SCF calculations for H 2 + , Li 2 + and LiH+ with atomic basis sets enlarged by bond functions

To simulate the charge distortion in the formation of a molecule from the separated atoms, a set of concentrics-type Gaussian functions is placed on the internuclear axis in addition to thes-type atomic basis functions to construct the molecular orbital for the one valence-electron systems H ₂ ⁺ , Li ₂ ⁺ and LiH⁺. This simple model gives 90.1%, 75.2% and 61.7%, respectively, of the improvement over minimal basis relative to Hartree-Fock energies.Supported in part by a research grant to Rice University from the Robert A. Welch Foundation.     

H+, Li+, and Na+ affinity study of N2, P2, and their isoelectronic species

We performed ab initio calculations for protonated P₂, N₂, NP, and their isoelectronic species, i.e., CO, CS, SiO, and SiS. The proton affinities at different sites were examined to characterize special properties of the second-row elements. To tune the acid strength, we also studied the Li⁺ and Na⁺ affinities for comparison. These systems are isovalent to acetylene and disilyne; their structural features such as linear or bent is of special interest. All calculations were performed by the GAUSSIAN 92 program using the 6-31G** basis set and the basis set at the Hartree-Fock and MP2(full) levels. Bent structures were found for XP⁺₂, CSH⁺, and SiSX (X = H⁺, Li⁺, Na⁺). © 1996 John Wiley & Sons, Inc.     

Vibrational energies of H2+ using fully nonadiabatic wavefunctions

Using variational Monte Carlo methods, we examine a number of fully nonadiabatic trial wavefunctions to determine which features best describe the lowest several vibrational states of H₂⁺. Our final energies are in excellent agreement with previous calculations. © 2012 Wiley Periodicals, Inc.     

Energie des systèmes H2, HHe+ et LiH

The ground state and first electronic transitions energies are calculated by the OMSCF method for H₂, HHe⁺ and LiH. The basis consists in a Slater type orbitals of atoms and in a product of these. First transition energies are improved in comparison with minimal basis.     

Semi-empirical Xα calculations in the vibronic framework. C2H+4 and H2O+ geometries

Linear electronic-vibrational coupling constants and equilibrium geometries of the ²B₁, ²A₁, and ²B₂ states of H₂O⁺ and the ²B_3u and ²B_3g states of C₂H⁺₄ are calculated with a semi-empirical Xα theory and compared to Hartree-Fock and experimental results.     

An ab initio potential energy surface for the reaction N+ + H2 → NH+ + H

Preliminary results of ab initio unrestricted Hartree-Fock calculations for the potential energy surface for the reaction N⁺ + H₂ → NH⁺ + H are reported. For the collinear approach of N⁺ to H₂, the ³Σ^? surface has no activation barrier and has a shallow well (ca. 1 eV). For perpendicular approach (C_2v symmetry) the ³B₂ state is of high energy, the ³A₂ state has a shallow well but as the bond angle increases the ³B₁ state decreases in energy to become the state of lowest energy. Neither the collinear nor the perpendicular approaches give adiabatic pathways to the deep potential well of ³B₁ (HNH)⁺.     

SCF MO LCGO studies on the hydration of ions: The systems H+H2O,Li+H2O,and Na+H2O

The energy surfaces of the systems LiOH ₂ ⁺ and NaOH ₂ ⁺ are studied for a number of different geometries within the SCF MO LCAO framework, using a gaussian basis set to approximate the wavefunction. In the minimum energy geometry of both systems the positive ion is bound to the oxygen atom of the water molecule. The computed binding energies and bond distances are: B ^SCF(LiOH ₂ ⁺ ) = 36.0 kcal/mole, d(LiO) = 3.57 a.u., and B ^SCF(NaOH ₂ ⁺ ) = 25.2 kcal/mole, d(NaO) = 4.23 a.u., resp. The results are compared with those of H₃O⁺ and discussed in view of ion-solvent interaction in aquous solutions.It is a pleasure to thank our technical staff for the careful preparation of the input for the programs and for its enthusiastic and skilful assistance in running the computer.     

Valence-bond studies of AH2 molecules

Minimal Slater basis set calculations are reported for H₂S. The calculations used both natural and hybrid atomic orbitals. The calculations were performed at H-S-H bond angles of 90 °, 92.2 ° and 95 °. The results are compared with similar calculations on H₂O and with calculations using the molecular orbital approximation. The only definite trend found in going from H₂O to H₂S is that the importance of the SH⁺H^– structure decreases. Changes in the relative importance of covalent and ionic structures depend upon which measure of importance is used. Calculations using a set of orthogonal hybrid orbitals again find the hybrid orbitals exhibiting non-perfect following behaviour with the hybrids remaining at about the equilibrium bond angle. Localized molecular orbitals were found to move in the opposite direction to the change in the H-S-H bond angle.     

Nodal surfaces of the wave functions of the hydrogen molecule in the triplet state 3Σu +

For molecular hydrogen in the triplet state ³Σ_u ⁺, the nodal surfaces of the wave function corresponding to the minimum basis set of Slater orbitals in the Hartree—Fock approximation and those of the wave function used in calculations by the diffusion quantum Monte Carlo method were plotted and analyzed. Taking account of the condition for antisymmetrical wave function of the triplet state ³ S of He atom, the Hartree-Fock approximation in the minimum basis set of one-electron orbitals is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWF). An MWF quantum chemical method developed by the authors is outlined. The alternative nodal surfaces for H₂ (³Σ_u ⁺) a priori specified in this method are presented.     

Theoretical study of the reaction Ne + H+2 → NEH+ + H in the 2A′ ground state

A three-dimensional potential energy surface for the ²A′ ground state of the system (Ne? H₂)⁺ (²Σ⁺ in collinear geometry) has been calculated at SCF and CEPA levels. This surface describes the abstraction reaction which is endoergic by 0.57 eV (ΔH⁰₀) and has been studied recently by different experimental groups at low collision energies. Our CEPA calculations yield an endoergicity of 0.55 eV (ΔH⁰₀). The ²A′ surface has a minimum at collinear geometry with R_Ne—H = 2.29 a₀ and R_{H? H} = 2.08 a₀ and a well depth of 0.49 eV relative to Ne + H⁺₂. The effects of electron correlation on the shape of the surface and on the well depth are discussed. An analytic fit of the collinear part of the surface has been constructed based on Simon's proposal of using polynomials in the coordinates (R? R_e)/R instead of (R? R_e). The fitted potential is used for quantum mechanical scattering calculations with the finite element method (FEM ). Preliminary results for reaction probabilities for H⁺₂ in different vibrationally excited states are given and compared to the experimental results.     

Ab initio Hartree-Fock calculations of electronic wave functions for the c 3πu state of H2

Theoretical electronic wave functions, potential curves, and expectation values of some one-electron properties are given for the c³II_u state of the hydrogen molecule. The calculations are carried out by the matrix Hartree-Fock method and use a 2-center basis of Slater-type orbitals. A total energy of ?0.7292 a.u. is obtained in the best calculation. Our potential curve is reasonably consistent with that calculated by Browne, but we have examined the region of small internuclear distances (those at and below R_e for the ground state) more extensively than any previous calculation. At R ≦ 1.6 a.u. our calculated potential curve is in excellent agreement with experiment.     

Modeling the H5+ potential-energy surface: a first attempt

 Ab initio molecular electronic structure calculations are performed for H₅ ⁺ at the QCISD(T) level of theory, using a correlation-consistent quadruple-zeta basis set. Structures, vibrational frequencies and thermochemical properties are evaluated for ten stationary points of the H₅ ⁺ hypersurface and are compared with previous calculations. The features of the H₃ ⁺…H₂ interaction at intermediate and large intermolecular distances are also investigated. Furthermore, an analytical functional form for the potential-energy surface of H₅ ⁺ is derived using a first-order diatomics-in-molecule perturbation theory approach. Its topology is found to be qualitatively correct for the short-range interaction region. Received: 15 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

Comparative study of unconventional 1s basis functions for the 1Σ ground state of H2 and He

We investigated various nonstandard 1s basis functions (generalized Slater-Gaussian, ellipsoidal Gaussian, floating spherical and ellipsoidal Gaussian, rational function, Hulthén approximation, two-Slater-type orbital, generalized Guillemin–Zener function, and various noninteger-n elliptical orbitals) for approximating the ¹Σ ground state of H₂ and He₂⁺⁺. A CI trial wave-function including Σ_g-type MO's is adopted and molecular integrals are evaluated numerically. The energy improvement on the 1s STO is small except for noninteger-n orbitals which closely approach the “SCF limit”.     

A surface hopping quasiclassical trajectory study of the H2+ + H2 and (H2 + D2)+ systems

In this work we use a complete surface hopping quasiclassical trajectory method to determine cross sections for the reactions H₂⁺ + H₂ → H₃⁺ + H and the isotopic variants (H₂⁺ + D₂ and D₂⁺ + H₂). Initial translational energies ranged between 0.5 and 6 eV. The vibrational quantum number (v⁺) of the charged diatom is either 0 or 3. Comparing these results with our previous results with a partial treatment of surface hopping, we find essentially no change for v⁺ = 0 and reductions in cross sections of up to 30% for v⁺ = 3 trajectories.     

Static dipole polarizability of electronically excited molecules: H2(B1Σu+)

The dipole polarizability of H₂(B¹Σ_u⁺) is computed using extended Gaussian basis sets and Hartree-Fock, multiconfiguration Hartree-Fock, and configuration interaction wavefunctions. Electron correlation contributions are found to be significant (≈ 25%) with the largest contribution arising from angular correlation. With a full CI wavefunction, the components of the dipole polarizability were computed to be (in au): α_⊥ = 50 and α_| = 257.     

On the Search for H5O2+centered Water Clusters in the Gas Phase

In searching for H₅O₂⁺-centered water clusters, we employed vibrational predissociation spectroscopy and ab initio calculations. Structures of the clusters were characterized by the free- and hydrogen-bonded-OH stretches of ion cores and solvent molecules. Systematic examination of H⁺(H₂O)_5–7 in a supersonic expansion reveals the presence of both cyclic and noncyclic forms of H₅O₂⁺-centered water clusters. The proton transfer intermediate H₅O₂⁺(H₂O)₄ was identified, for the first time, by its characteristic hydrogen-bonded-OH stretches of the ion core at 3178 cm^?1. Also discovered at n = 7 is the H₅O₂⁺-containing five-membered ring isomer, whose existence is evidenced by the observation of a bonded-OH stretching doublet at 3544 and 3555 cm^?1 of the solvent molecules. The observations are in accord with ab initio calculations which forecast that H₅O₂⁺(H₂O)₄ and H₅O₂⁺(H₂O)₅ are, respectively, the lowest-energy isomers of protonated water hexamers and heptamers.     

Valence bond studies of AH2 molecules

Minimal basis set (STO) molecular orbital and valence-bond calculations are reported for the³ B ₁ and¹ A ₁ states of CH₂. The open-shell molecular orbital calculations used the Roothaan formulation. The valence-bond calculations used the Prosser-Hagstrom biorthogonalisation technique to evaluate the cofactors required in using Löwdin's formulae. Optimisation of geometry and orbital exponents in the molecular orbital calculation on the³ B ₁ state gave a geometry of R_C-H=2.11 a.u. and H-C-H=123.2 °. The energy obtained was ?38.8355 a.u. The molecular orbital and valencebond calculations are compared. In the valence-bond calculations the variation with bond-length and bond-angle of the configuration energies was studied. Valence bond “build-up” studies are also reported. Valence-bond calculations using hybrid orbitals instead of natural atomic orbitals showed that the perfect-pairing approximation is not as good for CH₂ as BeH₂. The nature of the lone-pair and bonding orbitals is found to be significantly different between the³ B ₁ and¹ A ₁ states. In the³ B ₁ state the 2s and 2p orbitals are fairly equally mixed between both types of orbital. However in the¹ A ₁ state the bonding orbitals have mainly 2p character and the lone pair orbitals have mainly 2s character. As was found for H₂O, the bonding hybrid orbitals do not follow the hydrogen nuclei as the bond angle varies but continue to point approximately in their equilibrium directions.     

Natural orbital analysis of nonadiabatic H2+ wave functions

Previously determined nonadiabatic wave functions for H₂⁺ (containing several hundred terms) are analyzed by using natural orbitals. This is the first time that the natural orbital concept has been applied to other than purely electronic wave functions. We find that the natural orbital expansion converges rapidly and that five or six terms are sufficient to reproduce the exact expectation values. Several plots are given of the orbitals so found and these allow a visualization of the somewhat abstract nonadiabatic wave function in a format more reminiscent of everyday quantum-mechanical pictures.     

SCF-CI studies of correlation effects on hydrogen bonding and ion hydration

Previous single-determinant Hartree-Fock studies on the equilibrium structures and stabilities of H₂ O, H₃ O⁺ as well as of the monohydrated ionic systems Li⁺ · H₂O, F^? · H₂O and the hydrogen bonded water dimer, H₂ O · HOH, are extended by large scale configuration interaction calculations including all the possible single and double excitations arising from the canonical set of Hartree-Fock molecular orbitals. The correlation energy effects on the equilibrium geometrical parameters of the systems under consideration are found to be quite small. The contributions of the correlation energy to the total binding energies of the weakly interacting composed systems are obtained to be of the order of 1 kcal/mole, leading to a considerable increase of the hydrogen bond strength in F^? · H₂O and H₂O · HOH and to a small decrease of the binding energy in Li⁺ · H₂ O. The observed strengthening of the hydrogen bonding interaction due to correlation is shown to be partly compensated by the change in the vibrational zero-point energy of the composed systems compared to the non-interacting subsystems. Approximate force constants corresponding to the intersystem vibrations in Li⁺ · H₂O, F^? · H₂ O, and H₂O · HOH are deduced from the calculated potential curve data on the SCF and the CI level of accuracy.