Gerhard Hirsch

Ab initio CI study of the stability and electronic spectrum of the HOCl molecule

Abstract The characteristics of the HOCl molecule and its various dissociation products are investigated with the help of the ab initio MRD CI method; the HOCl dipole moment as well as the structural data for the isomeric HClO species are also calculated. The results obtained for the vertical spectrum of HOCl suggest that a feature observed experimentally at 3.87 eV does not correspond to a bona fide HOCl transition; the calculations indicate further thal all low-lying excited states of this molecule are unstable relative to dissociation into OH(2Π) + Cl(2P). The enthalpy of reaction for the process O(3P) + HCl (1Σ+) → OH(2Π) + Cl(2P) is obtained to be +3.6 kcal/mole (experimental + 1.0 kcal/mole) and the heat of formation of HOCL is estimated to be −19.2 ± 3.9 kcal/mole.

Comparison of perturbatively corrected energy results from multiple reference double‐excitation configuration‐interaction method calculations with exact full configuration‐interaction benchmark values

Perturbative corrections of various types are employed in conjunction with variational configuration‐interaction (CI) treatments in order to obtain estimates of the energy eigenvalues of a large series of full CI benchmark calculations recently reported by Bauschlicher et al. It is found that the best agreement is generally obtained when an extrapolation procedure based on the results of truncated secular equations is employed to estimate the zero‐threshold multiple reference double‐excitation configuration‐interaction (MRD‐CI) energy values, after which these intermediate results are then corrected for effects of higher excitations by means of a multireference analogue of the Davidson–Langhoff correction D1. A root‐mean‐square (rms) deviation of 0.94 kcal mol−1 relative to the full CI energy results for 66 cases is obtained with this perturbative method, which has been in general use now for most of the last decade. By comparison the T=0 variational MRD‐CI energy values give a higher rms deviation of 3.1...

Non-adiabatic coupling matrix elements for large CI wavefunctions

Abstract Non-adiabatic coupling matrix elements of the type z |∂/∂ Q Ψ β > are obtained for large-scale CI wavefunctions, whereby both contributions to the matrix elements, that originating exclusively from the dependence of the CI coefficients on the nuclear variables and that related to the changes in the MOs themselves, are evaluated by the method of finite differences. comparison is made between this procedure and that which employs an analytical fit for the individual CI coefficients followed by direct differentiation. Numerical applications of the present method include the interaction of two 4 A 2 states of CH + 2 as a function of the bending nuclear coordinate, the Rydberg- valence mixing between two 3 Π u states in O 2 and the interaction of four states of 3 Π g symmetry in the C 2 molecule. The influence of the AO basis and he size of the configuration space on the results is dicussed, and it is shown that contrary to experience reported in prior investigations the part of the matrix element which results from the molecular orbital dependence on the nuclear coordinates can be as important as the corresponding CI term in certain instances.

Ab initio study of NO2. V. Nonadiabatic vibronic states and levels of the X̃ 2A1/Ã 2B2 conical intersection

We have computed 1500 nonadiabatic levels of the X 2A1/A 2B2 conical intersection of NO2, up to 18 700 cm−1. By using a bond lengths–bond angle Hamiltonian, the molecular states have been expanded in a diabatic electronic basis and in primitive, optimized, and Born–Oppenheimer vibrational basis functions. We have optimized the diabatic potentials with respect to 191 observed bands up to 10 000 cm−1, with a root mean square deviation (RMSD) of 17.8 cm−1, and 691 nonadiabatic bands up to 15 000 cm−1 and 1060 up to 17 000 cm−1 have been converged within 1.9 and 4.4 cm−1, respectively, by using 6117 basis functions per symmetry, and several states have been assigned. Up to 9500 cm−1 we have essentially found 2A1 vibrational states, some of them mixed by the Delon–Jost resonances. The nonadiabatic coupling then begins near the 2B2 (0,0,0) origin, which we assign to an electronically mixed band at 9747 cm−1, and gradually increases via the interaction between bending states of 2A1 and 2B2. The vibronic mixing ...

Spin–orbit configuration interaction study of the potential energy curves and radiative lifetimes of the low‐lying states of bismuth hydride

An ab initio configuration interaction (CI) study including the spin–orbit coupling interaction is carried out for the lowest 23 states of the bismuth hydride molecule by employing relativistic effective core potentials for the bismuth atom. The computed spectroscopic constants are in good agreement with corresponding experimental data, although there is a tendency to overestimate bond lengths by 0.05–0.10 A and to underestimate the vibrational frequencies accordingly. The B0+ excited state is found to have no dissociation barrier, and its radiative lifetime is computed to be 4.3 μs, with parallel transitions to X10+ being significantly stronger than the perpendicular B–X21 species. The experimental E0+ state is assigned as the third root of this symmetry and its potential curve possesses a dissociation barrier of 1840 cm−1. This result explains the predissociation characteristics observed for this state and is also consistent with the failure to observe emission from it when attempts are made to form it ...

Diabatic representation of the Ã2A1[Btilde]2B2 conical intersection in NH2

We report large-scale MRD-CI calculations of the adiabatic and diabatic electronic energies, dipole and quadrupole electric moments, and first- and second-derivative vibronic couplings for the A2A1 and [Btilde]2B2 states of NH2 in the region of their conical intersection. The diabatic representation has been obtained by transforming the adiabatic one under the condition that a quadrupole component has equal diagonal matrix elements in the diabatic basis. The transformation removes the singularities of the vibronic terms at the intersection locus and gives a smooth and small electronic coupling and negligible vibronic terms between the diabatic states.

Comparison of spin-orbit configuration interaction methods employing relativistic effective core potentials for the calculation of zero-field splittings of heavy atoms with a 2Po ground state

Computational strategies for the treatment of relativistic effects including spin-orbit coupling at a highly correlated level are compared for a number of heavy atoms: indium, iodine, thallium, and astatine. Initial tests with perturbation theory emphasize the importance of high-energy singly excited configurations which possess large spin-orbit matrix elements with the ground state. A contracted basis consisting of L–S CI eigenfunctions (LSC–SO–CI) is found to give an accurate representation of both spin-perturbed 2Po components as long as key np→pi* singly excited configurations are included. Comparison is made with a more extensive treatment in which all selected configurations of various L–S symmetries form the basis for the multireference–spin-orbit–configuration interaction (MR–SO–CI). Good agreement is obtained with experimental SO splittings for the In, I, and At atoms at a variety of levels of treatment, indicating that the L–S contracted SO–CI approach can be implemented quite effectively with r...

Non-empirical CI potential curves for the ground and excited states of PH and its positive ion

A series of calculated potential curves is reported for the low lying valence and (selected) Rydberg states of the PH molecule by employing the multi-reference (single- and) double-excitation CI method. A large AO basis including f functions on phosphorous is chosen for this study and up to twenty main configurations are used to generate a given MRD-CI space in the accompanying theoretical treatment. Very good agreement is obtained between calculation and experiment for a variety of spectroscopic constants and a number of predictions for electronically excited states of PH are made for cases in which no comparable empirical data are yet available. The repulsive 5∑- state is shown to be responsible for the predissociation of several states of the neutral system and is also thought to explain the failure to detect a number of low lying Rydberg states experimentally. Analogous calculations for the PH+ molecular ion have also been carried out and spectroscopic constants for this system are reported. In this c...

AB INITIO RELATIVISTIC CONFIGURATION INTERACTION CALCULATIONS OF THE SPECTRUM OF BISMUTH OXIDE : POTENTIAL CURVES AND TRANSITION PROBABILITIES

A series of configuration interaction calculations employing relativistic effective core potentials including the spin–orbit interaction is reported for the X1 2Π1/2 ground and numerous low‐lying excited states of the bismuth oxide molecule up to 30 000 cm−1. Special difficulties connected with the treatment of open‐shell systems and double‐group irreducible representations are discussed and a feasible computation scheme is developed for dealing with them. The spin–orbit interaction is found to cause a high level of mixing between a variety of low‐lying λ–s states, producing a number of avoided crossings which play a key role in determining the character of the BiO spectrum. A comparison with existing experimental data for both the energy locations and intensities of a large number of band systems indicates that the present calculations are capable of predicting Te values to an accuracy of 0.1–0.2 eV. Corresponding radiative lifetime results generally agree within a factor of 2, with the best experience o...

Theoretical study of the energies and lifetimes of the low-lying states of bismuth fluoride

Abstract A series of CI calculations has been carried out for various low-lying electronic states of the bismuth fluoride molecule by employing relativistic effective core potentials including spin-orbit effects. It is found that the lowest 0 + excited state (A0 + ) of this system contains a large contribution from the π*→σ* 3 Π λ- s state, especially at bond distances which are equal to or greater than the equilibrium value for the X 1 0 + ground state. The B0 + state at somewhat higher energy is found to contain the largest portion of the b 1 ∑ + character arising from the π 4 π* 2 configuration, in disagreement with earlier calculations by Balasubramanian who only reports a single excited state of this (0 + ) symmetry. Results of the latter study for the X 1 0 + , X 2 1 and a2 states of lower energy are in good agreement with those of the present work, However. The relatively large r e value observed for the A0 + state is quite consistent with the present theoretical description, as well as the correspondingly lower vibrational frequency compared to that of X 1 0 + . Radiative lifetimes have also been obtained for a number of excited states and the results are found to be in reasonably good agreement with recent measured data. An explanation is also provided for the anomalous μ 0 /μ 1 ratio for the A0 + → X transitions, again based on the large amount of 3 Π character in the upper state. The present data also provide a clear assignment for the A′ and A″ states recently found for this system (Ω = 1 and 0 − ) respectively. The lifetime of the X 2 1 state is computed to be 1.05 ms and a zero-field splitting of 6937 cm −1 is obtained, both of which results are in good agreement with the corresponding measured values of 1.4 ms and 6768 cm −1 . The next-lowest-energy state (a2) is predicted to have a liftime which is 80 times larger, a result which is consistent with the failure to date to observe emission bands initiating from this state.