Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r12-)MR-CI. II. Ground-state energies of first-row atoms and positive atomic ions

The recently proposed (explicitly correlated) r12-MR-CI and r12-MR-ACPF (averaged coupled-pair functional) methods are applied to the computation of the clamped-nuclei nonrelativistic ground-state energies of the first-row atoms and their positive ions. For the neutral atoms we obtain accuracies of −0.05 (He and Li), −0.013 (Be), +0.12 (B), −0.1 (C and N), +0.3 (O) and +0.6 (F and Ne) mEh. Our energies of B–F are by far the best available. In all cases, the energy eigenvalues of the Schrodinger equation are calculated to better than chemical accuracy (1 kcal/mol). Since our method is completely general, this, for the first time, implies the possibility of performing quantum chemical calculations of general many-electron systems where the error of the computed energy is not any more very large compared to the desired accuracy.

[1]  A. Weiss.  Configuration Interaction in Simple Atomic Systems , 1961 .

[2]  J. Noga,et al.  The performance of the explicitly correlated coupled cluster method. I. The four‐electron systems Be, Li−, and LiH , 1995 .

[3]  Robert J. Gdanitz,et al.  A formulation of multiple-reference CI with terms linear in the interelectronic distances , 1993 .

[4]  H. Kleindienst,et al.  The atomic three‐body problem. An accurate lower bond calculation using wave functions with logarithmic terms , 1990 .

[5]  E. Davidson,et al.  Refinement of the Asymptotic Z Expansion for the Ground-State Correlation Energies of Atomic Ions , 1996 .

[6]  Davidson,et al.  Ground-state correlation energies for atomic ions with 3 to 18 electrons. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[7]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[8]  Thom H. Dunning,et al.  Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon , 1995 .

[9]  Trygve Helgaker,et al.  On the evaluation of derivatives of Gaussian integrals , 1992 .

[10]  William A. Lester,et al.  Recent Advances in Quantum Monte Carlo Methods , 1997 .

[11]  Harry Partridge,et al.  Near Hartree-Fock quality GTO basis sets for the first- and third-row atoms , 1989 .

[12]  Werner Kutzelnigg,et al.  r12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l , 1985 .

[13]  H. Kleindienst,et al.  NONRELATIVISTIC ENERGIES FOR THE BE ATOM : DOUBLE-LINKED HYLLERAAS-CI CALCULATION , 1998 .

[14]  E. Hylleraas.  Über den Grundterm der Zweielektronenprobleme von H−, He, Li+, Be++ usw. , 1930 .

[15]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. VI. Sextuple zeta correlation consistent basis sets for boron through neon , 1996 .

[16]  Robert J. Gdanitz,et al.  A formulation of multiple-referenceCIwith terms linear in the interelectronic distances. II. An alternative ansatz: FORMULATION OFr12-MR-CI , 1995 .

[17]  Wim Klopper,et al.  Orbital-invariant formulation of the MP2-R12 method , 1991 .

[18]  Robert J. Gdanitz,et al.  The averaged coupled-pair functional (ACPF): A size-extensive modification of MR CI(SD) , 1988 .

[19]  Davidson,et al.  Ground-state correlation energies for two- to ten-electron atomic ions. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[20]  Russell M. Pitzer,et al.  A progress report on the status of the COLUMBUS MRCI program system , 1988 .

[21]  G. Scuseria,et al.  A coupled‐cluster study of the electron affinity of the oxygen atom , 1992 .

[22]  Hans Lischka,et al.  A general multireference configuration interaction gradient program , 1992 .

[23]  Wim Klopper,et al.  Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory , 1991 .

[24]  Persson,et al.  Corrections to the beryllium ground-state energy. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[25]  E. Burke.  Variational Calculation of the Ground State of the Lithium Atom , 1963 .

[26]  P. Schleyer.  Encyclopedia of computational chemistry , 1998 .

[27]  C. Schwartz,et al.  Importance of Angular Correlations between Atomic Electrons , 1962 .

[28]  C. W. Bauschlicher,et al.  How large is the effect of 1s correlation on the De, ωe, and re of N2? , 1994 .

[29]  E. Davidson,et al.  A multireference CI determination of the isotropic hyperfine constants for first row atoms B–F , 1988 .

[30]  W. Lakin.  On Singularities in Eigenfunctions , 1965 .

[31]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[32]  T. Noro,et al.  Ground-state correlation energy of Ne , 1994 .

[33]  C. C. J. Roothaan,et al.  Self-Consistent Field Theory for Open Shells of Electronic Systems , 1960 .

[34]  N. Handy,et al.  CI-Hylleraas variational calculation on the ground state of the neon atom , 1976 .

[35]  C. F. Bunge.  Accurate determination of the total electronic energy of the Be ground state , 1976 .

[36]  J. Noga,et al.  A CCSD(T)-R12 study of the ten-electron systems Ne, F-, HF, H2O, NH3, NH4+ and CH4 , 1997 .

[37]  S. Goldman.  Uncoupling correlated calculations in atomic physics: Very high accuracy and ease , 1998 .

[38]  M. Yoshimine,et al.  Configuration-interaction study of atoms. I. Correlation energies of B, C, N, O, F, and Ne , 1974 .

[39]  T. Müller,et al.  Accurate inelastic scattering factors for lithium to argon calculated from MR-SDCI wavefunctions , 1995 .

[40]  Péter G. Szalay,et al.  New Versions of Approximately Extensive Corrected Multireference Configuration Interaction Methods , 1996 .

[41]  E. Hylleraas,et al.  Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium , 1929 .

[42]  Michael W. Schmidt,et al.  Effective convergence to complete orbital bases and to the atomic Hartree–Fock limit through systematic sequences of Gaussian primitives , 1979 .

[43]  Frederick W. King.  Lower bound for the nonrelativistic ground state energy of the lithium atom , 1995 .

[44]  R. Bartlett.  Recent advances in coupled-cluster methods , 1997 .

[45]  Rodney J. Bartlett,et al.  Multi-reference averaged quadratic coupled-cluster method: a size-extensive modification of multi-reference CI , 1993 .

[46]  Hans Lischka,et al.  Implementation of an electronic structure program system on the CYBER 205 , 1985 .

[47]  J. Rychlewski,et al.  Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom. , 1995, Physical review. A, Atomic, molecular, and optical physics.