Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.

Several monouranium and diuranium polyhydride molecules were investigated using quantum chemical methods. The infrared spectra of uranium and hydrogen reaction products in condensed neon and pure hydrogen were measured and compared with previous argon matrix frequencies. The calculated molecular structures and vibrational frequencies were used to identify the species present in the matrix. Major new absorptions were observed and compared with the previous argon matrix study. Spectroscopic evidence was obtained for the novel complex, UH₄(H₂)₆, which has potential interest as a metal hydride with a large number of hydrogen atoms bound to uranium. Our calculations show that the series of complexes UH₄(H₂)_1,2,4,6 are stable.

The ground state properties and absorption spectra of N-benzylideneaniline (NBA) have been studied at the density functional (DFT) and at the time-dependent density functional (TD-DFT) level of the theory. The equilibrium geometries of the E and Z isomers in the ground state and their vibrational frequencies have been computed. Furthermore, the excitation energies of the lowest excited singlet and triplet states and the potential energy curves along the torsion and the inversion isomerization coordinates were evaluated. The results are discussed in light of the available experimental data.

A new method is presented, which makes it possible to partition molecular properties like multipole moments and polarizabilities, into atomic and interatomic contributions. The method requires a subdivision of the atomic basis set into occupied and virtual basis functions for each atom in the molecular system. The localization procedure is organized into a series of orthogonalizations of the original basis set, which will have as a final result a localized orthonormal basis set. The new localization procedure is demonstrated to be stable with various basis sets, and to provide physically meaningful localized properties. Transferability of the methyl properties for the alkane series and of the carbon and hydrogen properties for the benzene, naphtalene, and anthracene series is demonstrated.

The two-photon spectrum of the 2¹A_g â†� 1¹A_g transition in trans-stilbene has been calculated at the complete active space self-consistent field (CASSCF) level of theory. Energies were obtained at the complete active space second-order perturbation (CASPT2) level of theory, while the geometries of both the initial and final states were optimized at the CASSCF level. The energy and the geometry optimizations were performed using an active space of 14 electrons in 14 active Ï€ orbitals. The vibrational frequencies of both states and the two-photon transition (TPT) cross-section were calculated with a smaller active space where the two lowest Ï€ orbitals were kept inactive. A newly implemented algorithm, in the quantum chemical package Molcas was used to determine the two-photon transition intensity. This method requires only the linear response of the CASSCF wavefunction. Furthermore, the vibronic structure of this TPT was studied. The Franck-Condon factors were obtained by calculating the overlap between the vibrational states involved, which were determined from the force fields of both the initial and final states, at the CASSCF level of theory. The results are in agreement with experiment.

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 lquantum 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.