****************************************** * 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 9 ------------------ s-type shell with K = 3 Exponents Contraction 33.8700000000 0.0060680000 5.0950000000 0.0453080000 1.1590000000 0.2028220000 s-type shell with K = 1 Exponents Contraction 0.3258000000 1.0000000000 s-type shell with K = 1 Exponents Contraction 0.1027000000 1.0000000000 s-type shell with K = 1 Exponents Contraction 0.0252600000 1.0000000000 p-type shell with K = 1 Exponents Contraction 1.4070000000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.3880000000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.1020000000 1.0000000000 d-type shell with K = 1 Exponents Contraction 1.0570000000 1.0000000000 d-type shell with K = 1 Exponents Contraction 0.2470000000 1.0000000000 ------------------ Atom n. 2 number of shells 9 ------------------ s-type shell with K = 3 Exponents Contraction 33.8700000000 0.0060680000 5.0950000000 0.0453080000 1.1590000000 0.2028220000 s-type shell with K = 1 Exponents Contraction 0.3258000000 1.0000000000 s-type shell with K = 1 Exponents Contraction 0.1027000000 1.0000000000 s-type shell with K = 1 Exponents Contraction 0.0252600000 1.0000000000 p-type shell with K = 1 Exponents Contraction 1.4070000000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.3880000000 1.0000000000 p-type shell with K = 1 Exponents Contraction 0.1020000000 1.0000000000 d-type shell with K = 1 Exponents Contraction 1.0570000000 1.0000000000 d-type shell with K = 1 Exponents Contraction 0.2470000000 1.0000000000 ------------------ Number of shells 18 ------------------ ------------------ Number of basis functions 50 ------------------ ---------------------------------------------------------- Number of states in ensemble = 2 ---------------------------------------------------------- ---------------------------------------------------------- Ensemble weights ---------------------------------------------------------- 1 1 0.90000000 2 0.10000000 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 ----------------------------------------------------------------------- 1-4 S 0.0000 0.0000 0.0000 3.38700000e+01 6.06800000e-03 5.09500000e+00 4.53080000e-02 1.15900000e+00 2.02822000e-01 3.25800000e-01 1.00000000e+00 1.02700000e-01 1.00000000e+00 2.52600000e-02 1.00000000e+00 ----------------------------------------------------------------------- 5-13 P 0.0000 0.0000 0.0000 1.40700000e+00 1.00000000e+00 3.88000000e-01 1.00000000e+00 1.02000000e-01 1.00000000e+00 ----------------------------------------------------------------------- 14-25 D 0.0000 0.0000 0.0000 1.05700000e+00 1.00000000e+00 2.47000000e-01 1.00000000e+00 ----------------------------------------------------------------------- 26-29 S 0.0000 0.0000 1.4000 3.38700000e+01 6.06800000e-03 5.09500000e+00 4.53080000e-02 1.15900000e+00 2.02822000e-01 3.25800000e-01 1.00000000e+00 1.02700000e-01 1.00000000e+00 2.52600000e-02 1.00000000e+00 ----------------------------------------------------------------------- 30-38 P 0.0000 0.0000 1.4000 1.40700000e+00 1.00000000e+00 3.88000000e-01 1.00000000e+00 1.02000000e-01 1.00000000e+00 ----------------------------------------------------------------------- 39-50 D 0.0000 0.0000 1.4000 1.05700000e+00 1.00000000e+00 2.47000000e-01 1.00000000e+00 ----------------------------------------------------------------------- 171 significant shell pairs computed in 0.016562 seconds 1 2 3 4 7 10 13 19 25 26 27 28 29 32 35 38 44 Computed ERIs in 0.786510 seconds Scaling integrals by 1.0000000000000000 Total CPU time for reading integrals = 0.415 seconds Lowdin orthogonalization ---------------------------------------------------------- Quadrature grid: SG-1 ---------------------------------------------------------- Radial precision = 0.1E-06 Number of radial points = 86 Number of angular points = 194 Total number of points = 16684 ************************************************ * 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: RVWN5 * ******************************************************************* ------------------------------------------------------------------------------------------ | # | E(KS) | Ex(KS) | Ec(KS) | Conv | nEl | ------------------------------------------------------------------------------------------ | 1 | 15.8042899247 | -0.7175250575 | -0.0986201229 | 0.067203 | 2.000020 | | 2 | -1.0724710715 | -0.5358533372 | -0.0891895730 | 0.050198 | 2.000000 | | 3 | -1.0742989054 | -0.5351227384 | -0.0892895195 | 0.012586 | 2.000000 | | 4 | -1.0744735106 | -0.5362033266 | -0.0894583008 | 0.000545 | 2.000000 | | 5 | -1.0744741249 | -0.5358937310 | -0.0894316193 | 0.000147 | 2.000000 | | 6 | -1.0744741510 | -0.5359057557 | -0.0894327042 | 0.000019 | 2.000000 | | 7 | -1.0744741609 | -0.5359122277 | -0.0894333228 | 0.000012 | 2.000000 | | 8 | -1.0744741660 | -0.5359119796 | -0.0894333191 | 0.000008 | 2.000000 | ------------------------------------------------------------------------------------------ ------------------------------------------------- Summary ------------------------------------------------- One-electron energy: -2.3475169676 au Kinetic energy: 1.0864501442 au Potential energy: -3.4339671118 au ------------------------------------------------- Two-electron energy: 0.5587570872 au Coulomb energy: 1.1841023860 au Exchange energy: -0.5359119796 au Correlation energy: -0.0894333191 au ------------------------------------------------- Electronic energy: -1.7887598803 au Nuclear repulsion: 0.7142857143 au Kohn-Sham energy: -1.0744741660 au ------------------------------------------------- KS HOMO energy: -11.965105 eV KS LUMO energy: -0.693059 eV KS HOMO-LUMO gap: 11.272046 eV ------------------------------------------------- ----------------------------------------- Kohn-Sham orbital coefficients ----------------------------------------- 1 2 3 4 5 1 -0.83798898 0.26561951 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0.00000000 -1.77356678 -0.44443422 -0.83545102 40 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 41 0.00491240 1.28670148 0.00000000 0.00000000 0.00000000 42 0.00000000 0.00000000 -1.77356678 -0.44443422 -0.83545102 43 -1.28670148 0.00491240 0.00000000 0.00000000 0.00000000 44 0.00000000 0.00000000 -0.64970607 1.25373461 -3.60029752 45 0.00000000 0.00000000 -3.24107745 -0.16894754 -1.00104535 46 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 47 -0.00121745 -0.31888515 0.00000000 0.00000000 0.00000000 48 0.00000000 0.00000000 -3.24107745 -0.16894754 -1.00104535 49 0.31888515 -0.00121745 0.00000000 0.00000000 0.00000000 50 0.00000000 0.00000000 -1.35480198 0.12029867 -1.84505178 --------------------------------------- Kohn-Sham orbital energies --------------------------------------- 1 1 -0.43970950 2 -0.02546944 3 -0.00781935 4 0.06081245 5 0.07740685 6 0.07740685 7 0.16822152 8 0.20304594 9 0.20304594 10 0.22436736 11 0.28059974 12 0.39348489 13 0.59669400 14 0.59669401 15 0.64511628 16 0.67219018 17 0.67219018 18 0.71181366 19 0.71181366 20 0.78981092 21 0.85781943 22 0.87817205 23 0.87817213 24 0.88853730 25 0.88853730 26 1.05081802 27 1.53951493 28 1.66526266 29 1.66526266 30 2.05741981 31 2.54901024 32 2.71243259 33 3.16746071 34 3.16746071 35 3.19823837 36 3.19823954 37 3.83253058 38 3.99593542 39 3.99593753 40 4.00469864 41 4.00469864 42 4.09244883 43 4.09244883 44 4.73227392 45 5.11485455 46 5.31053404 47 5.31053404 48 5.32180224 49 5.55252300 50 9.45839281 ------------------------------------------------- ENSEMBLE ENERGIES ------------------------------------------------- Ensemble energy: -1.0744741660 au GIC Ensemble energy: -1.0151012023 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL KINETIC ENERGIES ------------------------------------------------- Kinetic energy state 1: 1.1685278512 au Kinetic energy state 2: 0.3477507812 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL POTENTIAL ENERGIES ------------------------------------------------- Potential energy state 1: -3.6836870419 au Potential energy state 2: -1.1864877409 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL HARTREE ENERGIES ------------------------------------------------- Hartree energy state 1: 1.3372716513 au Hartree energy state 2: 0.3993086357 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL EXCHANGE ENERGIES ------------------------------------------------- Exchange energy state 1: -0.5920820758 au Exchange energy state 2: -0.0303811138 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL CORRELATION ENERGIES ------------------------------------------------- Correlation energy state 1: -0.0950412377 au Correlation energy state 2: -0.0389620511 au ------------------------------------------------- ------------------------------------------------- ENSEMBLE DERIVATIVE CONTRIBUTIONS ------------------------------------------------- x ensemble derivative state 1: 0.0164646697 au c ensemble derivative state 1: 0.0000000000 au xc ensemble derivative state 1: 0.0164646697 au x ensemble derivative state 2: -0.1481820269 au c ensemble derivative state 2: 0.0000000000 au xc ensemble derivative state 2: -0.1481820269 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL AND EXCITATION ENERGIES ------------------------------------------------- Individual energy state 1: -1.1342604690 au Individual energy state 2: 0.0573321984 au ------------------------------------------------- Excitation energy 1 -> 2: 1.1915926674 au x energy contribution : 0.5617009620 au c energy contribution : 0.0560791867 au xc energy contribution : 0.6177801486 au x ensemble derivative : -0.1646466966 au c ensemble derivative : 0.0000000000 au xc ensemble derivative : -0.1646466966 au ------------------------------------------------- Excitation energy 1 -> 2: 32.4248880520 eV x energy contribution : 15.2846617044 eV c energy contribution : 1.5259923959 eV xc energy contribution : 16.8106541002 eV x ensemble derivative : -4.4802648179 eV c ensemble derivative : 0.0000000000 eV xc ensemble derivative : -4.4802648179 eV ------------------------------------------------- Total CPU time for GOC-RKS = 47.814 seconds