Anab initio potential energy surface and dynamics calculations for vibrational excitation of I2 by He

We present newab initio calculations of the interaction potential and the elastic and inelastic cross sections for He scattering by I₂. The electronic structure calculations of the interaction potential are based on an extensive one-electron basis set (triple zeta plus ad set on each I, ans function plus ap set at the I₂ bond center, and quadruple zeta plus twop sets on He), a two-configuration-SCF orbital set, and a configuration interaction calculation based on all single and double excitations out of the two-configuration reference space. The calculations are performed at 16He-I₂ distances for nine combinations of I₂ vibrational displacement and orientation. A new form of analytic representation is presented that is particularly well suited to efficient and accurate fitting ofab initio interaction potentials that include vibrational displacements. Scattering calculations are performed by the vibrational close-coupling, rotational-infinite-order-sudden approximation with a converged vibrational basis.     

Semiempirical andab initio calculations of the full configuration interaction using iterated Krylov’s spaces

The algorithm proposed previously for calculating the full configuration interaction using the variation matrix of the wave operator involves the numerical solution of the corresponding incomplete eigenvalue problem based on iterated Krylov’s subspaces. In practice, that means using the multistep gradient method as a special version of the Lanczos method. The high efficiency of this algorithm, which can readily be used in personal computer calculations, is proved by particular ab initio calculations of the full configuration interaction for the helium and beryllium atoms as well as by semiempirical calculations of π-shells for naphthalene and diphenylene. The algorithm is of particular assistance in obtaining numerous excited states, which are used for determining various spectral sums (polarizability, van der Waals interaction constants, and photoionization cross sections). Translated fromZhumal Struktumoi Khimii, Vol. 38, No. 1, pp. 14–22, January–February, 1997.     

GRECP/MRD‐CI calculations on the Hg atom and HgH molecule

Multireference single‐ and double‐excitation configuration interaction (MRD‐CI) calculations of transition energies for the Hg atom and spectroscopic constants for the HgH molecule are carried out with the generalized relativistic effective core potential (GRECP) method. A new selection criterium for the reference configurations is discussed. The calculated spectroscopic constants are compared with experimental data and results of calculations of other groups. Improvement of accuracy is mainly observed for bond lengths from the GRECP/MRD‐CI calculations (without applying the T = 0 correction) with respect to the results of other groups. Analysis of the quality of the approximations employed is carried out. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Configuration selection as a route towards efficient vibrational configuration interaction calculations

A configuration selective vibrational configuration interaction (CI) approach is presented that efficiently reduces the variational space and thus leads to significant speedups in comparison to standard vibrational CI implementations. Deviations with respect to reference calculations are well below the accuracy of the underlying electronic structure calculations for the potential and hence are essentially negligible. Parallel implementations of the presented configuration selective vibrational CI approaches lead to further significant time savings. Benchmark calculations based on potential energy surfaces of coupled-cluster quality are presented for the fundamental modes of cis- and trans-difluoroethylene. The size-consistency error within the vibrational configuration interaction calculations of the difluoroethylene dimer has been studied in dependence on the excitation level.     

Removal of dependencies from nearly complete basis sets. Calculations on the helium dimer

A method is devised for dealing with almost linearly dependent basis sets that contain large sets of bond functions. Using the largest of such basis sets, LARSAT, the second-order Møller-Plesset polarization dispersion energy of the helium dimer is calculated to be - 17.08 K at R = 5.6 bohrs. MR-SDCI calculations, employing a set of 37 reference configurations, were performed for the helium dimer with several basis sets at 4.0 and 5.6 bohrs. Size-extensivity corrections were included to take into account the R dependency of the size-extensivity error in MR-SDCI calculations. The He₂ interaction energies computed with basis LARSAT are - 10.92 K at 5.6 bohrs and 295.1 K at 4.0 bohrs. The 37-MR-SDCI calculations with basis LARSAT almost reproduce the He₂ full configuration interaction (CI) interaction energies computed with the same basis, at notably smaller cost. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 805–815, 1997     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

Numerical studies for a theoretical analysis of semiempirical LCAO–CI methods

A numerical investigation of Del Re and Parr's formulas [1] for the treatment of π systems has been preformed in the case of five-membered rings, using two different expressions for the core Hamiltonian and different values for the effective charges. The results obtained are discussed by analysing the three stages of the calculation: (a) a non-iterative LCAO –MO calculation; (b) the same calculation with corrections for exchange and repulsion terms arising from fluctuations of the orbital populations; (c) configuration interaction. The calculations are interesting also because they do not involve the zero differential overlap approximation; a calculation without inclusion of overlap hse been carried out for pyrrole and the results have been compared with those including S . The main conclusions hold also for σ electrons, and can serve to assess better the validity of simple σ calculations.     

Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Configuration interaction and coupled cluster calculations are reported for He₂ using various orbital basis sets of the d-aug-AVXZ type, with the results being extrapolated to the one electron basis set limit both with counterpoise and without counterpoise correction. A generalized uniform singlet- and triplet-pair extrapolation scheme has been utilized for such a purpose. Using appropriate corrections to mimic full configuration interaction, the energies were predicted in excellent agreement with the best available estimates. The results also suggest that extrapolation to the complete basis set limit may be a general alternative to the counterpoise correction that yields a more accurate potential energy while being more economical.     

Contracted polarization functions for B to Ar

Using optimal exponents for B through Ne given by Dunning and those for Al through Ar by Woon and Dunning, d-type contracted polarization functions (2d/1d), (3d/1d), and (3d/2d) are generated from natural orbitals of atomic single and double excitation configuration interaction (SDCI) calculations, where the numbers before and after the slash are those of the primitive and contracted Gaussian type functions. The resulting contracted functions are tested on N₂ and P₂ molecules by self-consistent field and SDCI calculations, which clarify characteristics of the present polarization functions. Received: 5 June 1997 / Accepted: 20 August 1997     

Thermochemical spin-orbit corrections for atomic platinum (Pt)

In quantum chemistry calculations of molecular dissociation or atomization, the energies of many atoms require spin-orbit corrections (SOCs). This is to compensate for the lack of spin-orbit coupling in most calculations. Values for the corrections are normally derived from experimental atomic energy levels and their assignments to LS (Russell-Saunders) terms. However, this procedure produces erroneous values when terms are strongly mixed, as they are in Pt. Spin-orbit configuration interaction provides the LS-term composition of observed energy levels. Such data are used here to obtain SOCs for valence term energies of Pt. For the ground term (³D), a correction of −3948 ± 153 cm⁻¹ is recommended.     

Relativistic all-electron configuration interaction calculations on the gold atom

We present the results of relativistic and non-relativistic self-consistent field and configuration interaction calculations for the gold atom, using the spin-free no-pair Hamiltonian in a basis set expansion. A new basis set for the gold atom is discussed and its results in relativistic and non-relativistic self-consistent field calculations are compared to those of numerical Dirac-Hartree-Focic and Hartree-Fock calculations, respectively. Excitation energies, electron affinities and ionization potentials were calculated using a multi-reference configuration interaction technique and are in reasonable agreement with experiment in the relativistic case.     

Ab initio Hartree–Fock and configuration-interaction treatment of the interaction between two nickel atoms

The interaction between two nickel atoms in the configurations (3d)⁸(4s)² and (3d)⁹ (4s)¹ has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσ_g molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.     

A high‐accuracy theoretical study of the CHnP Systems n = 1–3

We have performed high‐level electronic structure computations on the most important species of the CH_nP systems n = 1–3 to characterize them and provide reliable information about the equilibrium and vibrationally averaged molecular structures, rotational constants, vibrational frequencies (harmonic and anharmonic), formation enthalpies, and vertical excitation energies. Those chemical systems are intermediates for several important reactions and also prototypical phosphorus‐carbon compounds; however, they are often elusive to experimental detection. The present results significantly complement their knowledge and can be used as an assessment of the experimental information when available. The explicitly correlated coupled‐cluster RCCSD(T)‐F12 method has been used for geometry optimizations and vibrational frequency calculations. Vibrational configuration interaction theory has been used to account for anharmonicity effects. Basis‐set limit extrapolations have been carried out to determine accurate thermochemical quantities. Electronic excited states have been calculated with coupled‐cluster approaches and also by means of the multireference configuration interaction method. © 2013 Wiley Periodicals, Inc.     

Two-body Reduced Density Matrix Reconstruction for Van der Waals Systems

A method for the calculation of the electronic energy of a correlated system is presented. This approach is based on the reconstruction of the total two-body reduced density matrix by doing separate configurations interaction calculations on fragments. The method has been tested on Van der Waals systems and has been implemented by considering restrictive N-representability conditions. It is shown that the computational strategy presented in this work can describe with good accuracy weak dispersion interactions, and considerably lowers the size-consistency error of a classical configuration interaction calculation.     

The spin coupling in the diiron complex [Fe2(hpdta)(H2O)3Cl

Density functional, multireference configuration interaction, and modified valence configuration interaction calculations are used to investigate the electronic structure and spin coupling of the dinuclear [Fe(2)(hpdta)(H(2)O)(3)Cl] complex (H(5)hpdta = Hydroxypropane-1,3-diamine-N,N,N',N'-tetraacetic acid). The density functional calculations give evidence of both, states with local high-spin iron centres and states with local low-spin iron centres, the relative energy of which strongly depends on the functional. The splitting of states due to the spin coupling between the high-spin iron centres varies by more than a factor of two for different functionals. In an attempt to study to what extent it is possible to undertake configuration interaction calculations on such binuclear compounds, multireference configuration interaction calculations are performed on a [Fe(2)(OH)(5)(H(2)O)(3)(NH(3))(2)Cl] model complex. The results show that, when correlating only the ten iron 3d orbitals and the four valence orbitals of the bridging OH group, the calculated splitting is still by a factor of about 3 smaller than the value for the splitting inferred from magnetic susceptibility measurements. Modified valence configuration interaction calculations are performed to approximately take into account the influence of orbital relaxation effects of all occupied orbitals in the excited configurations. The exchange splitting is significantly increased, but still smaller than the experimental value.     

Semiempirical NDDO/MC calculations of the excited states of the chromate ion

A new semiempirical method of calculating the excited states of transition metal complexes is developed. This technique uses the configuration interaction and semiempirical NDDO/MC methods to obtain the ground state of a set of Slater type valence spd-orbitals chosen from the optical spectra of transition metals together with the corresponding core integrals. The method is tested in calculations of the electronically excited states of the chromate ion. Good agreement with the experimental energies of vertical transitions and the results of ab initio calculations is achieved.     

Simultaneous ab initio calculations of isoelectronic diatomic molecules

Large gaussian basis sets are employed in simultaneous configuration interaction calculations for the ground states of isoelectronic diatomic molecules. The resulting potential energy curves for three members respectively of four different isoelectronic molecule sequences show the applicability of the method. Comparisons with available results of standard configuration interaction calculations for selected molecules are given. Using our method we often get lower upper bounds for the electronic energy, save computer time and treat physically totally different molecules simultaneously.     

Intermolecular and intramolecular interactions calculated with ab initio perturbative configuration interaction method using strongly localized orbitals

We have applied the ab initio formulation of the perturbative configuration interaction using localized orbitals (PCILO ) method up to third order to calculate intermolecular and intramolecular interaction energies going beyond the ab initio Hartree–Fock calculation. For the rotational barrier in ethane our results agree well with the experimental value and the cis- and even the trans-barriers in HOOH are at least qualitatively reproduced with the aid of the STO -3G basis set. In the case of the water dimer we obtain an equilibrium intermolecular distance and interaction energy which are confirmed by other calculations. We can further conclude from our studies that one has to include higher orders in the perturbation expansion as the system becomes more complicated. It is especially the last aspect which hinders the application of the ab initio PCILO to estimate the major part of the electron correlation energy for large molecules.     

Ab initio calculations of the ground-state potential energy surface for the C?F bond decomposition in n-fluoropropane within the method for approximation of the frozen molecular fragment

The recently proposed ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by a frozen molecular fragment was tested further in a case of the dissociation reaction of the C? F bond in n-fluoropropane. Results from the Hartree–Fock, multiple reference double-excitation configuration–interaction and second-order Møller–Plesset methods are presented. The reproduction of potential energy surfaces as well as the reproduction of electron density distribution are in excellent agreement with extended basis-set calculations. Different choices of fragments to be frozen have been examined.     

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.