The accuracy of the pseudopotential approximation. I. An analysis of the spectroscopic constants for the electronic ground states of InCl and InCl3using various three valence electron pseudopotentials for indium

Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with a compactly supported numerical atom-centered basis, obtained from atomic ground-state DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on a priori error estimates to guide our choice of an adaptive finite element mesh as well as the time step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretizations. Notably, we attain a 50-100 times speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear responses by studying the absorption spectra in sodium clusters, the linear to nonlinear response transition in the green fluorescence protein chromophore, and the higher harmonic generation in the magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to ∼1000 processors, using a benchmark system of a 50-atom sodium nanocluster.

Helical gold nanorods as chiral recognition nanostructures: a relativistic density functional theory study

We establish helical gold nanorods as the first examples of chiral recognition nanostructures by examining the simple chiral molecule CClHDT adsorbed on the helical Au40 nanorod. We calculate the vibrational circular dichroism (VCD) spectra of the R and S enantiomers of CClHDT adsorbed on the R (or S) enantiomer of Au40 using relativistic density functional theory. The highest adsorption energy is found when the Cl atom of CClHDT binds to a low-coordinated Au atom at the edge of Au40. There are three adsorption modes (essentially identical in energy) corresponding to three orientations of the HDT moiety. We show that, for each adsorption mode, the VCD spectra are distinctly different for the Au40(R)-ClHDT(R) and Au40(R)-CClHDT(S) complexes, and we give a qualitative explanation for this based on the principle of chirality transfer. For comparison with the results for Au40, we calculate the VCD spectra of the R and S enantiomers of CClHDT adsorbed on the achiral Au20 tetrahedral cluster. Again, there are three adsorption modes (essentially identical in energy) corresponding to three orientations of the HDT moiety. However, we show that, for each adsorption mode, the VCD spectra are mirror symmetric but otherwise essentially identical for the Au20-CClHDT(R) and Au20-CClHDT(S) complexes. Thus, the inherent chirality of the helical Au40 nanorod is essential for its chiral recognition functionality.

Characterization of gas phase WC²⁺: a thermodynamically stable carbide dication

Using an ab initio methodology, we performed a detailed theoretical study of the gas phase WC(2+) dication. These calculations were done using a multiconfigurational method in connection with a large basis set, where relativistic effects were taken into account. This dication is identified here as the first thermochemically stable doubly charged diatomic carbide in the gas phase. Our work hence confirms the stability of this dication in the gas phase and its earlier observations by atom probe mass spectrometry. Our calculations show that the shape of the potential energy curves of its lowest electronic states changes drastically upon consideration of relativistic effects. For instance, the electronic ground state possesses a Morse-like potential without spin-orbit that evolves to the usual volcanic behavior, and with a columbic 1/R evolution at large internuclear separation after inclusion of spin-orbit. We predict a set of thermochemical and spectroscopic data for this molecular species.

The pseudopotential approximation in electronic structure theory

A short review is presented on one of the most successful theories for electronic structure calculations, the pseudopotential approximation, originally introduced by Hans G. A. Hellmann in 1934. Recent developments in relativistic quantum theory allow for the accurate adjustment of pseudopotential parameters to valence spectra, producing results for properties of atoms, molecules, and the solid-state in excellent agreement with more accurate all-electron results if a small-core definition is used. Thus the relativistic pseudopotential approximation is now the most widely applied method for systems containing heavy elements.

Ab initiofinite field (hyper)polarizability computations on stoichiometric gallium arsenide clusters GanAsn (n=2–9)

We report reliable ab initio finite field (hyper)polarizability values at Hartree-Fock and second order Moller-Plesset perturbation theory (MP2) levels of theory for different geometrical configurations of small gallium arsenide clusters Ga(n)As(n) with n=2-5. We relied on all-electron basis sets and pseudopotentials suitable for (hyper)polarizability calculations. In each case, we used structures that have been established in the literature after we optimized their geometries at B3LYP/cc-pVTZ-PP level of theory. Our results suggest that the first order hyperpolarizability (beta) is much more sensitive to the special geometric features than the second order hyperpolarizability (gamma). For the most stable configurations up to ten atoms the second order hyperpolarizability at MP2 level of theory varies between 15 x 10(4) and 32 x 10(4) e(4)a0 (4)Eh(-3). In addition, we examined the polarizability per atom evolution versus the cluster size for Ga(n)As(n) with n=2-9. Our work extends earlier theoretical studies which were limited to eight atoms and exposes that the polarizability/atom of the most stable stoichiometric configurations up to Ga(9)As(9) continues the monotonic downward trend with increasing size. Lastly, from the methodological point of view, our analysis shows that apart from polarizabilities, augmented pseudopotentials yield reliable first and second hyperpolarizability values as well.

High-order electron-correlation methods with scalar relativistic and spin-orbit corrections

An assortment of computer-generated, parallel-executable programs of ab initio electron-correlation methods has been fitted with the ability to use relativistic reference wave functions. This has been done on the basis of scalar relativistic and spin-orbit effective potentials and by allowing the computer-generated programs to handle complex-valued, spinless orbitals determined by these potentials. The electron-correlation methods that benefit from this extension are high-order coupled-cluster methods (up to quadruple excitation operators) for closed- and open-shell species, coupled-cluster methods for excited and ionized states (up to quadruples), second-order perturbation corrections to coupled-cluster methods (up to triples), high-order perturbation corrections to configuration-interaction singles, and active-space (multireference) coupled-cluster methods for the ground, excited, and ionized states (up to active-space quadruples). A subset of these methods is used jointly such that the dynamical correlation energies and scalar relativistic effects are computed by a lower-order electron-correlation method with more extensive basis sets and all-electron relativistic treatment, whereas the nondynamical correlation energies and spin-orbit effects are treated by a higher-order electron-correlation method with smaller basis sets and relativistic effective potentials. The authors demonstrate the utility and efficiency of this composite scheme in chemical simulation wherein the consideration of spin-orbit effects is essential: ionization energies of rare gases, spectroscopic constants of protonated rare gases, and photoelectron spectra of hydrogen halides.

Evaluation of Effective Core Potentials and Basis Sets for the Prediction of the Geometries of Alkyltin Halides

A systematic comparison of the optimized geometries of five organotin compounds, Cl(n)Sn(CH(3))(4-n), n = 0-4, with the available gas-phase electron diffraction results is reported. All optimizations were carried out with the B3LYP density functional method. Comparison of 10 basis sets and three effective core potentials leads to the conclusion that the combination of the SDB-aug-cc-pVTZ basis set and the LANL2 effective core potential for tin, together with the 6-31G(d,p) basis set for the other atoms, is recommended for the prediction of the geometries of organotin compounds.

Relativistic small-core energy-consistent pseudopotentials for the alkaline-earth elements from Ca to Ra

Small-core ten-valence electron energy-consistent scalar- and two-component relativistic pseudopotentials for the alkaline-earth elements from Ca to Ra are presented. The accuracy and reliability of these pseudopotentials are discussed in terms of their ability to reproduce all-electron calculated and experimental dipole polarizabilities and ionization potentials.

Extensive theoretical studies on the low-lying electronic states of indium monochloride cation, InCl+

The global potential energy curves for the 14 low-lying doublet and quartet Lambda-S states of InCl+ are calculated at the scalar relativistic MR-CISD+Q (multireference configuration interaction with single and double excitations, and Davidson's correction) level of theory. Spin-orbit coupling is accounted for via the state interaction approach with the full Breit-Pauli Hamiltonian, which leads to 30 Omega states. The computed spectroscopic constants of nine bound Lambda-S states and 17 bound Omega states are in good agreement with the available experimental data. The transition dipole moments and Franck-Condon factors of selected transitions are also calculated, from which the corresponding radiative lifetimes are derived.

Relativistic pseudopotentional incorporating core/valence polarization and nonlocal effects

A relativistic pseudopotentional (RPP) for use in ab initio molecular electronic structure calculations is derived in the context of the relativistic effective core potential (REP) method of Lee et al. The resulting atom-specific RPP has salient features of the REP imbedded within it while retaining the form of a functional that is dynamically defined at runtime when used in calculations on molecules. The RPP is determined from Dirac-Fock wave functions for the isolated atom. Outer core two-electron interactions are incorporated into the RPP by means of variable coefficients that are defined in the context of the final molecular wave function. This form permits polarization of the outer core shells analogous to that occurring in all-electron molecular Hartree-Fock calculations while retaining these shells as part of the atomic pseudopotentional. Use of the RPP in post-Hartree-Fock molecular calculations permits the incorporation of core/valence correlation effects.

Formal analysis of effective core potential methods

Effective core potentials are analyzed from the standpoint of the underlying frozen core approximation. The content of the pseudoorbital, the content of the potential, and the properties of both are elaborated, showing the points at which they differ from the frozen core approximation and where possible deficiencies might lie.

Nodeless valence (pseudo)spinors

Atomic calculations using small-core relativistic effective core potentials (RECPs) explicitly treating outer core electrons are used to define two-component nodeless valence spinors (NVSs) and nodeless valence pseudospinors (NVPSs). Errors attributable to nonlocal electron repulsion interactions that arise from large-core RECPs are shown to result from the inherent arbitrariness in the choice of match points and number of derivatives that define shape-consistent pseudospinors, as well as the positions of radial nodes that reside in the outer core regions of atoms. Self-consistent field calculations in omegaomega-coupling for InH and InCl using RECPs derived from NVSs and NVPSs are reported. Increased bond distances relative to those calculated using very-large-core RECPs for In agree with those due to frozen 4d(3/2) and 4d(5/2) spinors and a small-core RECP. Results for AmCl+2 also reveal that the shortening in the bond length is recovered when the very-large-core RECP is derived using nodeless valence (pseudo)spinors.

Molecular Structure of a Monomeric, Base-Free Metal(I) Amide, TlN[Si(CH(3))(3)](2), by Gas Electron Diffraction and by Density Functional Theory and ab Initio MP2 Calculations

Thallium bis(trimethylsilyl)amide is a monomer in the gas phase. The molecular symmetry is C(2), the Tl-N bond length is 214.8(12) pm by gas electron diffraction as compared to about 258 pm in the crystalline dimer (Klinkhammer, K. W.; Henkel, S. J. Organomet. Chem. 1994, 480, 167). Structure optimization by DFT or ab initio (MP2) calculations with the ECP basis set on the Tl atom fails to reproduce the experimental Tl-N bond distance unless the 5s,5p,5d electrons on the metal are described explicitly and the atomic basis set includes both polarization and diffuse functions.