Gaussian type orbital basis sets for the calculation of continuum properties in molecules: The photoionization cross section of H2 (original) (raw)
Physical Review A, 1998
The now well-established L2 techniques applied to the description of the electronic continuum of small molecules and generally implemented with suitable oscillating basis sets are here adapted and used in connection with Gaussian type orbital (GTO) functions. As a test, a K-matrix approach associated with extended sets of GTOs is employed to compute with satisfactory accuracy partial wave phase shifts and both the integral and differential photoionization cross sections of the hydrogen molecule. It is apparently possible to greatly extend the range of applicability of the usual L2 techniques beyond the limited set of molecular systems amenable to the one center expansion approximation.
Chemical Physics, 2000
The integral and the differential cross sections of the valence one-photon ionization of C H are computed in the 2 2 2 Ž . Random Phase Approximation using large L basis sets of Gaussian Type Orbitals GTO's and a K-matrix based technique. The use of special Polynomial Spherical GTO's allows an adequate representation of the short range part of the orbitals lying in the electronic continuum. Ionization channels originating from the 1p , 3s , 2s and 2 s occupied orbitals are u g u g considered, both in Separated and Interacting Channel approaches. An accurate account of the effect of the interaction between the different ionization channels is found to be mandatory in order to reproduce some of the features observed in photoelectron experimental spectra. q 2000 Elsevier Science B.V. All rights reserved.
An efficient basis set representation for calculating electrons in molecules
Molecular Physics, 2016
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one-and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N )) multiplication operations, not O(N 4 ), where N is the number of basis functions; N = n 3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one-(He + , H + 2 ), two-(H2, He), ten-(CH4) and 56-electron (C8H8) systems.
The Journal of Chemical Physics, 2013
Phys. 130, 064104 (2009)] we introduced a new L 2 ab initio method for the calculation of total molecular photoionization cross-sections. The method is based on the ab initio description of discretized photoionized molecular states within the many-electron Green's function approach, known as algebraic diagrammatic construction (ADC), and on the application of Stieltjes-Chebyshev moment theory to Lanczos pseudospectra of the ADC electronic Hamiltonian. Here we establish the accuracy of the new technique by comparing the ADC-Lanczos-Stieltjes cross-sections in the valence ionization region to the experimental ones for a series of eight molecules of first row elements: HF, NH 3 , H 2 O, CO 2 , H 2 CO, CH 4 , C 2 H 2 , and C 2 H 4. We find that the use of the second-order ADC technique [ADC(2)] that includes double electronic excitations leads to a substantial systematic improvement over the first-order method [ADC(1)] and to a good agreement with experiment for photon energies below 80 eV. The use of extended second-order ADC theory [ADC(2)x] leads to a smaller further improvement. Above 80 eV photon energy all three methods lead to significant deviations from the experimental values which we attribute to the use of Gaussian single-electron bases. Our calculations show that the ADC(2)-Lanczos-Stieltjes technique is a reliable and efficient ab initio tool for theoretical prediction of total molecular photo-ionization cross-sections in the valence region.
Chemical Physics, 1994
The photoionization cross sections and asymmetry parameters of the four main valence ionization processes in H2S, corresponding to the formation of respectively 2b,, 5a,, 2bZ and 4a, holes, have been calculated in the random phase approximation (RPA) . By resorting to a recently proposed computational procedure, based on the K-matrix technique, the WA equations for the four coupled ionization channels have been projected on a basis set of Lz functions and solved, at any excitation energy above the ionization threshold, in a way that allows to recover the electronic continuum degeneracy. 0301-0104/94/$07.00 0 1994 Elscvier Science B.V. All rights reserved SSDIO301-0104 (94)00032-6 1. Cacdli et al. /Chemical Physics 184 (1994) 213-223
Accurate Gaussian basis sets for atoms from H to Ba were obtained by means of the generator coordinate Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations (GWHF). The discretization of the GWHF equations in this procedure is based on a mesh of points not equally distributed in contrast with the original GCHF method. The results of atomic Hartree-Fock energies demonstrate the capability of these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the maximum error found when compared to numerical values is only 0.788 mHartree for indium. Some test calculations with the B3LYP exchange-correlation functional for N2, F2, CO, NO, HF, and HCN show that total energies within 1.0 to 2.4 mHartree compared to the cc-pV5Z basis sets are attained with our contracted bases with a much smaller number of polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required only a tiny fraction of the computational time when compared to B3LYP/cc-pV5Z calculations
Chemical Physics, 1984
Partial and total photoionisation cross sections for H 2 0 and NH 3 are evaluated employing a discrete basis set and using the Stieltjes imaging technique to obtain the continuum oscillator strength densities. Bound and continuum electronic eigenfunctions at the ground-state equilibrium geometry are described in the independent-channel approximation using large basis sets of integrable functions centered on the heavy atom. Besides the usual STO functions, hydrogenic Rydberg functions and diffuse oscillatory functions are used in order to improve the description of the bound excited orbitals and of'the continuum orbitals respectively. The generally good agreement with recent experimental measurements and previous theoretical works for H 2 0 confirms that the one-center expansion is adequate to describe photoionisation processes in molecules having the electron charge largely localized around the heavy atom. The single-channel approximation provides satisfactory photoionisation cross sections although it appears very likely that multi-channel effects should be taken into account to improve agreement with experimental data. Results for the discrete region of the spectra are also presented.
Hybrid Gaussian–B-spline basis for the electronic continuum: Photoionization of atomic hydrogen
Physical Review A, 2014
As a first step towards meeting the recent demand for new computational tools capable of reproducing molecular-ionization continua in a wide energy range, we introduce a hybrid Gaussian-B-spline basis (GABS) that combines short-range Gaussian functions, compatible with standard quantum-chemistry computational codes, with B splines, a basis appropriate to represent electronic continua. We illustrate the performance of the GABS hybrid basis for the hydrogen atom by solving both the time-independent and the time-dependent Schrödinger equation for a few representative cases. The results are in excellent agreement with those obtained with a purely B-spline basis, with analytical results, when available, and with recent above-threshold ionization spectra from the literature. In the latter case, we report fully differential photoelectron distributions which offer further insight into the process of above-threshold ionization at different wavelengths.