Donor–Acceptor Bond in Nontransition and Transition Element Complexes: Studies with Natural Bonding Orbital Approach

Electronic structures of tin, antimony, titanium, and niobium chloride complexes were analyzed using density functional theory. Parameters of nuclear quadrupole resonance spectra calculated using pseudopotential and all-electron basis states were compared with the experimental values. It was shown that the use of the central atom pseudopotential leads to a significant deviation of the atomic quadrupole coupling constants from their experimental values. The bonding in complexes was analyzed by making use of the natural orbitals of metal–chlorine and metal–ligand bonds. Donor–aceptor interactions in complexes of main group elements are described within the framework of sp-hybridization, while those in the transition element complexes, within the sd-hybridization framework.     

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Summary Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M^(Z–28)+-core orbitals of the second row transition elements and the M^(Z–60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.     

A comparative study ofab-initio effective core potential and all-electron calculations for molecular structures and transition states

The reliability of theab-initio effective core potential method for calculating molecular geometries was tested for several polyatomic molecules by using the energy gradient technique. The calculated geometries are in good agreement with those of all-electron calculation not only for equilibrium but also for transition states. The heat of reaction and the activation barrier height compare very well with those of all-electron calculation as well.     

An approximate frozen core approach to valence only molecular calculations

A simple valence electron-only theory based on an approximate frozen core approach and an exact core-valence strong orthogonality condition is developed for atomic and molecular systems. A unique reduced basis is introduced in which both core and valence orbitals are expanded. The core representation is roughly approximated, and the valence orbital overlap with the corresponding all-electron reference functions is nearly exact. The size of the reduced basis in terms of primitive functions is practically the same as that adopted by effective core potential methods in which the valence orbitals have the correct nodal properties. Results obtained with the present approach are presented for LiO, BeO and CaO molecules, and compared with the corresponding all-electron frozen core calculations. In addition, a detailed investigation on Li _n Be clusters (n=1,..., 6) is carried out.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Vanadium oxide compounds with quantum Monte Carlo

Calculations with the diffusion quantum Monte Carlo method are presented for vanadium oxide molecules VO0/+0(n) with n = 1-4 and for V2O5. Atomization and ionization energies are calculated as well as oxygen abstraction energies. The fixed-node approximation is compared for guide functions with orbitals from B3LYP and BP86 calculations and higher accuracy was obtained with the latter orbitals. Additionally, all-electron and pseudopotential calculations are compared for the oxygen atom. The overall accuracy is found to be comparable to CCSD(T) calculations where experimental data is available.     

Impact of finite-temperature and condensed-phase effects on theoretical X-ray absorption spectra of transition metal complexes

The impact of condensed-phase and finite-temperature effects on the theoretical X-ray absorption spectra of transition metal complexes is assessed. The former are included in terms of the all-electron Gaussian and augmented plane-wave approach, whereas the latter are taken into account by extensive ensemble averaging along second-generation Car–Parrinello ab initio molecular dynamics trajectories. We find that employing the periodic boundary conditions and including finite-temperature effects systematically improves the agreement between our simulated X-ray absorption spectra and experimental measurements. © 2018 Wiley Periodicals, Inc.     

Basis set modeling for molecular calculations using effective core potential

A new approach for developing of basis sets to be used along with effective core potential is systematically studied. The behavior of the LCAO coefficients versus the ln(α) of the respective primitives can provide simple guidelines to establish the range over which the basis set should be developed or modified, especially when using effective core potential. Double-zeta basis sets were modeled for SBK pseudopotential from all-electron basis sets for a series of compounds containing elements of the second period of the periodic table. Application of the modeled basis sets at the Hartree–Fock and MP2 levels of theory shows that the new method provides molecular properties as accurate as those calculated by all-electron calculations. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1918–1929, 1997     

Compact and efficient basis sets of s- and p-block elements for model core potential method

We propose compact and efficient valence-function sets for s- and p-block elements from Li to Rn to appropriately describe valence correlation in model core potential (MCP) calculations. The basis sets are generated by a combination of split MCP valence orbitals and correlating contracted Gaussian-type functions in a segmented form. We provide three types of basis sets. They are referred to as MCP-dzp, MCP-tzp, and MCP-qzp, since they have the quality comparable with all-electron correlation consistent basis sets, cc-pVDZ, cc-pVTZ, and cc-pVQZ, respectively, for lighter atoms. MCP calculations with the present basis sets give atomic correlation energies in good agreement with all-electron calculations. The present MCP basis sets systematically improve physical properties in atomic and molecular systems in a series of MCP-dzp, MCP-tzp, and MCP-qzp. Ionization potentials and electron affinities of halogen atoms as well as molecular spectroscopic constants calculated by the best MCP set are in good agreement with experimental values.     

Quantum Monte Carlo study of the Ne atom and the Ne+ ion

We report all-electron and pseudopotential calculations of the ground-state energies of the neutral Ne atom and the Ne(+) ion using the variational and diffusion quantum Monte Carlo (DMC) methods. We investigate different levels of Slater-Jastrow trial wave function: (i) using Hartree-Fock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finite-time-step and fixed-node biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered.     

Testing the arbitrariness and limits of a pseudopotential technique through calculations on the series of diatoms HF,AlH, HCl,AlF, AlCl,F2, Cl2

The pseudopotential techniques present some degrees of freedom, the influence of which on molecular calculations must be tested to assess the stability and accuracy of the results. The present work uses a semi-local pseudopotential extracted from near Hartree-Fock atomic calculations; the shape of the inner part of the pseudoorbital, the analytic form of the pseudopotential are shown to have less influence than the choice of the valence basis set which must be optimized. The calculated molecular constants perfectly agree with the large basis set all-electron calculations, even for polar molecules.Equipe de Recherche Associée au CNRS No. 821.     

Plane wave/pseudopotential implementation of excited state gradients in density functional linear response theory: a new route via implicit differentiation

This work presents the formalism and implementation of excited state nuclear forces within density functional linear response theory using a plane wave basis set. An implicit differentiation technique is developed for computing nonadiabatic coupling between Kohn-Sham molecular orbital wave functions as well as gradients of orbital energies which are then used to calculate excited state nuclear forces. The algorithm has been implemented in a plane wave/pseudopotential code taking into account only a reduced active subspace of molecular orbitals. It is demonstrated for the H(2) and N(2) molecules that the analytical gradients rapidly converge to the exact forces when the active subspace of molecular orbitals approaches completeness.     

Pseudopotential method for the direct construction of localized orbitals by multiconfiguration self-consistent field theory

The orbital equations for the direct construction of localized fixed orbitals by multiconfiguration self-consistent field theory (MCSCF-FXO) are transformed without approximation into pseudopotential form by a two-step process. First the utilization of a particular family of localization is shown to separate the set of orbital equations into two sets of coupled equations, one describing “valence” orbitals and one describing “core” orbitals. In addition we obtain by appropriate choice of localization potential three different sets of MCSCF-FXO orbitals, namely: maximally screened, “one-center” and “intermediate” orbitals. In the second step the orbital equations are transformed into pseudopotential form and explicit non-local pseudopotentials yielding and core orbitals are obtained. Finally, several different physically motivated approximations to the exact pseudopotentials, and the frozen-core approximation are discussed.     

Analysis of the Electronic Structure of Aqueous Urea and Its Derivatives: A Systematic Soft X‐Ray–TD‐DFT Approach

Soft X‐ray emission (XE), absorption (XA), and resonant inelastic scattering (RIXS) experiments have been conducted at the nitrogen K‐edge of urea and its derivatives in aqueous solution and were compared with density functional theory and time‐dependent density functional theory calculations. This comprehensive study provides detailed information on the occupied and unoccupied molecular orbitals of urea, thiourea, acetamide, dimethylurea, and biuret at valence levels. By identifying the electronic transitions that contribute to the experimental spectral features, the energy gap between the highest occupied and the lowest unoccupied molecular orbital of each molecule is determined. Moreover, a theoretical approach is introduced to simulate resonant inelastic X‐ray scattering spectra by adding an extra electron to the lowest unoccupied molecular orbital, thereby mimicking the real initial state of the core‐electron absorption before the subsequent relaxation process.     

Dissociation energy of the water dimer from quantum Monte Carlo calculations

We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo techniques. We have performed variational quantum Monte Carlo and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP type single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mhartree, yielding a DMC energy of -76.428 30(5) hartree, which is only 10 mhartree above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger, and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcalmol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) D and dimer dipole moments which range between 2.628(6) and 2.672(5) D.     

Accurate Ab Initio Calculations for LiH and its Ions, LiH+ and LiH−

Ab initio calculations were performed for LiH using a pseudopotential approach with CPP corrections and huge basis sets on both atoms. A wide range of ^1,3Σ⁺ electronic adiabatic states have been investigated, from the ground state up to those dissociating into Li(5p)+H. Permanent and transition electric dipole moments are also considered for the first few excited states. Comparison with experiments and recent all-electron calculations, reveals an excellent global accuracy, only the bottom of the ground state being better described by all-electron approaches. Using almost identical basis sets, coupled cluster all-electron calculations are performed for the ground states of LiH⁺, LiH⁻ and LiH. High care has been given to the correct relative position of the asymptotes, allowing for this rather complete set of accurate ab initio data to be useful for further molecular physics studies.     

Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments: test calculations for Au, AuF, and Sn(n) cluster (n ≤ 20)

The response of the electronic wavefunction to an external electric or magnetic field is widely considered to be a typical valence property and should, therefore, be adequately described by accurately adjusted pseudopotentials, especially if a small-core definition is used within this approximation. In this paper we show for atomic Au and Au(+), as well as for the molecule AuF and tin clusters, that in contrast to the case of the static electric dipole polarizability or the electric dipole moment, core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation. This error increases with increasing size of the core chosen. For tin clusters, which are of interest in ongoing molecular beam experiments currently carried out by the Darmstadt group, the diamagnetic and paramagnetic isotropic components of the magnetizability tensor almost cancel out and large-core pseudopotentials do not even predict the correct sign for this property due to erroneous results in both the diamagnetic and (more importantly) the paramagnetic terms. Hence, all-electron calculations or pseudopotentials with very small cores are required to adequately predict magnetizabilities for atoms, molecules and the solid state, making it computationally more difficult to obtain this quantity for future investigations in heavy atom containing molecules or clusters. We also demonstrate for this property that all-electron density functional calculations are quite robust and give results close to wavefunction based methods for the atoms and molecules studied here.     

Core localization and sigma* delocalization in the O 1s core-excited sulfur dioxide molecule

Electron-ion-ion coincidence measurements of sulfur dioxide at discrete resonances near the O 1s ionization edge are reported. The spectra are analyzed using a model based upon molecular symmetry and on the geometry of the molecule. We find clear evidence for molecular alignment that can be ascribed to symmetry properties of the ground and core-excited states. Configuration interaction (CI) calculations indicate geometry changes in accord with the measured spectra. For the SO(2) molecule, however, we find that the localized core hole does not produce measurable evidence for valence localization, since the transition dipole moment is not parallel to a breaking sigma* O-S bond, in contrast to the case of ozone. The dissociation behavior based upon the CI calculations using symmetry-broken orbitals while fixing a localized core-hole site is found to be nearly equivalent to that using symmetry-adapted orbitals. This implies that the core-localization effect is not strong enough to localize the sigma* valence orbital.     

Pseudopotential and electron propagator methods for the calculation of the photoelectron spectra of anionic silicon clusters: predictions on Si10-

Photoelectron spectra of anionic clusters of silicon require reliable theoretical calculations for their assignment and interpretation. Electron propagator calculations in the outer valence Green's-function approximation with two well-characterized, all-electron basis sets on vertical electron detachment energies (VEDEs) of anions are compared to similar calculations that employ Stuttgart pseudopotentials. Tests on Si(n) (-) clusters with n=3-7 exhibit an encouraging agreement between the all-electron and pseudopotentials results and between electron propagator predictions and experiments and values obtained from coupled-cluster calculations. To illustrate the capabilities of the new approach based on a Si pseudopotential and electron propagator methods, VEDE calculations on Si(10) (-) are presented.