Search

New basis sets of the atomic natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically symmetric atoms. These calculations include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the experimental values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.

The lower electronic states of the molecule PbO have been studied using a newly developed basis set of the atomic natural orbital (ANO) type. The method includes scalar relativistic effects through the use of a Douglas-Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). Spin-orbit coupling is added a posteriori by means of the RASSCF state interaction (RASSI) method, with all electronic states originating from Pb(s(2)p(2),P-3, D-1, S-1) and O(s(2)p(4), (3)p) included in the Cl expansion. Computed spectroscopic constants for the 0(+) ground level are: R-e = 1.926(1.922)angstrom, D-0 = 4.00(3.83) eV, omega(e), = 723(721) cm(-1), with experimental data within parentheses. Corresponding data for the 11 lowest excited levels are also presented. The dipole moment for the ground state has been computed to be 1.73(1.83) a.u. using finite field perturbation theory. The effect of spin-orbit coupling is to reduce the value with 0.03 a.u. This illustrative calculation shows that an approach that adds scalar relativistic effects to a nonrelativistic wave function, and treats spin-orbit coupling by a configuration interaction method, can be used to obtain accurate properties also for molecules containing heavy main group elements. (Less)

Several recently proposed zeroth-order Hamiltonians for open-shell perturbation theory include terms non-linear in the number operators. These Hamiltonians are, in general, described as a correction, which is to be added to a conventional Fock operator. It has previously been pointed out that one of these corrections, OPT2, gives energies for twisted ethylene that vary with rotation among the singly occupied orbitals, and in a recent article a new operator, called the IOPT operator, was proposed as a remedy. However, this proposed cure is worse than the disease, since the resulting theory has an unacceptably large size consistency error. The properties of a molecule will depend upon the properties of infinitely removed molecules, and this unphysical action at distance is of the same or larger order of magnitude as the proposed correction. The problem is demonstrated by the singlet-triplet splitting of methylene, which varies by 5.5 kcal/mol when other atoms are placed at 1000.0 α 0 distance.

The lowest-energy band of the electronic spectrum of pyrrole has been studied with vibrational resolution by using multiconfigurational second-order perturbation theory (CASPT2) and its multistate extension (MS–CASPT2) in conjunction with large atomic natural orbital-type basis sets including Rydberg functions. The obtained results provide a consistent picture of the recorded spectrum in the energy region 5.5–6.5 eV and confirm that the bulk of the intensity of the band arises from a ππ∗ intravalence transition, in contradiction to recent theoretical claims. Computed band origins for the 3s,3p Rydberg electronic transitions are in agreement with the available experimental data, although new assignments are suggested. As illustrated in the paper, the proper treatment of the valence–Rydberg mixing is particularly challenging for ab initio methodologies and can be seen as the main source of deviation among the recent theoretical results as regards the position of the low-lying valence excited states of pyrrole. serrano@uv.es ; merchan@uv.es

This article presents a numerical quadrature intended primarily for evaluating integrals in quantum chemistry programs based on molecular orbital theory, in particular density functional methods. Typically, many integrals must be computed. They are divided up into different classes, on the basis of the required accuracy and spatial extent. Ideally, each batch should be integrated using the minimal set of integration points that at the same time guarantees the required precision. Currently used quadrature schemes are far from optimal in this sense, and we are now developing new algorithms. They are designed to be flexible, such that given the range of functions to be integrated, and the required precision, the integration is performed as economically as possible with error bounds within specification. A standard approach is to partition space into a set of regions, where each region is integrated using a spherically polar grid. This article presents a radial quadrature which allows error control, uniform error distribution and uniform error reduction with increased number of radial grid points. A relative error less than 10−14 for all s-type Gaussian integrands with an exponent range of 14 orders of magnitude is achieved with about 200 grid points. Higher angular l quantum numbers, lower precision or narrower exponent ranges require fewer points. The quadrature also allows controlled pruning of the angular grid in the vicinity of the nuclei.

It has recently been shown that Moller-Plesset perturbation calculations may diverge for single configuration dominated systems in extended basis sets. We examine the origin of this divergence using the neon atom as a test example. The lowest energies for total symmetric states are calculated for values of the perturbation parameter strength zϵ[−1, 1]. For z ≈ (−0.9)−(−0.8) avoided crossings between the Hartree-Fock configuration dominated state and states dominated by quintuple and higher excitations are observed. The origin of the divergence is therefore “back door” intruder states, that are highly excited relative to the Hartree-Fock state.

The complete active space (CAS) SCF method in conjunction with multiconfigurational second-order perturbation theory (CASPT2) has been used to study the electronic spectra of a large number of molecules. The wave functions and the transition properties are computed at the CASSCF level, while dynamic correlation contributions to the excitation energies are obtained through the perturbation treatment. The methods yield energies, which are accurate to at least 0.2 eV, except in a few cases, where the CASSCF reference function does not characterize the electronic state with sufficient accuracy. The applications comprise: the polyenes from ethene to octatetraene (cis- and trans-forms); a number of cyclic pentadienes; norbornadiene; benzene, phenol, phosphabenzene, and the azabenzenes; free base porphin; and the nucleic acid base monomers cytosine, uracil, thymine, and guanine. Finally, the photochemistry of the molecules aminobenzonitrile (ABN) and dimethylaminobenzonitrile (DMABN) has also been studied, in particular the double fluorescence that occurs in DMABN. Taken together these studies comprise large amounts of new spectroscopic data of high accuracy, which either confirm existing assignments of experimental data or lead to new predictions and qualitative as well as quantitative understanding of a large number of electronic spectra. Most studies are restricted to ground state geometries (vertical energies), but in a few cases (octatetraene, ABN, and DMABN) also excited state geometries have been determined, thus yielding 0-0 transition energies and emission spectroscopic data.

The exercises in this book have been selected from those used at the European Summer-school in Quantum Chemistry, with a few additions. The proveniences of these exercises are sometimes unclear; however, we gratefully acknowledge contributions, work and communications with Lars Pettersson, Jeppe Olsen, Trygve Helgaker, Peter Taylor, Bjorn Roos, and Nicholas Handy. To you, and to any of the inevitably forgotten problem-text authors, thank you very much, and forgive us the liberties taken.

The performance of multiconfigurational second order perturbation theory has been analyzed for the description of the bonding in CuH, Cu2, NiH, and Ni2. Large basis sets based on atomic natural orbitals (ANOS) were employed. The effects of enlarging the active space and including the core‐valence correlation contributions have also been analyzed. Spectroscopic constants have been computed for the corresponding ground state. The Ni2 molecule has been found to have a 0+g ground state with a computed dissociation energy of 2.10 eV, exp. 2.09 eV, and a bond distance of 2.23 Å. The dipole moments of NiH and CuH are computed to be 2.34 (exp. 2.4±0.1) and 2.66 D, respectively. pou@uv.es ; merchan@uv.es ; nebot@uv.es

A mathematical object is defined by a loose analogy to objects in the syntax of ordinary languages. The objects are those parts of a formula that are combined to form other objects, substituted for other objects, or mapped onto other objects, while the “verbs” are designators of how to combine, or which mapping to apply. Obviously, this classification depends on context, upon the usage of the formula, but also on the interpreters attitude: One man’s operations are another man’s objects.

Modern ab initio quantum chemical methods have been employed to compute excitation energies and transition moments of the nucleic acid base monomers cytosine, uradil, thymine, adenine, and guanine for the lower ir electron excited states. Full configuration interaction is allowed among the (pi)-electrons and the orbitals are optimized individually for each excited state. The multi-configurational self-consistent field method used allows full relaxation of both the (sigma)- and the (pi)-orbitals and includes correlation between the it-electrons. Basis sets of double-zeta quality have been used in these preliminary investigations. The calculated values for oscillator strengths and transition moment directions are in good agreement with experiment, where such comparisons can be made. The calculated excitation energies are, however, often too large due to the lack of (sigma)-(pi) correlation terms in the wave function.

A multiconfigurational approach to the quantum chemistry of heavy element compounds is described. Relativistic effects are treated in two steps, both based on the Douglas–Kroll Hamiltonian. Scalar terms are included in the basis set generation and are used to determine wave functions and energies, which include static (through the use of the CASSCF method) and dynamic correlation effects (using multiconfigurational perturbation theory, CASPT2). Spin–orbit coupling is treated in a configuration interaction model, which uses CASSCF wave functions as the basis states. The method is shown to work for all atoms of the periodic system, with the possible exception of the heavier fifth row main group atoms. Illustrative results are presented for the main group atoms (spin–orbit splittings), the electronic spectrum of the iridium atom, the ground state of Tl2 and Pb2, and for the electronic spectrum of PbO. Some applications in actinide chemistry are also discussed.

Ab initio complete active space (CAS) SCF and contracted CI calculations have been carried out for all valence and the lower Rydberg states of the benzene molecule. The CASSCF active space comprised 12 π‐type molecular orbitals and the basis set included both polarization functions and diffuse functions in order to describe properly both valence and Rydberg type orbitals. Resulting excitation energies for the Rydberg states are in close agreement with experiment. CASSCF results for the valence states give errors ranging from 0.0 for the covalent states up to more than 1.0 eV for the most ionic states. Inclusion of σ–π correlation effects reduces the errors in the ionic states to less than 0.6 eV. The 1E1u state is computed to lie 7.4 eV above the ground state with a transition moment of 1.70 a.u., experimental values are 7.0 eV and 1.61 a.u., respectively.

An efficient scheme for calculating one- and two-electron transition density matrices for two wave functions is described. The method applies to CAS (complete active space) wave functions and certain multireference CI expansions. The orbital sets of the two wave functions are not assumed to be equal. They are transformed to a biorthonormal basis, and the corresponding transformation of the CI coefficients is carried out directly, using the one-electron coupling coefficients.

An alternative to the linear CI expansion is presented, which is based on the spectral resolution of the double excitation CI coefficients arranged as a symmetric matrix. The resulting energy expression is a quartic function of the new variables, where the double excitation operator is given as T2 = ∑IMωI(dI)2, where ddI is a single excitation operator: dI =∑Ia,dIiaEai. Since M is a small number, the number of variables is reduced considerably compared to normal SDCI, with only little loss in accuracy. A program for non-linear CI calculations has been written and is presented with results for H2O and N2. The method can easily be extended to include orbital optimization and cluster terms in the wavefunction, still yielding a fully variational approximation to the Schrodinger equation.

A method is described to calculate the matrix elements of one- and two-electron operators for CASSCF wavefunctions employing individually optimized orbitals. The computation procedure is very efficient, and matrix elements between CAS wavefunctions with up to a few hundred thousand configurations are easily evaluated. An implementation of this method is presented, which sets up and solves the Hamiltonian secular problem in a basis of independently optimized CASSCF wavefunctions. In the program, the only restriction imposed is that the AO basis set and the number of active orbitals is the same for all states. The method is illustrated by calculations on π-excited states of some aromatic molecules.

Preliminary results show the feasability of extending modern basis set MCSCF methods to apply also to numerical calculations. Rectangular finite elements are used as one-electron basis. Quadratic convergence is demonstrated for atoms, fast linear convergence for diatomics, with quaranteed convergence to a energy minimum.