06499460 7.52658798 0.00000000 0.00000000 0.48850483 10 -1.28622628 -1.60101862 0.00000000 0.00000000 0.72425957 11 0.58590555 -26.74478696 0.00000000 0.00000000 -0.43477869 12 -0.20305317 0.84604381 0.00000000 0.00000000 0.15389352 13 0.00000000 0.00000000 0.22157306 -0.63040830 0.00000000 14 0.00000000 0.00000000 0.63040830 0.22157306 0.00000000 15 0.01822510 -0.41264218 0.00000000 0.00000000 0.76263191 16 0.00000000 0.00000000 -0.11067751 0.31489396 0.00000000 17 0.00000000 0.00000000 -0.31489396 -0.11067751 0.00000000 18 -1.06496999 7.52658775 0.00000000 0.00000000 -0.48850474 16 17 18 1 0.00000000 0.00000000 -4.38462679 2 0.00000000 0.00000000 8.42643209 3 0.00000000 0.00000000 -0.46391465 4 1.06174571 0.12695657 0.00000000 5 -0.12695657 1.06174571 0.00000000 6 0.00000000 0.00000000 -2.17121215 7 -0.78826194 -0.09425518 0.00000000 8 0.09425518 -0.78826194 0.00000000 9 0.00000000 0.00000000 2.29105456 10 0.00000000 0.00000000 4.38462717 11 0.00000000 0.00000000 -8.42643227 12 0.00000000 0.00000000 0.46391471 13 -1.06174475 -0.12695645 0.00000000 14 0.12695645 -1.06174475 0.00000000 15 0.00000000 0.00000000 -2.17121167 16 0.78826158 0.09425513 0.00000000 17 -0.09425513 0.78826158 0.00000000 18 0.00000000 0.00000000 2.29105436 --------------------------------------- Kohn-Sham orbital energies --------------------------------------- 1 1 -0.58918780 2 -0.07822059 3 -0.02646831 4 0.04222686 5 0.06329478 6 0.06329478 7 0.21650666 8 0.26709981 9 0.26709981 10 0.34655097 11 0.42251914 12 0.84349611 13 1.12229310 14 1.12229310 15 1.56492535 16 1.74836441 17 1.74836441 18 3.11342806 ------------------------------------------------- ENSEMBLE ENERGIES ------------------------------------------------- Ensemble energy: -0.7694411656 au GIC Ensemble energy: -0.6479817186 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL KINETIC ENERGIES ------------------------------------------------- Kinetic energy state 1: 1.2874001192 au Kinetic energy state 2: 0.7197113522 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL POTENTIAL ENERGIES ------------------------------------------------- Potential energy state 1: -3.8313611597 au Potential energy state 2: -1.7855669342 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL HARTREE ENERGIES ------------------------------------------------- Hartree energy state 1: 1.4291078731 au Hartree energy state 2: 0.5967671234 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL EXCHANGE ENERGIES ------------------------------------------------- Exchange energy state 1: -0.6641496633 au Exchange energy state 2: -0.2576792214 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL CORRELATION ENERGIES ------------------------------------------------- Correlation energy state 1: -0.0652725108 au Correlation energy state 2: -0.0463789757 au ------------------------------------------------- ------------------------------------------------- ENSEMBLE DERIVATIVE CONTRIBUTIONS ------------------------------------------------- x ensemble derivative state 1: 0.0600726307 au c ensemble derivative state 1: -0.0030887069 au xc ensemble derivative state 1: 0.0569839238 au x ensemble derivative state 2: -0.0734221042 au c ensemble derivative state 2: 0.0037750862 au xc ensemble derivative state 2: -0.0696470179 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL AND EXCITATION ENERGIES ------------------------------------------------- Individual energy state 1: -1.0730057035 au Individual energy state 2: -0.1285079594 au ------------------------------------------------- Excitation energy 1 -> 2: 0.9444977441 au x energy contribution : 0.4064704419 au c energy contribution : 0.0188935351 au xc energy contribution : 0.4253639770 au x ensemble derivative : -0.1334947349 au c ensemble derivative : 0.0068637932 au xc ensemble derivative : -0.1266309417 au ------------------------------------------------- Excitation energy 1 -> 2: 25.7010927110 eV x energy contribution : 11.0606241014 eV c energy contribution : 0.5141192768 eV xc energy contribution : 11.5747433782 eV x ensemble derivative : -3.6325767623 eV c ensemble derivative : 0.1867733257 eV xc ensemble derivative : -3.4458034366 eV ------------------------------------------------- Total CPU time for GOC-RKS = 7.402 seconds