Optimal basis set for electronic structure calculations in periodic systems

An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a single (i.e., common to all points in the Brillouin zone) basis set for the expansion of the electronic orbitals. Considerations from k.p-approximation theory help to understand the efficiency of the method. The accuracy and the convergence properties of the method as a function of the optimal basis set size are analyzed for a test calculation on a 16-atom Na supercell.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Total and single differential cross sections for simple resonant collisions using a fully orthonormal continuum-distorted-wave basis

Simple electron capture processes are studied using an orthonormal two state continuum-distorted-wave (CDW) basis. The suitability of the basis set is tested by comparing predictions for total and differential cross sections with available experimental data. Overall good agreement is obtained and the authors conclude that a relatively small CDW basis set may be suitable to model a wide variety of low-energy collisions if the members of this extended set are astutely chosen.

Conformations, vibrational frequencies and Raman intensities of short-chain fatty acid methyl esters using DFT with 6-31G(d) and Sadlej pVTZ basis sets

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of three short-chain fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n = 3-5). In all three FAMEs, the lowest energy conformer has a simple 'all-trans' structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. One result of this is that the solid samples we studied do not appear to consist entirely of the lowest energy conformer. Indeed, to account for the 'extra' bands that were observed in the Raman data but were not predicted for the all-trans conformer, it was necessary to add-in contributions from other conformers before a complete set of vibrational assignments could be made. Provided this was done, the agreement between experimental Raman frequencies and 6-31G(d) values (after scaling) was excellent, RSD = 12.6 cm(-1). However, the agreement between predicted and observed intensities was much less satisfactory. To confirm the validity of the approach followed by the 6-3 1 G(d) basis set, we used a larger basis set, Sadlej pVTZ, and found that these calculations gave accurate Raman intensities and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment. In addition, the unscaled Sadlej pVTZ, and the scaled 6-3 1 G(d) calculations gave the same vibrational mode assignments for all bands in the experimental data. This work provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-3 1 G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the much more CPU-expensive Sadlej pVTZ basis set calculations.

Reduced-size polarized basis sets for calculations of molecular electric properties. III. Second-row atoms

Reduced-size polarized (ZmPolX) basis sets are developed for the second-row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced-size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.

Towards a spectroscopically accurate set of potentials for heavy hydride laser cooling candidates: effective core potential calculations of BaH

BaH (and its isotopomers) is an attractive molecular candidate for laser cooling to ultracold temperatures and a potential precursor for the production of ultracold gases of hydrogen and deuterium. The theoretical challenge is to simulate the laser cooling cycle as reliably as possible and this paper addresses the generation of a highly accurate ab initio $^{2}\Sigma^+$ potential for such studies. The performance of various basis sets within the multi-reference configuration-interaction (MRCI) approximation with the Davidson correction (MRCI+Q)is tested and taken to the Complete Basis Set (CBS) limit. It is shown that the calculated molecular constants using a 46 electron Effective Core-Potential (ECP) and even-tempered augmented polarized core-valence basis sets (aug-pCV$n$Z-PP, n= 4 and 5) but only including three active electrons in the MRCI calculation are in excellent agreement with the available experimental values. The predicted dissociation energy De for the X$^2\Sigma^+$ state (extrapolated to the CBS limit) is 16895.12 cm$^{-1}$ (2.094 eV), which agrees within 0.1$\%$ of a revised experimental value of <16910.6 cm$^{-1}$, while the calculated re is within 0.03 pm of the experimental result.

Energy levels and transition probabilities for nitrogen-like Fe xx

Energies of the 700 lowest levels in Fe XX have been obtained using the multiconfiguration Dirac-Fock method. Configuration interaction method on the basis set of transformed radial orbitals with variable parameters taking into account relativistic corrections in the Breit-Pauli approximation was used to crosscheck our presented results. Transition probabilities, oscillator and line strengths are presented for electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1) transitions among these levels. The total radiative transition probabilities from each level are also provided. Results are compared with data compiled by NIST and with other theoretical work.

Multi-state CDW approximation to electron capture during slow p-H collisions

The first complete multi-state CDW close coupling calculations which use a fully normalized basis set are performed. The results obtained at impact energies in the region of 10 keV for total and n = 2 capture cross sections are in reasonably good accord with experiment despite the fact that only the ground states of both species and the n = 2 states of the projectile are incorporated into the model. The theory has significant advantages over other atomic and molecular expansions which may require extensive bases to obtain similar accuracy.

Prediction of the formation and stabilities of energetic salts and ionic liquids based on ab initio electronic structure calculations

A computational approach to predict the thermodynamics for forming a variety of imidazolium-based salts and ionic liquids from typical starting materials is described. The gas-phase proton and methyl cation acidities of several protonating and methylating agents, as well as the proton and methyl cation affinities of many important methyl-, nitro-, and cyano- substituted imidazoles, have been calculated reliably by using the computationally feasible DFT (B3LYP) and MP2 (extrapolated to the complete basis set limit) methods. These accurately calculated proton and methyl cation affinities of neutrals and anions are used in conjunction with an empirical approach based on molecular volumes to estimate the lattice enthalpies and entropies of ionic liquids, organic solids, and organic liquids. These quantities were used to construct a thermodynamic cycle for salt formation to reliably predict the ability to synthesize a variety of salts including ones with potentially high energetic densities. An adjustment of the gas phase thermodynamic cycle to account for solid- and liquid-phase chemistries provides the best overall assessment of salt formation and stability. This has been applied to imidazoles (the cation to be formed) with alkyl, nitro, and cyano substituents. The proton and methyl cation donors studied were as follows: HCl, HBr, HI, (HO)(2)SO2, HSO3CF3 (TfOH), and HSO3(C6H4)CH3 (TsOH); CH3Cl, CH3Br, CH3I, (CH3O)(2)SO2, CH3SO3CF3 (TfOCH3) and CH3SO3(C6H4)CH3 (TsOCH3). As substitution of the cation with electron-withdrawing groups increases, the triflate reagents appear to be the best overall choice as protonating and methylating agents. Even stronger alkylating agents should be considered to enhance the chances of synthetic success. When using the enthalpies of reaction for the gas-phase reactants (eq 6) to form a salt, a cutoff value of - 13 kcal mol(-1) or lower (more negative) should be used as the minimum value for predicting whether a salt can be synthesized.

Lowest energy potentials of Li2 + F accessible at ultracold temperatures

Ab initio calculations for the strongly exoergic Li2+F harpoon reaction are presented using density-functional theory, complete active space self-consistent field, and multireference configuration interaction methods to argue that this reaction would be an ideal candidate for investigation with ultracold molecules. The lowest six states are calculated with the aug-correlation-consistent polarized valence triple-zeta basis set and at least two can be accessed by a ground rovibronic Li2 molecule with zero collision energy at all reaction geometries. The large reactive cross section (characteristic of harpoon reactions) and chemiluminescent products are additional attractive features of these reactions.

Electronic states and spin-forbidden cooling transitions of AlH and AlF

The feasibility of laser cooling AlH and AlF is investigated using ab initio quantum chemistry. All the electronic states corresponding to the ground and lowest two excited states of the Al atom are calculated using multi-reference configuration interaction (MRCI) and the large AV6Z basis set for AlH. The smaller AVQZ basis set is used to calculate the valence electronic states of AlF. Theoretical Franck-Condon factors are determined for the A(1)Pi -> X(1)Sigma(+) transitions in both radicals and found to agree with the highly diagonal factors found experimentally, suggesting computational chemistry is an effective method for screening suitable laser cooling candidates. AlH does not appear to have a transition quite as diagonal as that in SrF (which has been laser cooled) but the A(1)Pi -> X(1)Sigma(+) transition transition of AlF is a strong candidate for cooling with just a single laser, though the cooling frequency is deep in the UV. Furthermore, the a (3)Pi -> X(1)Sigma(+) transitions are also strongly diagonal and in AlF is a practical method for obtaining very low final temperatures around 3 mu K.

The RMT method for many-electron atomic systems in intense short-pulse laser light

We describe a new ab initio method for solving the time-dependent Schrödinger equation for multi-electron atomic systems exposed to intense short-pulse laser light. We call the method the R-matrix with time-dependence (RMT) method. Our starting point is a finite-difference numerical integrator (HELIUM), which has proved successful at describing few-electron atoms and atomic ions in strong laser fields with high accuracy. By exploiting the R-matrix division-of-space concept, we bring together a numerical method most appropriate to the multi-electron finite inner region (R-matrix basis set) and a different numerical method most appropriate to the one-electron outer region (finite difference). In order to exploit massively parallel supercomputers efficiently, we time-propagate the wavefunction in both regions by employing Arnoldi methods, originally developed for HELIUM.

Ab initio potentials of F + Li-2 accessible at ultracold temperatures

Ab initio calculations for the strongly exoergic Li-2 + F harpoon reaction are presented using density-functional theory, complete active space self-consistent field, and multireference configuration interaction methods to argue that this reaction would be an ideal candidate for investigation with ultracold molecules. The lowest six states are calculated with the aug-correlation-consistent polarized valence triple-zeta basis set and at least two can be accessed by a ground rovibronic Li-2 molecule with zero collision energy at all reaction geometries. The large reactive cross section (characteristic of harpoon reactions) and chemiluminescent products are additional attractive features of these reactions.

Time delay between photoemission from the 2p and 2s subshells of neon

The R-matrix incorporating time (RMT) method is a method developed recently for solving the time-dependent Schrödinger equation for multielectron atomic systems exposed to intense short-pulse laser light. We have employed the RMT method to investigate the time delay in the photoemission of an electron liberated from a 2p orbital in a neon atom with respect to one released from a 2s orbital following absorption of an attosecond xuv pulse. Time delays due to xuv pulses in the range 76-105 eV are presented. For an xuv pulse at the experimentally relevant energy of 105.2 eV, we calculate the time delay to be 10.2±1.3 attoseconds (as), somewhat larger than estimated by other theoretical calculations, but still a factor of 2 smaller than experiment. We repeated the calculation for a photon energy of 89.8 eV with a larger basis set capable of modeling correlated-electron dynamics within the neon atom and the residual Ne ion. A time delay of 14.5±1.5 as was observed, compared to a 16.7±1.5 as result using a single-configuration representation of the residual Ne⁺ ion. 

Recoil-induced electronic excitation and ionization in one-and two-electron ions

The electronic redistribution of an ion or atom induced by a sudden recoil of the nucleus occurring during the emission or capture of a neutral particle is theoretically investigated. For one-electron systems, analytical expressions are derived for the electronic transition probabilities to bound and continuum states. The quality of a B-spline basis set approach is evaluated from a detailed comparison with the analytical results. This numerical approach is then used Io study the dynamics of two-electron systems (neutral He and Ne ) using correlated wavefunctions for both the target and daughter ions. The total transition probabilities to discrete states, autoionizing states and direct single- and double-ionization probabilities are calculated from the pseudospectra. Sum rules for transition probabilities involving an initial bound state and a complete final series are discussed.