Daniele Toffoli

Convergence of the multicenter B-spline DFT approach for the continuum

A multicenter approach for the calculation of the electronic continuum spectrum based on the B-spline functions and employing a Kohn–Sham density functional hamiltonian is introduced. The method is based on a large expansion on the origin, supplemented by a limited number of off-center functions located on the positions of the nuclei. The method has been applied to study the photoionization of Cl2, of the model system ðCOÞ 2 and of CrðCOÞ 6 . The method has proven very efficient: the convergence to the exact results is obtained with matrices which are much smaller than those involved in one center expansion calculations and the algorithm is numerically stable up to very high photoelectron energies (200 eV). The importance of the asymptotic moment basis set requirement is pointed out and rationalized with the help of a simple model. Preliminary calculations on CrðCOÞ 6 are then presented and their convergence discussed. 2002 Elsevier Science B.V. All rights reserved.

New Formulation and Implementation of Vibrational Self-Consistent Field Theory

A new implementation of the vibrational self-consistent field (VSCF) method is presented on the basis of a second quantization formulation. A so-called active terms algorithm is shown to be a significant improvement over a standard implementation reducing the computational effort by one order in the number of degrees of freedom. Various types of screening provide even further reductions in computational scaling and absolute CPU time. VSCF calculations on large polyaromatic hydrocarbon model systems are presented. Further, it is demonstrated that in cases where distant modes are not directly coupled in the Hamiltonian, down to linear scaling of the required CPU time with respect to the number of vibrational modes can be obtained. This is illustrated with calculations on simple model systems with up to 1 million degrees of freedom.

Vibrational absorption spectra calculated from vibrational configuration interaction response theory using the Lanczos method

The Lanczos method is used to efficiently obtain the linear vibrational response function for all frequencies in an arbitrary interval. The complex part of the response function gives the absorption spectrum which can subsequently be analyzed. The method provides a way to obtain global information on the absorption spectrum without explicitly converging all vibrational eigenstates of the system. The tridiagonal Lanczos matrix used to obtain the response functions needs only be constructed once for each operator. Example calculations on cyclopropene and uracil are presented.

Time dependent density functional photoionization of CH4, NH3, H2O and HF

Abstract The time dependent density functional theory (TD-DFT) and the Kohn–Sham (KS) schemes have been employed to calculate the cross section and the asymmetry parameter profiles of all the orbitals (from outer valence to core 1s) of CH 4 , NH 3 , H 2 O and HF, employing a one centre expansion of B-spline functions. The comparison between the KS and TD-DFT results shows that the screening effects play an important role even for the first row hydrides. The comparison of the TD-DFT results with the available experimental data shows that TD-DFT gives quantitative accuracy. Well defined trends are identified along the series, with respect to the nature of the ionized orbitals. Inner valence cross section is the most difficult to be described even at the TD-DFT level, and this has been attributed to shake-up processes not considered at the present level of the theory. In general, the good accuracy of the TD-DFT method and its computational economy makes it a good candidate to application to more extended and complicated molecules.

Using Electronic Energy Derivative Information in Automated Potential Energy Surface Construction for Vibrational Calculations

The availability of an accurate representation of the potential energy surface (PES) is an essential prerequisite in an anharmonic vibrational calculation. At the same time, the high dimensionality of the fully coupled PES and the adverse scaling properties with respect to the molecular size make the construction of an accurate PES a computationally demanding task. In the past few years, our group tested and developed a series of tools and techniques aimed at defining computationally efficient, black-box protocols for the construction of PESs for use in vibrational calculations. This includes the definition of an adaptive density-guided approach (ADGA) for the construction of PESs from an automatically generated set of evaluation points. Another separate aspect has been the exploration of the use of derivative information through modified Shepard (MS) interpolation/extrapolation procedures. With this article, we present an assembled machinery where these methods are embedded in an efficient way to provide both a general machinery as well as concrete computational protocols. In this framework we introduce and discuss the accuracy and computational efficiency of two methods, called ADGA[2gx3M] and ADGA[2hx3M], where the ADGA recipe is used (with MS interpolation) to automatically define modest sized grids for up to two-mode couplings, while MS extrapolation based on, respectively, gradients only and gradients and Hessians from the ADGA determined points provides access to sufficiently accurate three-mode couplings. The performance of the resulting potentials is investigated in vibrational coupled cluster (VCC) calculations. Three molecular systems serve as benchmarks: a trisubstituted methane (CHFClBr), methanimine (CH2NH), and oxazole (C3H3NO). Furthermore, methanimine and oxazole are addressed in accurate calculations aiming to reproduce experimental results.

Accurate multimode vibrational calculations using a B-spline basis: theory, tests and application to dioxirane and diazirinone

The use of B-spline basis sets is explored in the context of a vibrational program for automatic potential energy surface (PES) construction and multimode anharmonic vibrational wave function calculation. Results are compared with calculations using localized Gaussians and harmonic oscillator basis functions. Potential energy surfaces are constructed in an iterative fashion using a recently developed adaptive density-guided approach. The basis set requirements for an accurate representation of the vibrational wave functions are met by both B-spline basis sets as well as the well-known distributed Gaussian basis sets. Furthermore, the property of minimal support of the B-spline functions makes the use of B-spline basis more advantageous compared to harmonic oscillator basis functions, when combined with the adaptive procedure for PES construction used in this work. The methodology is tested for model potentials and water and subsequently applied to study vibrational states of dioxirane and diazirinone. The latter have proven to be elusive to experimental characterization and high level vibrational calculations based on accurate PES may offer a guidance for the experimental work.

Potential energy surfaces for vibrational structure calculations from a multiresolution adaptive density-guided approach: implementation and test calculations.

A multiresolution procedure to construct potential energy surfaces (PESs) for use in vibrational structure calculations is developed in the framework of the adaptive density-guided approach. The implementation of the method allows the construction of hybrid PESs with different mode-coupling terms calculated with a variety of combinations of electronic structure methods and basis sets. Furthermore, the procedure allows the construction of hybrid PESs that incorporate a variety of contributions and corrections to the electronic energy, such as infinite basis set extrapolation and core correlation effects. A full account of the procedure is given together with a rather large set of benchmark calculations on a set of 20 small molecules, from diatomics to tetratomics.

Vibrational Contributions to Indirect Spin-Spin Coupling Constants Calculated via Variational Anharmonic Approaches.

Zero-point vibrational contributions to indirect spin-spin coupling constants for N2, CO, HF, H2O, C2H2, and CH4 are calculated via explicitly anharmonic approaches. Thermal averages of indirect spin-spin coupling constants are calculated for the same set of molecules and for C2X4, X = H, F, Cl. Potential energy surfaces have been calculated on a grid of points and analytic representations have been obtained by a linear least-squares fit in a direct product polynomial basis. Property surfaces have been represented by a fourth-order Taylor expansion around the equilibrium geometry. The electronic structure calculations employ density functional theory, and vibrational contributions to indirect spin-spin coupling constants are calculated employing vibrational self-consistent-field and vibrational configuration-interaction methods. The performance of vibrational perturbation theory and various approximate variational calculations are discussed. Thermal averages are computed by state-specific and virtual vibrational self-consistent-field methods.

Application of the relativistic time-dependent density functional theory to the photoionization of xenon

Absolute photoionization cross section profiles, branching ratios and asymmetry parameters of xenon have been calculated with the time-dependent density functional theory (TDDFT) approach in a wide photon energy range, from threshold up to 740 eV. The relativistic TDDFT (RTDDFT) equations have been implemented employing a B-spline finite basis set with a non-iterative algorithm for the calculation of the response-induced potential, thus eliminating the well known convergence difficulties associated with their iterative solution. The use of the gradient-dependent LB94 exchange-correlation potential, which allows the existence of bound Rydberg states, has permitted the description, for the first time at RTDDFT level, of the autoionization resonances. Generally, an excellent reproduction of experimental results is obtained, always at least as accurate as that obtained with the computationally more expensive relativistic random phase approximation approach, making the B-spline RTDDFT formulation a very promising approach for the calculation of photoionization processes in heavy-atom systems.

Ab initio potential energy and dipole moment surfaces of the F−(H2O) complex

We present full-dimensional, ab initio potential energy and dipole moment surfaces for the F(-)(H2O) complex. The potential surface is a permutationally invariant fit to 16,114 coupled-cluster single double (triple)/aVTZ energies, while the dipole surface is a covariant fit to 11,395 CCSD(T)/aVTZ dipole moments. Vibrational self-consistent field/vibrational configuration interaction (VSCF/VCI) calculations of energies and the IR-spectrum are presented both for F(-)(H2O) and for the deuterated analog, F(-)(D2O). A one-dimensional calculation of the splitting of the ground state, due to equivalent double-well global minima, is also reported.