Byron H. Lengsfield

General second order MCSCF theory: A density matrix directed algorithm

A quadratically convergent general MCSCF algorithm is presented which is suitable for both ground state and excited state calculations. This method converges more rapidly than annihilation of singles techniques and is computationally very attractive as it does not involve the contraction of a potentially large Hamiltonian matrix on each interation. Sample calculations are performed on the two lowest states of the same symmetry for Li2, Li4, and BeO. For BeO, a symmetry restricted full valence MCSCF (81 configuration state functions) and a first order CI calculation using the MCSCF orbitals yielded good agreement with the experimental splitting of the two lowest 1Σ+ states. The results demonstrate that the algorithm described is capable of providing an efficient solution of large, general, MCSCF problems.

On the evaluation of nonadiabatic coupling matrix elements using SA‐MCSCF/CI wave functions and analytic gradient methods. I

A method for the efficient evaluation of nonadiabatic coupling matrix elements of the form 〈ΨI‖∂/∂RαΨJ〉 is presented. The wave functions ΨI and ΨJ are assumed to be multiconfiguration self‐consistent field (MCSCF) wave functions optimized within the state averaged approximation. The method, which can treat several states simultaneously, derives its efficiency from the direct solution of the coupled perturbed state averaged MCSCF equations and the availability of other appropriate derivative integrals. An extension of this approach to SA‐MCSCF/CI wave functions is described. Here it is shown that computational efficiencies can be achieved by exploiting analogies with analytic CI gradient methods. Numerical examples for C2v approach of Mg to H2 are presented.

Multireference CI gradients and MCSCF second derivatives

A set of simple and efficient formulas for the calculation of multireference CI gradients and MCSCF second derivatives is presented. The CI gradient formalism is extended to include a general class of references in the CI. This extension is necessary for the calculation of gradients for a commonly employed class of CI wave functions for which the reference configurations are selected from a generalized CAS MCSCF wave function. In addition, we report the first general multireference CI gradient calculations. The calculations are for the reaction Be+H2→BeH2 constrained to C2v symmetry. Structures of the reactant and transition state and the activation energy calculated at the selected reference CI level compare favorably to the full second order CI results. MCSCF second derivatives are found to be useful for the optimization of the CI structures.

On the evaluation of non-adiabatic coupling matrix elements for large scale CI wavefunctions

Abstract The implementation of a recently proposed technique for evaluating matrix elements of the form 〈Ψ J ( r ; R )|∂Ψ I ( r ; R )/t6 R α 〉 r using analytic gradient techniques is described. The Ψ K ( r ; R ) are developed from state-averaged multiconfiguration self-consistent-field/configuration interaction (CI) wavefunctions. The CI wavefunctions are determined using the shape driven graphical unitary group approach. The method is shown to be considerably more efficient than presently existing approaches based on divided differences. As an illustration of the potentialities of this approach non-adiabatic coupling matrix elements are determined for the collinear charge transfer reaction: Mg( 1 S) + FH( 1 Σ + )→MgF( 2 Σ + )+H( 2 S).

On the use of corresponding orbitals in the calculation of nonorthogonal transition moments

Full valence and first‐order CI wave functions are invariant with respect to unitary transformations among the valence orbitals. We exploit this degree of freedom and show that by transforming the valence orbitals into a corresponding orbital basis, nonorthogonal transition moment calculations become an easily managed task. Sample full valence calculations on several states of O+2 and OF are also presented.

On the evaluation of nonadiabatic coupling matrix elements for MCSCF/CI wave functions using analytic derivative methods. III. Second derivative terms

A method for the efficient evaluation of nonadiabatic coupling matrix elements of the form 〈Ψ J(r;R)‖(∂2/∂R2α) Ψ I(r;R)〉r is presented. The electronic wave functions Ψ J and Ψ I are assumed to be MCSCF/CI wave functions whose common molecular orbital basis is determined within the state averaged MCSCF (SA‐MCSCF) approximation. The method derives its efficiency by exploiting analogies with analytic CI second derivative techniques and from the first and second derivative coupled perturbed SA‐MCSCF equations. This method is compared with an existing finite difference procedure which is reformulated to take maximal advantage of analytic gradient methods.

The lower electronic states of ClOO: A computational investigation

Eight doublet and eight quartet states of ClOO were investigated by ab initio CI techniques. The potential energy surfaces of the four lowest energy doublet states of both A″ and A′ symmetry indicate that only the 1 2A″ state is bound. In contrast to the model provided by the HO2 radical, all of the excited doublet states investigated were repulsive with respect to dissociation to Cl+O2 and metastable or bound with respect to dissociation to ClO+O. The transitions to the excited states investigated span the visible and near UV spectral regions, but the transition moments indicate that they are very weak. Since the photolysis products are the same as those of the rapid thermal dissociation, photolysis is not expected to be an important atmospheric process. The soft bending potential for the 1 2A′ state and the shape of the 1 4A″ state in the entrance channel of the ClO+O → Cl+O2 reaction provide a qualitative explanation for the underprediction of the low temperature reaction rate by previous trajectory ca...

On the low‐lying states of MgO. II

Using a double zeta plus polarization basis set of Slater orbitals, full valence MCSCF (FVMCSCF) calculations were performed for the low‐lying states of MgO. For each state the FVMCSCF calculations were used to identify the important configurations which are then used in an MCSCF calculation and subsequently as references in a single and double excitation CI calculation. This approach is found to treat all states equivalently, with the maximum error in the computed Te’s and Re’s of 800 cm−1 and ∼0.03 , respectively. The b 3Σ+ state which has yet to be characterized experimentally is predicted to have a Te of ∼8300 cm−1 and a bond length of 1.79 A. A spectroscopic analysis of the potential curves indicates that their shapes are in quite reasonable agreement with the range of experimental results.

Theoretical study of the radiative lifetime for the spin‐forbidden transition a 3Σ+u→X 1Σ+g in He2

The radiative lifetime for the spin‐forbidden, dipole‐allowed transition a3Σ+u→X1Σ+g in neutral He2 was calculated. This transition is assumed to derive its intensity by spin–orbit (SO) induced couplings which are treated using first‐order perturbation theory. The first‐order corrections to the wave functions are calculated directly in the configuration state function (CSF) basis by solving a system of linear equations given by first‐order perturbation theory for the perturbation to the zeroth‐order X1Σ+g and a3Σ+u wave functions. This approach eliminates the need to solve explicitly for many eigenstates of the unperturbed Hamiltonian which would be required if the spectral representation for the perturbed wave function were used. The results show a rapidly changing electric transition dipole moment as a function of internuclear seperation, R(He–He), over the bound region of the a3Σ+u potential energy curve, i.e., R(He–He)=1.5 to 4.0 bohr. The transition dipole reaches a maximum near the small barrier to ...

On the Mg(3P)–He(1S) interaction using SA‐MCSCF/ICF‐CI wave functions

State averaged‐multiconfiguration self‐consistent‐field (SA‐MCSCF)/interacting correlated fragment‐configuration interaction (ICF‐CI) wave functions developed from an extended basis of Slater type orbitals are used to determine the portion of the nonrelativistic Born–Oppenheimer 3Σ+ and 3Π potential energy curves (PEC’s), relevant to fine structure changing collisions in the system Mg(3P)‐He(1S). Using the finite perturbation method the parallel and perpendicular polarizabilities of Mg(3P) at the SA‐MCSCF level are found to be α∥ =120 a.u.3 and α⊥ =84.5 a.u.3 The PEC’s exhibit the requisite (weak) long‐range attraction, with E(3Σ+) α⊥. The 3Σ+ and 3Π curves, which are rigorously degenerate at R(Mg–He)=∞, cross near R(Mg–He)=14 a.u. The 3Σ+ curve exhibits a very shallow minimum (∼1.5 cm−1) near R(Mg–He)=13.7 a.u. while a deeper minimum ∼16 cm−1 is found for the 3Π curve near R(Mg–He)=7.9 a.u. The effects of spin‐orbit coupling are incorporated in a semiempirical manner...