ALBERT

Notes: Expressions for the analytic energy gradients and the nonadiabatic derivative couplings are derived for the effective valence shell Hamiltonian theory (a variant of degenerate/quasidegenerate many-body perturbation theory) using the diagonal and off-diagonal Hellmann–Feynman formulas and a generalized set of coupled perturbed Hartree–Fock equations to evaluate the derivatives of the molecular orbitals. The method is designed for efficiently treating the energy derivatives and nonadiabatic couplings for several states simultaneously. The generalized coupled perturbed Hartree–Fock equations arise because the reference space orbitals are optimized for simultaneously describing the ground and excited states, a feature lost with the traditional partitioning where the virtual orbitals provide a poor choice for representing the low lying states. A simple correspondence emerges between the new generalized coupled perturbed Hartree–Fock and the traditional coupled-perturbed Hartree–Fock methods enabling the use of the former with straightforward modifications. The derivatives of the second and higher order portions of the effective Hamiltonian are readily obtained using a diagrammatic representation that will be described elsewhere. © 1998 American Institute of Physics.

Notes: We have applied the highly correlated ab initio effective valence shell Hamiltonian (Hv) method to determine the energy difference between the cyclic and linear isomers of propynlidyne (C3H). Calculations are also described for the vertical excitation energies, ionization potentials, electron affinities, dipole moments, oscillator strengths, and some harmonic vibrational frequencies, which are all determined using the third order Hv method. Computations at both the experimental and theoretically optimized geometries are used to illustrate the geometrical dependence of the computed properties. The Hv optimized geometry is obtained using a two-configurational reference function describing the two dominant resonance structures. Our third-order vertical excitation energy to the lowest excited state in the cyclic isomer, dipole moments, and ground state isomer conformational energy difference are all in good agreement with experiment and with other highly correlated many-body calculations. The computations for higher excited states and for ionization potentials, electron affinities, and oscillator strengths represent the first reports of these quantities. An explanation is provided for persistent theoretical difficulties in computing b1 bending vibrational frequencies of the cyclic isomer. © 2000 American Institute of Physics.

Notes: The ab initio effective valence shell Hamiltonian (Hυ) method is used to compute the excitation energies and oscillator strengths for resonance transitions in Mg-like ions, as well as their lowest ionization potentials. The computed excitation energies and oscillator strengths from the Hυ method are in excellent agreement with experiment and with the best values from other high level correlated computations, where available. Several previous discrepancies between theory and experiment are now removed. The present work also investigates the dependence of the calculated Hυ oscillator strengths on the nature and choice of the valence orbitals and provides a comprehensive study of the convergence of Hυ calculations with respect to the enlargement of the valence space. © 1998 American Institute of Physics.

Notes: High order perturbative computations for the lowest lying singlet states of the CH2 molecule are used to analyze the efficacy of various multireference perturbation methods (MRPTs). Whereas traditional Möller–Plesset MRPT calculations produce divergent perturbation expansions, the effective Hamiltonian Hv and intermediate Hamiltonian Hint approaches produce well behaved expansions for well-chosen reference spaces. The three methods are compared to assess their convergence properties, the sources of divergence when appropriate, their accuracy when truncated at low orders, and their behavior when applied in conjunction with large reference spaces. The analysis of the sources of divergent or slowly convergent perturbation expansions provides insights into necessary ingredients for useful MRPT methods as well as into possible approaches for further improving these methods. Calculations are also presented for a simple problem whose divergent traditional MRPT perturbation expansion mimics that commonly encountered when these methods are applied in transition state or bond breaking regions of potential surfaces. © 1997 American Institute of Physics.

Notes: High order perturbation energies are computed for excited 1A1 states of BeH2 at geometries near the Be→H2 symmetric insertion transition state. The equations of multireference perturbation theory are solved through 30th order to study the difficulties in selecting the appropriate zeroth order Hamiltonian, orbitals, orbital energies, and reference functions for the computations of smooth molecular potential energy surfaces. The origin of the perturbative divergence produced by Möller–Plesset and Epstein–Nesbet partitionings is analyzed using a conceptually simple two-state model constructed using one state each from the reference and orthogonal spaces. The optimized zeroth order partitioning scheme (OPT) for double reference space computations with configurations 1a122a123a12 and 1a122a121b22 produces a truly convergent perturbation expansion through 30th order. The OPT energies are accurate in low orders as compared to the exact (197 dimensional) solution within the basis. The forced valence orbital degeneracy partitioning method (FD) also generates a truly convergent expansion for the same double reference space calculation, with slightly poorer low order energies than the OPT scheme. The BeH2 system facilitates the consideration of larger reference spaces (constructed using three through six orbitals) where the FD method produces highly accurate energies in low orders despite the asymptotic nature of the FD perturbation expansion. The "delayed'' perturbative divergence behavior with the FD partitioning scheme (for large reference spaces) is shown to occur due to the incorrect ordering between the zeroth order energies of some reference and complementary space levels. © 1997 American Institute of Physics.

Notes: The ab initio effective valence shell Hamiltonian (Hv) is used to compute the low lying vertical excitation energies and oscillator strengths for ethylene, trans-butadiene, benzene and cyclobutadiene. Calculated excitation energies and oscillator strengths of ethylene, trans-butadiene and benzene to various valence and Rydberg states are in good agreement with experiment and with values from other highly correlated computations. The present work further investigates the dependence of Hv computations on the nature and choice of the molecular orbitals and provides a comprehensive study of the convergence with respect to the enlargement of the valence space. Minimal valence space Hv computations yield very accurate estimates of the excitation energies for the low lying excited triplet states and are slightly poorer (a deviation of ≤0.5 eV from experiment) for low lying excited singlet states. More accurate low lying singlet state excitation energies are achieved by slightly enlarging the valence space to include Rydberg functions. The computed oscillator strengths from the Hv method are in excellent agreement with experiment and compare favorably with the best theoretical calculations. A very quick estimation of the transition dipoles and oscillator strengths may be obtained from second order Hv computations. The accuracy of these calculations is almost as good as those from the more expensive third order Hv computations and far superior to those from other quick methods such as the configuration interactions singles technique. Although no experimental data are available for the excitation energies and oscillator strengths of cyclobutadiene, our predicted values should be quite accurate and should aid in observing its π→π* transitions. We also provide the first correlated computations of oscillator strengths for excited→excited singlet and triplet transitions. © 1997 American Institute of Physics.

Notes: We describe a computationally efficient ab initio many-body method that can be used as a "packageable approximation" for computing excited state properties for small to large molecular systems, including those of multiconfigurational character. The method is based on first order multi-reference many-body perturbation theory (MR-MBPT), where the unoccupied valence orbitals are obtained by using an extension of Huzinaga's improved virtual orbital (IVO) generation technique. Because the method employs a complete active space (CAS) which contains singly, doubly, and higher excited state configurations with respect to the zeroth order ground state configuration, the approach (IVO-CASCI) is capable of providing a more accurate description of the excited states than the widely used packageable configuration interaction with singles (CIS) at a fraction of computational labor. Moreover, unlike the CASSCF approach this IVO-CASCI method does not require iterations and therefore is more computationally efficient and free of the convergence problems that sometimes plague CASSCF calculations with increasing size of the CAS. Excited state energies are compared with energies from the widely used CIS, MCSCF, and CASSCF methods for the C2H+, C2H, CaOH, cyclic-C3H, and porphin molecules. The computed IVO-CASCI transition energies are generally more accurate than the CASSCF. For example, our energies are comparable to CIS energies for CaOH and porphin, while the C2H+, C2H, and C3H IVO-CASCI transition energies are more accurate than the CASSCF and CIS energies. © 2001 American Institute of Physics.

Notes: The minimum basis set hydrogen rectangular system (HRS), consisting of four hydrogen atoms arranged in a rectangle, is examined using a variety of partitionings of the Hamiltonian H for high order single and double reference perturbation computations. The potential energy surface is mapped out over a range of geometries in which the length L of one side of the rectangle is varied. Several criteria are derived governing the necessary conditions for perturbative convergence of two-state systems, and these criteria are useful in explaining the behavior of the HRS for the range of geometries and partitioning methods investigated. The divergence caused by intruder states, observed by Zarrabian and Paldus [Int. J Quantum Chem. 38, 761 (1990)] for the nondegenerate, double reference space perturbation expansions at L=3.0 a.u. with traditional partitioning methods, is shown to correspond to avoided crossings with negative real values of the perturbation parameter—backdoor intruder states. These intruder state induced divergences result from too small zeroth order energy differences between the high lying reference space state and an orthogonal space intruder state whose identity depends on the partitioning method. Forcing the valence orbitals to be degenerate enlarges these zeroth order energy differences and, thus, yields a convergent perturbative expansion for L=3.0 a.u.The convergent or divergent behavior of all the partitioning method computations and the locations of their avoided crossings are accurately predicted by using two-state models composed of the high lying reference space state and the intruder state. A partitioning method is introduced in which the zeroth order state energies are selected to optimize the convergence in low orders of the perturbation expansion. This optimization method yields perturbative convergence which is both rapid and free of intruder state for geometries between L=2.0 and 3.0 a.u. The divergent behavior for various partitioning methods at L=5.0 a.u., also observed by Zarrabian and Paldus, is caused by one or more orthogonal space states and the high lying reference space state that are strongly coupled and have close expectation values of H. The two-state model illustrates why no partitioning choice with a double reference space can yield a satisfactory rate of perturbative convergence for L=5.0. Therefore, the entire potential energy surface is treated using more than one reference space: a double reference space for L≤3.0 a.u. and a single reference space for L(approximately-greater-than)3.0 a.u. The entire potential surface of interest, which is generated with the optimized partitioning method and the two different reference spaces, is very accurate by third order, with eigenvalues for all geometries considered differing from the FCI by no more than 1 kcal/mol. © 1995 American Institute of Physics.

Notes: The correlated, size extensive ab initio effective valence shell Hamiltonian (HV) method is used to compute three-dimensional potential energy surfaces for the ground and several excited electronic states of the H2S molecule. A single calculation of the HV simultaneously generates all states of interest as well as ionization potentials. Particular emphasis is placed on the two lowest 1 1A″ excited surfaces (one valencelike and the other Rydberg-type) that are involved in recent experiments probing nonadiabatic photodissociation processes. Supplementary effective operator calculations generate three-dimensional surfaces of dipole moments and transition dipole matrix elements, but emphasis is placed on the transition dipoles relevant to the dissociation process. Comparisons to both experiment and previous calculations for this system support the ability of multireference perturbation methods to describe global potential energy surfaces for open shell systems. We discuss the implication of our calculations for interpreting and reproducing experimental observations of the dissociation dynamics. © 1996 American Institute of Physics.