Nonadiabatic eigenvalues and adiabatic matrix elements for all isotopes of diatomic hydrogen

Abstract For all bound and quasibound levels of the ground electronic state of all six isotopes of diatomic hydrogen, wavefunctions obtained from the most recent ab initio potentials are used to calculate expectation values of the nuclear kinetic energy, of various powers of R , and of the average polarizability and polarizability anisotropy, together with the off-diagonal matrix elements of the polarizability required for predicting the intensities of Raman transitions for Δ J = 0, ±2 and Δ v = 0, −1, and −2. A scaling procedure for treating the nonadiabatic eigenvalue corrections is developed, which allows an extrapolation beyond results reported for H 2 , HD, and D 2 to yield nonadiabatic level shift predictions for the three tritium isotopes. Features of this procedure which take account of implicit centrifugal distortion effects lead to significant improvements in the agreement between theory and experiment.

[1]  D. M. Bishop,et al.  Radiative corrections for the vibrational energy levels of the X 1Σ+g state of the hydrogen molecule , 1978 .

[2]  J. Poll,et al.  ON THE VIBRATIONAL FREQUENCIES OF THE HYDROGEN MOLECULE , 1966 .

[3]  L. Wolniewicz,et al.  Variational calculation of the long-range interaction between two ground- state hydrogen atoms , 1974 .

[4]  B. Taylor,et al.  New Results From Previously Reported NBS Fundamental Constant Determinations. , 1985, Journal of research of the National Bureau of Standards.

[5]  G. Herzberg,et al.  The Lyman and Werner Bands of Deuterium , 1973 .

[6]  W. Stwalley Mass‐reduced quantum numbers: Application to the isotopic mercury hydrides , 1975 .

[7]  R. L. Roy,et al.  Orbiting resonance model for recombination of physisorbed atoms , 1984 .

[8]  J. Hunt,et al.  Ab initio calculation of properties of the neutral diatomic hydrogen molecules H2, HD, D2, HT, DT, and T2 , 1984 .

[9]  R. L. Roy,et al.  Shape Resonances and Rotationally Predissociating Levels: The Atomic Collision Time‐Delay Functions and Quasibound Level Properties of H2(X 1Σg+) , 1971 .

[10]  A. D. Smith,et al.  Uniform semiclassical calculation of resonance energies and widths near a barrier maximum , 1981 .

[11]  W. Liu,et al.  Energies and widths of quasibound levels (orbiting resonances) for spherical potentials , 1978 .

[12]  L. Wolniewicz,et al.  Polarizability of the Hydrogen Molecule , 1967 .

[13]  L. Wolniewicz The X 1Σ+g state vibration‐rotational energies of the H2, HD, and D2 molecules , 1983 .

[14]  J. D. Garcia Radiative Corrections to the Energies of Atoms and Molecules , 1966 .

[15]  L. Wolniewicz,et al.  Accurate Adiabatic Treatment of the Ground State of the Hydrogen Molecule , 1964 .

[16]  J. Rychlewski Frequency dependent polarizabilities for the ground state of H2, HD, and D2 , 1983 .

[17]  R. Zare,et al.  Rotation-vibration spectrum of HT: Line position measurements of the 1-0, 4-0, and 5-0 bands , 1987 .

[18]  P. Bunker,et al.  The breakdown of the Born-Oppenheimer approximation: the effective vibration-rotation hamiltonian for a diatomic molecule , 1977 .

[19]  A. H. Wapstra,et al.  The 1983 atomic mass evaluation: (I). Atomic mass table , 1985 .

[20]  R. Levine,et al.  Thermodynamic functions of molecular hydrogen from ab initio energy levels , 1974 .

[21]  W. J. Meath,et al.  On the evaluation of high-order interaction energies using pseudo state methods , 1974 .

[22]  J. V. Vleck On the Isotope Corrections in Molecular Spectra , 1936 .

[23]  J. Rychlewski An accurate calculation of the polarizability of the hydrogen molecule and its dependence on rotation, vibration and isotopic substitution , 1980 .

[24]  W. Kołos,et al.  Improved Theoretical Ground‐State Energy of the Hydrogen Molecule , 1968 .

[25]  J. K. Cashion,et al.  Testing of Diatomic Potential‐Energy Functions by Numerical Methods , 1963 .

[26]  P. Bunker,et al.  Application of the effective vibration-rotation hamiltonian to H2 and D2 , 1977 .

[27]  W. J. Deal The long-range interaction between two hydrogen atoms , 1970 .

[28]  L. Wolniewicz,et al.  Improved potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule , 1975 .

[29]  G. Herzberg,et al.  The absorption and emission spectra of HD in the vacuum ultraviolet , 1976 .

[30]  R. L. Roy,et al.  Eigenvalues and Certain Expectation Values for All Bound and Quasibound Levels of Ground‐State (X 1Σg+) H2, HD, and D2 , 1971 .

[31]  J. W. Cooley,et al.  An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields , 1961 .

[32]  R. Bernstein,et al.  DISSOCIATION ENERGY AND VIBRATIONAL TERMS OF GROUND-STATE (X ¹$Sigma$/ sub g/$sup +$) HYDROGEN. , 1968 .

[33]  H. Monkhorst,et al.  New Born–Oppenheimer potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule , 1986 .

[34]  I. Dabrowski The Lyman and Werner bands of H2 , 1984 .

[35]  D. Veirs,et al.  Raman line positions in molecular hydrogen: H2, HD, HT, D2, DT, and T2 , 1987 .

[36]  D. M. Bishop,et al.  An effective Schrödinger equation for the rovibronic energies of H2 and D2 , 1976 .

[37]  M. Karplus,et al.  A Variation‐Perturbation Approach to the Interaction of Radiation with Atoms and Molecules , 1963 .

[38]  D. M. Bishop,et al.  Dynamic dipole polarizability of H2 and HeH , 1980 .

[39]  A. Buckingham,et al.  The polarizability of a pair of hydrogen atoms at long range , 1973 .

[40]  F. Weinhold,et al.  Dynamic polarizabilities of two-electron atoms, with rigorous upper and lower bounds , 1976 .

[41]  D. M. Bishop,et al.  Relative raman line intensities for H2 and for D2. Correction factors for molecular non-rigidity , 1981 .