Improved Theoretical Ground‐State Energy of the Hydrogen Molecule
TL;DR: In this paper, the potential energy curve for the electronic ground state of the hydrogen molecule has been calculated for double precision using a 100-term expansion of the electronic wavefunction, and the vibrational equation has been solved for all isotopes and for the rotational quantum number.
Abstract: The potential‐energy curve for the electronic ground state of the hydrogen molecule has been calculated for 1 ≤ R ≤ 3.2 a.u. in double precision and using a 100‐term expansion for the electronic wavefunction. Accuracy of the previously computed diagonal corrections for nuclear motion has been tested. The vibrational equation has been solved for all isotopes of the hydrogen molecule and for the rotational quantum number J ≤ 10. The calculated adiabatic dissociation energy of H2, corrected for relativistic and radiative effects, is by 3.8 cm−1 larger than the experimental value, hence the theoretical total energy is by the same amount lower than the experimental value. The calculated vibrational quanta for H2 are by 0.5–0.9 cm−1 larger than the experimental ones.
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TL;DR: In this article, the ground state energies of H2, LiH, Li2, and H2O are calculated by a fixed-node quantum Monte Carlo method, which is presented in detail.
Abstract: The ground‐state energies of H2, LiH, Li2, and H2O are calculated by a fixed‐node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions ΨT are chosen. Each ΨT consists of a single Slater determinant of molecular orbitals multiplied by a product of pair‐correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schrodinger equation by treating it as a diffusion equation. In this approach, ΨT serves as a ‘‘guiding function’’ for a random walk of the electrons through configuration space. In the fixed‐node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of ΨT. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The e...
893 citations
TL;DR: In this article, a statistical adiabatic channel model is proposed to calculate the rate of unimolecular processes by means of a simple interpolation procedure, where the coupling between the various vibrational-rotational motions is taken into account.
Abstract: The rate of unimolecular processes is calculated by means of a statistical adiabatic channel model. The rates are mainly determined by the maxima of the channel energies. The channels are constructed by correlating reactant and product states; the channel energies are computed by a simple interpolation procedure. The coupling between the various vibrational-rotational motions is taken into account. The influence of parameters of the potential surface on channel energies and on rate constants is studied. Numerical results for the NO2, CH4, CD4, C2H6 and C2D6 dissociation – recombination kinetics are compared to experimental data. The statistical adiabatic channel model gives similar results as minimum local entropy models. Both these approaches lead to stronger curvatures of k(E) and smaller activation energies for the thermal rate constant k∞ than the corresponding RRKM calculations.
Die Geschwindigkeit unimolekularer Zerfallsreaktionen wird mit Hilfe eines Modells adiabatischer Kanale statistisch berechnet. Wesentlich fur die Reaktionsgeschwindigkeiten sind die Maximalenergien der Kanale, die durch Korrelation von Zustanden der Reaktanten und Produkte und einfache Interpolation bestimmt werden. Die Kopplung der Schwingungs-Rotationsbewegungen wird beachtet. Der Einflus von Potentialflachenparametern auf Kanalenergien und Geschwindigkeitskonstanten wird studiert. Numerische Ergebnisse fur die Dissoziations-Rekombinationskinetik von NO2, CH4, CD4, C2H6 und C2D6 werden mit experimentellen Daten verglichen. Das Modell adiabatischer Kanale ergibt ahnliche Ergebnisse wie Modelle mit aktivierten Komplexen, die an Stellen minimaler Zustandsdichte lokalisiert werden. Beide Ansatze fuhren zu einer starkeren Krummung der k(E)-Kurven und zu geringeren Arrhenius-Aktivierungsenergien fur die thermischen Geschwindigkeitskonstanten k∞ als entsprechende RRKM Rechnungen.
466 citations
TL;DR: In this paper, an expression for the correlation energy of a multiconfiguration wave function is developed using perturbation theory, and three levels of extrapolation based on the asymptotic convergence of pair natural orbital expansions are examined.
Abstract: An expression for the ’’correlation energy’’ of a multiconfiguration wave function is developed using perturbation theory. The asymptotic form of this expression for an N‐configuration pair natural orbital expansion is Error(N×N)?(Σμ = 1NCμ)2 (−225/4608)N−1. The asymptotic form attributes the dominant variation in multiconfiguration pair correlation errors to an interference effect between low‐lying natural orbitals. Three levels of extrapolation based on the asymptotic convergence of pair natural orbital expansions are examined. The first requires separate calculations with 5 and 14 natural orbitals. When applied to the helium atom, for which E(5) = −2.897 484 and E(14) = −2.901 697, the extrapolated value, E = −2.903 724, is accurate to within 0.05% of the error from the 14 natural orbital wave function (i.e., the absolute accuracy is ≲0.000 001 hartree). The second extrapolation requires separate calculations with 5 and 14 pair MCSCF configurations and is accurate to within 2% of the MCSCF (14) error (...
382 citations
TL;DR: The unity bond index-quadratic exponential potential (UBI-QEP) method was proposed in this article for determining metal surface reaction energetics with a typical accuracy of 1.3 kcal/mol.
344 citations
TL;DR: The recently developed high-accuracy extrapolated ab initio thermochemistry method for theoretical thermochemistry, which is intimately related to other high-precision protocols such as the Weizmann-3 and focal-point approaches, is revisited.
Abstract: The recently developed high-accuracy extrapolated ab initio thermochemistry method for theoretical thermochemistry, which is intimately related to other high-precision protocols such as the Weizmann-3 and focal-point approaches, is revisited. Some minor improvements in theoretical rigor are introduced which do not lead to any significant additional computational overhead, but are shown to have a negligible overall effect on the accuracy. In addition, the method is extended to completely treat electron correlation effects up to pentuple excitations. The use of an approximate treatment of quadruple and pentuple excitations is suggested; the former as a pragmatic approximation for standard cases and the latter when extremely high accuracy is required. For a test suite of molecules that have rather precisely known enthalpies of formation {as taken from the active thermochemical tables of Ruscic and co-workers [Lecture Notes in Computer Science, edited by M. Parashar (Springer, Berlin, 2002), Vol. 2536, pp. 25...
306 citations
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TL;DR: In this article, an accurate method for calculating the nuclear wave functions and vibrational-rotational energies of diatomic molecules with some economy in the number of values of the internuclear potential required is presented.
Abstract: 1. Introduction. The wave equation for the nuclear motion of a diatomic molecule, in the Born-Oppenheimer approximation, is one which is encountered frequently in quantum-theoretical calculations. Numerical methods for its solution have been developed and used [1, 2, 3, 4] over many years for atomic problems where the potential is one obtained by Hartree-Fock self-consistent fields or the Thomas-Fermi-Dirac statistical field methods. Only relatively recently have computational techniques and the application of electronic computers enabled one to obtain accurate theoretical internuclear potentials at enough internuclear distances to calculate the wave functions for the motion of the nuclei and use them to obtain averages, over the nuclear motion, of molecular properties. The present investigation is concerned with obtaining an accurate method for calculating the nuclear wave functions and vibrational-rotational energies of diatomic molecules with some economy in the number of values of the internuclear potential required. An improved formula for the correction of trial eigenvalues, which does not depend so much for its accuracy upon the smallness of the stepsize in the radial coordinate, and an analysis of the convergence of the procedure are given. A computer subroutine was written and numerical results obtained from it are described for a case where exact analytical solutions are known. In what follows, the vibrational quantum number v, v = 0, 1, 2, , will be used as a subscript to index the eigenvalues Ev with the usual convention that Eo < E1 ? E2 ?
1,118 citations
TL;DR: In this article, the ground-state energy of H2 has been extended to include large internuclear distances and accurate potential energy curve for 0.4≤R≤4.0 a.u.
Abstract: Previous calculation of the ground‐state energy of H2 has been extended to include large internuclear distances and accurate potential‐energy curve for 0.4≤R≤10.0 a.u. is presented. For 0.4≤R≤4.0 a.u. expectation values of several operators have also been calculated. The calculation was made using a wavefunction in the form of an expansion in elliptic coordinates. The wavefunction depends on the interelectronic distance but, in contrast to the James—Coolidge expansion, is flexible enough to describe properly the dissociation of the molecule. Extensive calculations have also been made for the repulsive 3Σu+ state (1.0≤R≤10.0) and for the 1Πu state (1.0≤R≤10.0). In the former case a van der Waals minimum has been found at R=7.85 a.u. and 4.3 cm−1 below the dissociation limit. For the 1Πu state the computed binding energy De=20 490.0 cm−1 and the equilibrium internuclear distance Re=1.0330 A are in a satisfactory agreement with the experimental values De=20 488.5 cm−1 and Re=1.0327 A. In this case a van der ...
1,078 citations
TL;DR: In this paper, the ground-state energies of the hydrogen molecule have been computed using wavefunctions in the form of expansions in elliptic coordinates and including explicitly the interelectronic distance.
Abstract: Accurate ground‐state energies of the hydrogen molecule have been computed using wavefunctions in the form of expansions in elliptic coordinates and including explicitly the interelectronic distance. The computations have been made with 54‐term expansions (0.4≤R≤3.7) and with 80‐term expansions (0.5≤R≤2.0). For the equilibrium internuclear distance, the best total energies obtained in the two cases are —1.1744701 a.u. and —1.1744746 a.u., respectively, the corresponding binding energies being 38 291.8 and 38 292.7 cm—1. Employing the 54‐term wavefunctions, the relativistic corrections and the diagonal corrections for nuclear motion have been computed for several internuclear distances. For equilibrium their contributions to the binding energy have been found to be —0.526 and 4.947 cm—1, respectively. Thus the final theoretical binding energy for H2 amounts to 38 297.1 cm—1 and is a little larger than the experimental value 38 292.9±0.5 cm—1. The discrepancy may be due to the adiabatic approximation.
515 citations
TL;DR: In this article, the rotational and vibrational constants of the Lyman bands of H2 were investigated under high resolution with a view to improving the ground state rotational constants.
Abstract: The Lyman bands of H2 have been investigated under high resolution with a view to improving the rotational and vibrational constants of H2 in its ground state. Precise Bv and ΔG values have been ob...
283 citations
TL;DR: In this article, the Schrodinger equation for the relative motion of the electrons and nuclei in a diatomic molecule is used to obtain the electronic wave functions of the wave function.
Abstract: The electronic -vibrational wave functions are obtained from the Schrodinger equation for the relative motion of the electrons and nuclei in a diatomic molecule. Numerical computation for the ground state of the hydrogen molecule is carried out. (R.E.U.)
254 citations