Born-Oppenheimer Potential Energy Curves Research Articles

The ƒ3Σ+u State of the Hydrogen Molecule

The Born-Oppenheimer potential energy curve and the adiabatic corrections for the ƒ3Σ+u state of the hydrogen molecule have been calculated using explicitly correlated wavefunctions in elliptic coordinates. The calculated potential energy curve is more accurate than any previous results for this state. The energies of the vibrational levels and rotational constants for the ƒ3Σ+u state also have been computed. It is shown that the discrepancy between theoretical and experimental term values for H2 and D2 cannot be attributed to any known effect. The above discrepancies in Tv for D2 are caused presumably by a heterogeneous nonadiabatic effect. In conclusion we suggest that for H2 the experimental term values for v = 0 should be revised.

An improved potential energy curve for the C 1Π u state of H 2

An improved Born—Oppenheimer potential energy curve for the C 1Π u state of H 2 is reported for the bond length range 0.8 ⩽ R/ a 0 ⩽ 12. It is obtained from variational calculation using explicitly correlated, 149-term, Gaussian geminal wavefunctions. It is lower than the previous best calculations by as much as 3.5 μhartree ≈ 0.76 cm −1 at R = 5 a 0. The transition moment function for the X 1Σ + g → C 1Π u transition (Werner band) is calculated for the bond length range 0.8 ⩽ R/ a 0 ⩽ 2.6.

FORTRAN routine to compute Born–Oppenheimer potential energy curves directly from spectroscopic data

AbstractA computer program that calculates Born–Oppenheimer potential energy curves of diatomic molecules directly from spectroscopic data is presented. Rather than performing the usual preliminary fitting of the experimental data to a single polynomial in the variable (v + 1/2), where v is the vibrational quantum number, the program contains an accurate built‐in interpolation routine by which each experimental input point belongs to its own polynomial. The program is tested on the ground state of the H2 molecule and results are compared with the most accurate ab initio calculations available. © 1993 John Wiley & Sons, Inc.

Improved theoretical dissociation energy and ionization potential for the ground state of the hydrogen molecule

A new 155-term electronic wave function for the ground state of the hydrogen molecule has been selected which gives a more accurate Born–Oppenheimer potential energy curve in the range 3.2≤R≤7.2 bohr. The largest improvement 0.112 cm−1 has been found for R=4.8 bohr. The adiabatic corrections have also been calculated in the full range of R giving more accurate values. These new results have been employed to calculate the dissociation energies and ionization potentials for H2, HD, and D2. The agreement between resulting dissociation energies and recently published experimental data are excellent; the discrepancy is within the experimental error limits. For the ionization potential the agreement is fairly good, although not ideal. There is still room for improvement from both theoretical and experimental side.

Double-minimum potential-energy curves resulting from adiabatic effects: The 4s 3 Sigma g+ state of the hydrogen molecule.

Born-Oppenheimer potential-energy curve and adiabatic corrections for the 4s $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathit{g}}^{+}$ state of the hydrogen molecule have been computed using an explicitly correlated wave function in elliptic coordinates. It is shown that, in contrast to the Born-Oppenheimer results, the adiabatic potential-energy curve for this state is characterized by a double-minimum function. The energies of the vibrational levels and rotational constants have also been computed. Large and irregular differences have been found between thoeretical and experimental results.

Molecular hydrogen n=3 triplet gerade complex disentangled.

Nonadiabatic calculations have been performed for the {ital g}, {ital h}, {ital i}, and {ital j} states of H{sub 2}, HD, and D{sub 2}, yielding the lowest rovibrational levels ({nu},{ital N}=0,1,2,3). Born-Oppenheimer potential-energy curves were taken from literature. Irregularly shaped rotational and vibrational couplings were significantly reduced by an appropriate electronic basis transformation. In the diabatic electronic basis introduced here the rotational matrix elements were fixed to their united-atom-limit values, and the vibrational matrix elements were adjusted to reproduce experimental data. Apart from the hydrogen {sup 3}{Sigma}{sub g}{sup +} state {nu}=2 and 3 series that we suspect are misassigned, we obtained agreement with experiment down to a wave number for all calculated energy levels. Calculated branching ratios for radiative decay, which are very sensitive to the excited-state electronic composition, are found to agree with experimental data (following paper, Phys. Rev. A 44, 4171 (1991)). The confusion in the nomenclature of the adiabatic electronic {sup 3}{Sigma}{sub {ital g}}{sup +} states is addressed.

The 4 d delta states of the hydrogen molecule

Born-Oppenheimer (BO) potential energy curves for the S 1Δ g and s 3Δ g states of the hydrogen molecule have been computed using explicitly correlated wavefunctions in elliptic coordinates. The energies of the vibrational levels and rotational constants for both states have been computed. The results are compared with the available experimental data, and it appears that the discrepancy between theory and experiment is mainly mass-dependent. This indicates that the adiabatic and nonadiabatic effects are mainly responsible for it. In addition, the previously published BO energy for j 3Δ g state of H 2 at R = 1.2 Bohr, which has been found to be wrong, is corrected in this paper.

Unusual double-minimum potential energy curves: The h and g3Σ g+ states of the hydrogen molecule

Born-Oppenheimer potential energy curves and adiabatic corrections for the h and g 3Σ g + states of the hydrogen molecule have been computed using explicitly correlated wavefunctions in elliptic coordinates. The calculated potential energy curves are more accurate than any previous results for the above states. It is shown that, in contrast to the Born-Oppenheimer results, the adiabatic potential energy curves for the h and g states are characterized by double-minimum functions. The energies of the vibrational levels and rotational constants for both states have been computed. Large differences have been found between theoretical and experimental results. It is, however, possible that the irregular changes of the rotational constant with increasing vibrational excitation, found in the present work, if taken into account, may change the assignment of the experimental term values.

Adiabatic potential energy curves for the b and e3Σ u+ states of the hydrogen molecule

Calculations of the Born-Oppenheimer (BO) potential energy curves and adiabatic corrections for the b and e 3Σ u + states of the hydrogen molecule have been performed using explicitly correlated wavefunctions in elliptic coordinates. The calculated potential energy curves are more accurate than any previous results for the above-mentioned states. The energies of the vibrational levels and rotational constants for the e 3Σ u + state have been computed and very good agreement with experimental data has been found. It is shown that the homogeneous nonadiabatic corrections, estimated in this work, if taken into account, improve the agreement between theory and experiment. If, in addition, the small convergence error in the BO calculation, estimated as 0.3 cm −1 in the vicinity of the equilibrium, is added to the theoretical dissociation energy, D 0, perfect agreement for the lowest vibrational levels of H 2 and D 2 is obtained.

The multiconfiguration time-dependent Hartree–Fock method based on a closed-shell-type multiconfiguration self−consistent field reference state and its application to the LiH molecule

The linear response calculations in the multiconfiguration time-dependent Hartree–Fock (MCTDHF) approximation with a closed-shell-type MCSCF state as the time-independent reference state are discussed. The application to the LiH molecule with a small basis set ([4s2p1d/2s1p]) shows validity of our MCTDHF approach to the singlet ground state. Our MCSCF correlation energy is 97% of the total (=full CI) correlation energy and the MCTDHF excitation energies are in good agreements with the Δ full CI excitation energies. The Born–Oppenheimer potential energy curves for the lowest three singlet states of LiH and the corresponding vibrational level spacings, the transition moments, the oscillator strengths, and the frequency-dependent dipole polarizabilities are reported. All of these results imply the potentiality of our MCTDHF method for the future work with the larger basis set. One of such basis sets ([9s8p4d/8s7p1d]) is referentially used only at the single-configuration TDHF level, and the resultant near-Hartree–Fock polarizability and Thomas–Reiche–Kuhn sum rule is very promising.

The Born-Oppenheimer potential energy curve for the h3Σ g+ state of the hydrogen molecule

An ab initio potential energy curve for the h 3Σ g + state of H 2 is calculated for a wide range of internuclear distances using an explicitly correlated wavefunction. The vibrational levels are computed for H 2, HD, and D 2 in the Born-Oppenheimer approximation. Comparison with experimental term values of H 2, HD, and D 2 suggests that at least some levels of the h state have been misassigned.

Relativistic pseudopotential calculations for HBr+, HBr, HBr−, HI+, HI, and HI−

Valence SCF/CI calculations using nonrelativistic, relativistic, and semiempirical pseudopotentials have been carried out for the ground states of HBri and HIi (i=+1,0, −1). Autoionization of HBr− and HI− is characterized by the crossing points between the Born–Oppenheimer potential energy curves of the negative and neutral molecules. Relativistic and correlation effects are discussed for several molecular properties. Using semiempirical pseudopotentials+valence-CI, our calculated values for HX and HX+ (X=Br, I) are in good agreement with experiment. The crossing between the 1Σ+ (HX) and 2Σ+(HX−) curves is calculated to occur at 1.70 Å for HBr/HBr− and 1.84 Å for HI/HI−. Dissociative attachment energies for HX/HX− are compared with results from low-energy electron scattering experiments.

New Born–Oppenheimer potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule

The Born–Oppenheimer potential energy curve for the electronic ground state of the hydrogen molecule has been computed for internuclear distances 0.2≤R≤12.0 bohr. At all R the energies are lower than any previously reported values. At the equilibrium distance the improvement is negligible; its largest value, 0.47 cm−1, has been obtained for R=2.4 bohr. Vibrational energies have been computed for all isotopic species using the new potential energy curve. For H2, HD, and D2 the recent nonadiabatic corrections of Wolniewicz have been included. The resulting dissociation energies of H2 and HD agree with the experimental values within the experimental error limits; for D2 the discrepancy amounts to 0.6±0.3 cm−1.

Investigation of negative ion states in HCl and HF by configuration interaction methods

Multi-reference configuration interaction calculations are employed for the study of Born-Oppenheimer potential energy curves in HF/HF- and HCl/HCl-. Large gaussian basis sets including negative ion functions as well as diffuse s, p and d AOs are employed thereby. In HCl- a repulsive 2Σ+ state emerges from the calculations approximately 4·2 eV above the HCl X 1Σ+ ground state; no such entity could be observed in HF- in the energy range treated. All other CI roots which produce potential curves parallel to and above the X 1Σ+ curve are found to possess quite diffuse charge distributions in the basis set variations undertaken and can therefore not be considered resonant states but rather as discrete representations of free-electron species in the HX + e- continuum. For large internuclear distances the HF- and HCl- curves lie below those of the neutral species, whereby the crossing between the X 2Σ+ ionic and X 1Σ+ curves are calculated to occur at 3·2 a 0 in HCl/HCl- and 2·6 a 0 in HF/HF-. Finally it is arg...

ChemInform Abstract: AB INITIO POTENTIAL ENERGY CURVE FOR THE J1ΔG STATE OF THE HYDROGEN MOLECULE

Abstract The Born-Oppenheimer potential energy curve for the J 1 Δ g state of the hydrogen molecule was computed using highly flexible wavefunction in the form of a 60-term expansion in elliptic coordinates. The vibrational Schrodinger equation for the J state was solved for H 2 , HD, and D 2 . For H 2 the resulting energies are compared with the experimental values and it is shown that the adiabatic effects are likely to be responsible for the main part of the existing discrepancy between theoretical and experimental values. For HD the disagreement is too great to be attributable to approximations in the present work and therefore it is suggested that the J state of HD was incorrectly determined.

Ab initio potential energy curve for the J1Δ g state of the hydrogen molecule

The Born-Oppenheimer potential energy curve for the J 1Δ g state of the hydrogen molecule was computed using highly flexible wavefunction in the form of a 60-term expansion in elliptic coordinates. The vibrational Schrödinger equation for the J state was solved for H 2, HD, and D 2. For H 2 the resulting energies are compared with the experimental values and it is shown that the adiabatic effects are likely to be responsible for the main part of the existing discrepancy between theoretical and experimental values. For HD the disagreement is too great to be attributable to approximations in the present work and therefore it is suggested that the J state of HD was incorrectly determined.

Adiabatic corrections for the [formula omitted] state of the hydrogen molecule

An adiabatic potential energy curve for the B′ 1 Σ u + state of H 2 and its isotopes has been computed using a variational wavefunction in the form of an expansion in elliptic coordinates and depending explicitly on the interelectronic distance. The adiabatic binding energies, D e, are 8891.80, 8905.21, and 8918.62 cm −1 for H 2, HD, and D 2, respectively. The vibrational levels, vibrational quanta, and rotational constants have also been computed. It is shown that the remaining small discrepancies between theoretical and experimental values are mainly due to inaccuracy of the Born-Oppenheimer potential energy curve.

Adiabatic corrections for the [formula omitted] state of the hydrogen molecule

Adiabatic corrections to the Born-Oppenheimer potential energy curve for the B″ 1 Σ u + state of the hydrogen molecule has been computed using a 60-term variational wavefunction in the form of an expansion in elliptic coordinates and depending explicitly on the interelectronic distance. For three internuclear separations new Born-Oppenheimer energies are also given which represent corrections of the previously published values. For H 2 the adiabatic correction to the dissociation energy amounts to 57.5 cm −1. The computed dissociation energies for H 2, HD, and D 2 are by 23–25 cm −1 smaller than the experimental values, the discrepancy being probably due to the convergence error of the Born-Oppenheimer potential. A few lowest vibrational levels and vibrational quanta have been calculated for H 2, HD and D 2, and compared with the experimental results.

The computation of nuclear motion and mass polarization adiabatic energy corrections for several states of the hydrogen molecule

This paper reports the computation of the diagonal matrix elements of the nuclear motion and mass polarization operators (often referred to as adiabatic corrections) for several electronic states of the hydrogen molecule. It is observed that reasonably simple wavefunctions will yield accurate expectation values for the nuclear motion operators. The present calculation covers a greater range of R for the X 1Σ+g and B 1Σ+u states than is covered in the very accurate work of Kolos and Wolniewicz, and includes computations for the C 1Πu and D 1Πu states for which no theoretical results have been previously reported. For the latter states the present diagonal corrections have been used in conjunction with the very recent Born–Oppenheimer potential energy curves of Kolos and Rychlewski [J. Mol. Spectrosc. 62, 109 (1976)] to compute vibrational level energies for both H2 and D2. The diagonal corrections largely remove the mass-dependent part of the discrepancy between theory and experiment for these vibrational level energies.

New ab initio Potential Energy Curve and Vibrational Levels for the B1Σu+ State of the Hydrogen Molecule

The Born–Oppenheimer potential energy curve for the B1Σu+ state of the hydrogen molecule has been computed using a wave-function in the form of an 88 term expansion in elliptic coordinates and including the interelectronic distance. At R = Re the computed energy is 5.2 cm−1 lower than the previous most accurate value, in agreement with the prediction by Dabrowski and Herzberg. The new potential energy curve, with the previously computed adiabatic corrections, has been used to calculate the vibrational levels for H2, HD, and D2. The resulting dissociation energies differ from the experimental values by less than 1 cm−1. The discrepancies between the theoretical and experimental energies for various vibrational levels amount up to 12 cm−1 for H2 and 8 cm−1 for D2. Their analysis suggests that most of the discrepancy is due to the nonadiabatic effects, but partly also to incomplete convergence of the Born–Oppenheimer potential energy curve, especially at large internuclear separations.