****************************************** * 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 0.82500000 2 0.17500000 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 0.000819 seconds 1 2 3 6 9 10 11 12 15 Computed ERIs in 0.017390 seconds Scaling integrals by 1.0000000000000000 Total CPU time for reading integrals = 0.009 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 | 4.3093116530 | -0.8122512242 | -0.0899711057 | 0.097748 | 2.000009 | | 2 | -0.9814857406 | -0.4503404607 | -0.0714996304 | 0.093299 | 2.000000 | | 3 | -1.0015944827 | -0.4862747572 | -0.0741252839 | 0.043906 | 2.000001 | | 4 | -1.0073169803 | -0.5184927075 | -0.0763929417 | 0.000511 | 2.000001 | | 5 | -1.0073172733 | -0.5184769685 | -0.0763938659 | 0.000153 | 2.000001 | | 6 | -1.0073173316 | -0.5183638847 | -0.0763852276 | 0.000009 | 2.000001 | ------------------------------------------------------------------------------------------ ------------------------------------------------- Summary ------------------------------------------------- One-electron energy: -2.2371114210 au Kinetic energy: 1.0408201175 au Potential energy: -3.2779315385 au ------------------------------------------------- Two-electron energy: 0.5155083751 au Coulomb energy: 1.1102574874 au Exchange energy: -0.5183638847 au Correlation energy: -0.0763852276 au ------------------------------------------------- Electronic energy: -1.7216030459 au Nuclear repulsion: 0.7142857143 au Kohn-Sham energy: -1.0073173316 au ------------------------------------------------- KS HOMO energy: -12.894057 eV KS LUMO energy: -1.020192 eV KS HOMO-LUMO gap: 11.873865 eV ------------------------------------------------- ----------------------------------------- Kohn-Sham orbital coefficients ----------------------------------------- 1 2 3 4 5 1 -0.73317309 -0.31268013 0.21376493 0.41318814 0.00000000 2 -0.14395471 -0.05838745 0.21267920 6.07185391 0.00000000 3 -0.00771639 -2.81937854 -0.62846871 -4.47681089 0.00000000 4 0.00000000 0.00000000 0.00000000 0.00000000 0.01394046 5 0.00000000 0.00000000 0.00000000 0.00000000 0.02468689 6 -0.02325487 0.02675765 0.01498430 -0.05229710 0.00000000 7 0.00000000 0.00000000 0.00000000 0.00000000 0.24772816 8 0.00000000 0.00000000 0.00000000 0.00000000 0.43869694 9 0.00945379 0.17999739 0.02351235 1.08620822 0.00000000 10 -0.73316709 0.31272517 0.21365670 -0.41321012 0.00000000 11 -0.14387914 0.05845265 0.21299265 -6.07185881 0.00000000 12 -0.00771702 2.81921703 -0.62894248 4.47684697 0.00000000 13 0.00000000 0.00000000 0.00000000 0.00000000 0.01394122 14 0.00000000 0.00000000 0.00000000 0.00000000 0.02468823 15 0.02325454 0.02675445 -0.01498991 -0.05229677 0.00000000 16 0.00000000 0.00000000 0.00000000 0.00000000 0.24770976 17 0.00000000 0.00000000 0.00000000 0.00000000 0.43866435 18 -0.00947420 0.18000187 -0.02367153 1.08621386 0.00000000 6 7 8 9 10 1 0.00000000 0.37570020 0.00000000 0.00000000 0.57087072 2 0.00000000 -0.90220792 0.00000000 0.00000000 -29.59651526 3 0.00000000 0.46610464 0.00000000 0.00000000 3.00272351 4 0.02468689 0.00000000 -0.01232158 -0.00079778 0.00000000 5 -0.01394046 0.00000000 0.00079778 -0.01232158 0.00000000 6 0.00000000 0.01190323 0.00000000 0.00000000 0.01737073 7 0.43869694 0.00000000 1.97327738 0.12776272 0.00000000 8 -0.24772816 0.00000000 -0.12776272 1.97327738 0.00000000 9 0.00000000 1.19846098 0.00000000 0.00000000 -7.41473684 10 0.00000000 0.37569423 0.00000000 0.00000000 -0.57085364 11 0.00000000 -0.90194480 0.00000000 0.00000000 29.59650958 12 0.00000000 0.46613406 0.00000000 0.00000000 -3.00271270 13 0.02468823 0.00000000 0.01231890 0.00079761 0.00000000 14 -0.01394122 0.00000000 -0.00079761 0.01231890 0.00000000 15 0.00000000 -0.01190353 0.00000000 0.00000000 0.01737100 16 0.43866435 0.00000000 -1.97328562 -0.12776325 0.00000000 17 -0.24770976 0.00000000 0.12776325 -1.97328562 0.00000000 18 0.00000000 -1.19852682 0.00000000 0.00000000 -7.41470526 11 12 13 14 15 1 -1.33846656 1.59092957 0.00000000 0.00000000 0.70396508 2 0.62487672 25.39441901 0.00000000 0.00000000 -0.41945344 3 -0.21116772 -0.75528152 0.00000000 0.00000000 0.14757916 4 0.00000000 0.00000000 -0.13908832 -0.65448057 0.00000000 5 0.00000000 0.00000000 -0.65448057 0.13908832 0.00000000 6 -0.01604692 -0.44337794 0.00000000 0.00000000 -0.76326703 7 0.00000000 0.00000000 0.06686744 0.31464499 0.00000000 8 0.00000000 0.00000000 0.31464499 -0.06686744 0.00000000 9 1.00350243 7.17918703 0.00000000 0.00000000 0.47702570 10 -1.33846753 -1.59093515 0.00000000 0.00000000 0.70396226 11 0.62553712 -25.39441519 0.00000000 0.00000000 -0.41944632 12 -0.21125258 0.75527678 0.00000000 0.00000000 0.14758234 13 0.00000000 0.00000000 -0.13908774 -0.65447785 0.00000000 14 0.00000000 0.00000000 -0.65447785 0.13908774 0.00000000 15 0.01604791 -0.44337749 0.00000000 0.00000000 0.76326882 16 0.00000000 0.00000000 0.06686834 0.31464923 0.00000000 17 0.00000000 0.00000000 0.31464923 -0.06686834 0.00000000 18 -1.00366998 7.17918343 0.00000000 0.00000000 -0.47702858 16 17 18 1 0.00000000 0.00000000 -4.41060688 2 0.00000000 0.00000000 8.15148827 3 0.00000000 0.00000000 -0.45539747 4 -1.06761665 0.05893486 0.00000000 5 0.05893486 1.06761665 0.00000000 6 0.00000000 0.00000000 -2.16518144 7 0.77630400 -0.04285374 0.00000000 8 -0.04285374 -0.77630400 0.00000000 9 0.00000000 0.00000000 2.21258425 10 0.00000000 0.00000000 4.41060873 11 0.00000000 0.00000000 -8.15148864 12 0.00000000 0.00000000 0.45539725 13 1.06761838 -0.05893496 0.00000000 14 -0.05893496 -1.06761838 0.00000000 15 0.00000000 0.00000000 -2.16518091 16 -0.77630547 0.04285382 0.00000000 17 0.04285382 0.77630547 0.00000000 18 0.00000000 0.00000000 2.21258453 --------------------------------------- Kohn-Sham orbital energies --------------------------------------- 1 1 -0.47384786 2 -0.03749137 3 -0.00906389 4 0.06944710 5 0.10605287 6 0.10605287 7 0.25451838 8 0.30355038 9 0.30355038 10 0.38744571 11 0.47461907 12 0.91774749 13 1.21808560 14 1.21808560 15 1.66305707 16 1.83724416 17 1.83724416 18 3.22006220 ------------------------------------------------- ENSEMBLE ENERGIES ------------------------------------------------- Ensemble energy: -1.0073173316 au GIC Ensemble energy: -0.9188389827 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL KINETIC ENERGIES ------------------------------------------------- Kinetic energy state 1: 1.1712266996 au Kinetic energy state 2: 0.4260462304 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL POTENTIAL ENERGIES ------------------------------------------------- Potential energy state 1: -3.6914800851 au Potential energy state 2: -1.3283455329 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL HARTREE ENERGIES ------------------------------------------------- Hartree energy state 1: 1.3587918789 au Hartree energy state 2: 0.4445712775 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL EXCHANGE ENERGIES ------------------------------------------------- Exchange energy state 1: -0.6104513191 au Exchange energy state 2: -0.0842374084 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL CORRELATION ENERGIES ------------------------------------------------- Correlation energy state 1: -0.0836758462 au Correlation energy state 2: -0.0424005250 au ------------------------------------------------- ------------------------------------------------- ENSEMBLE DERIVATIVE CONTRIBUTIONS ------------------------------------------------- x ensemble derivative state 1: 0.0272419921 au c ensemble derivative state 1: -0.0013635125 au xc ensemble derivative state 1: 0.0258784796 au x ensemble derivative state 2: -0.1284265342 au c ensemble derivative state 2: 0.0064279873 au xc ensemble derivative state 2: -0.1219985469 au ------------------------------------------------- ------------------------------------------------- INDIVIDUAL AND EXCITATION ENERGIES ------------------------------------------------- Individual energy state 1: -1.1154244780 au Individual energy state 2: 0.0079212090 au ------------------------------------------------- Excitation energy 1 -> 2: 1.1233456869 au x energy contribution : 0.5262139107 au c energy contribution : 0.0412753212 au xc energy contribution : 0.5674892319 au x ensemble derivative : -0.1556685263 au c ensemble derivative : 0.0077914998 au xc ensemble derivative : -0.1478770265 au ------------------------------------------------- Excitation energy 1 -> 2: 30.5677931209 eV x energy contribution : 14.3190098536 eV c energy contribution : 1.1231586980 eV xc energy contribution : 15.4421685516 eV x ensemble derivative : -4.2359563609 eV c ensemble derivative : 0.2120175081 eV xc ensemble derivative : -4.0239388528 eV ------------------------------------------------- Total CPU time for GOC-RKS = 7.788 seconds