Valence Double-zeta Basis Set Research Articles

A non-self-consistent tight-binding electronic structure potential in a polarized double-ζ basis set for all spd-block elements up to Z = 86.

Existing semiempirical molecular orbital methods suffer from the usually minimal atomic-orbital (AO) basis set used to simplify the calculations. Here, a completely new and consistently parameterized tight-binding electronic structure Hamiltonian evaluated in a deeply contracted, properly polarized valence double-zeta basis set (vDZP) is described. The inner-shell electrons are accounted for by standard, large-core effective potentials and approximations to them. The primary target of this so-called density matrix tight-binding method is to reproduce the one-particle density matrix P of a molecular ωB97X-V range-separated hybrid density functional theory (DFT) calculation in exactly the same basis set. Additional properties considered are orbital energies, dipole polarizabilities and dipole moments, and dipole polarizability derivatives. The key features of the method are as follows: (a) it is non-self-consistent with an overall fixed number of only three required matrix diagonalizations; (b) only AO overlap integrals are needed to construct the effective Hamiltonian matrix; (c) new P-dependent terms emulating non-local exchange are included; and (d) only element-specific empirical parameters (about 50 per element) need to be determined. The method globally achieves a high accuracy for the target properties at a speedup compared to the ωB97X-V/vDZP reference of about 3-4 orders of magnitude. It performs robustly for difficult transition metal complexes, for highly charged or zwitterionic systems, and for chemically unusual bonding situations, indicating a generally robust approximation of the (self-consistent) Kohn-Sham potential. As an example application, the vibrational Raman spectrum of an entire protein with 327 atoms with respect to the DFT reference calculation is shown. This method may be used out-of-the-box to generate molecular/atomic features for machine learning applications or as the basis for accurate high-speed DFT methods.

Synthesis and elucidation of binuclear thiazole-based complexes from Co(II) and Cu(II) ions: Conductometry, cytotoxicity and computational implementations for various verifications

A new thiazole-based ligand was prepared and investigated then used to preparing its Co(II) and Cu(II) complexes. All available analytical (CHN analysis & TGA) and spectral (IR, UV–Vis, 1H NMR, Mass, SEM, XRD & EDX) techniques were applied to elucidate the chemical formulae of new compounds. The ligand behaved as a neutral tetradentate towards binuclear metal ions in the two complex via N-H, two C = N and C-S groups. A tetrahedral geometry was suggested for Co(II) complex according to 4A2(F)→4T1(F)(ʋ3) transition at 15,873 cm−1. While, a square-planer geometry was suggested for Cu(II) complex according to 2B1g →2B2g (ʋ1) and 2B1g → 2Eg transitions. The magnetic moment values of the two complexes were appeared lower than the normal values, due to binuclear presence minimized electron spinning. The mass spectra of the complexes recorded their molecular ion peaks that match to the molecular formula after expel of crystal water molecules. A conductometry study was executed for the complex formed from nano-sized CuCl2 and the ligand in solution to extract the association and formation constants as well as the M : L molar ratio. The stereo structures of the ligand and its binuclear complexes were optimized by DFT method under valence double-zeta basis set. The distribution of N(1)-N(10), C(11)-S(12) and C(15)-N(13) groups is suitable for their coordination with the two metal ions without bond strain. The in vitro assay was performed for the new compounds against HePG2, PC3 and MCF-7 cancer cell lines. The two complexes exhibited high toxicity against breast cancer cells. This result was confirmed interestingly via in silico ways as pharmacophore query and MOE-docking. The interaction parameters and docking patterns reflect the superiority of Co(II) and Cu(II) complexes in controlling breast cancer cell which agree with that obtained in vitro.

In-silico studies for kinetin hormone and its alkaline earth metal ion complexes as anti-aging cosmetics; synthesis, characterization and ability for controlling collagen-inhibitors

New Ca(II) and Mg(II) complexes were prepared from kinetin hormone at slightly basic medium. The isolated complexes were characterized by analytical and spectral (IR, Raman & 1H NMR) techniques to reach the most fitted chemical formulae. So simple molar ratio was suggested (1M:1L), which corresponds to lower molecular weights. According to spectral data, neutral bidentate mode of bonding was proposed for kinetin ligand, through N7and N10 donors. DFT method under valence double-zeta basis set in Gaussian 09, the compounds were optimized and their computational files were exported. Moreover, Fukui indices were also calculated by Materials Studio package, to extract global softness and electrophilicity features. All exported physical indexes as well as electrostatic potential maps, assert on mode of bonding and reflect the superiority of complexes in their features, specifically Mg(II) complex. Unit-cell for the tested compounds were drawn to put a simple view about their packing system within the crystal. In-silico assay was performed by drug-likeness software and Molecular Operating Environmental module. Drug-likeness parameters represent distinguish characteristics of kinetin and the two complexes at all. MOE-docking approach was performed towards co-crystal proteins as 1D8M, 1UKM and 5CJ8 that belong to collagen-inhibitors as well as 2UY5 as kinetin-protein itself. Potential interaction validity excreted data and patterns that clarify the excellent role of Mg(II) complex in controlling collagen-inhibitors. A promising future may be expected strongly for anti-aging cosmetic role of such kinetin-complex.

A quantum chemical study of the structure and energy of β-diketonates. XVII. Internal rotation of radical substituents in β-diketonate molecules

A quantum chemical study of the internal rotation of CX3 (X = H, F, CH3) radical substituents in scandium and calcium β-diketonate complexes is performed. Calculations are carried out using the GAUSSIAN-03 program at the HF and DFT/B3LYP levels with relativistic effective core pseudo-potentials and valence double zeta basis sets. Analytical expressions V(φ) are obtained that describe the potential energy variation during the rotation of CX3 groups. The rotation of CH3 and CF3 groups is shown to be described by a simple potential of the form V = V0/2 + V3cos(3φ), while for the description of the rotation of tert-butyl groups it is required to use a more complex function V = V0/2 + V3cos(3φ) + V6cos(6φ). Based on the obtained expressions for V(φ), the effective torsion angles φef of the rotation of CX3 groups are calculated for different temperatures. It is shown that φef obtained based on the quantum chemical calculations are close to the values obtained in electron diffraction experiments.

Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics

We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H(2)O, NH(3), and CH(4), are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.

On the influence of basis sets and quantum chemical methods on the prediction accuracy of COSMO-RS

This paper examines how the accuracy of activity coefficients at infinite dilution calculated from the conductor-like screening model for real solvents (COSMO-RS) depends on the basis set and the quantum chemical method used. Activity coefficients at various temperatures serve as experimental parameters for optimising the COSMO-RS parameters. A modification of the electrostatic misfit term of the energy function of COSMO-RS is presented that leads to a slightly higher accuracy. COSMO-RS parameter sets for nine different systematically varied basis sets using the density functional theory with the BP86 functional show that at least a valence double-zeta basis set is necessary for good accuracy. Larger basis sets show no advantages. Investigations of eight different quantum chemical calculation methods using a valence triple-zeta basis set are documented. Hartree-Fock and local density approximations give relatively poor results. The gradient-corrected density functionals investigated and the B3LYP hybrid functional show practically identical accuracy. The most accurate parameterisation was obtained with MP2.

Exploring NLO response of 9,10- donor-acceptor substituted Bichromophoric Anthracene Derivatives

Ab-initio finite field SCF calculations with split valence double zeta basis set indicate that 9, 10- donor-acceptor substituted anthracene derivatives have large quadratic hyperpolarizabilities for suitable combinations of donor and acceptor moieties. A difference in the first hyperpolarizabilitie s (βtotal) of isomeric organic chromophores containing the same donor and acceptor groups indicate the possible role of intramolecular charge transfer (ICT) in shaping the NLO response in these π-conjugated molecular chromophores. A correlation is sought to be established among calculated βtotal on one hand and the donor strength, the strength of the acceptor, donor-acceptor interaction and the donor-acceptor separation, on the other by using Genetic Algorithm (GA) to search through the relevant parameter space. It appears that βtotal of a molecule is dominantly determined by additive contributions from the donors and the acceptors. The results might be helpful in designing new NLO materials using the bichromophoric anthracene derivatives.

Density functional theory study of the mechanism for Ni(NHC) 2 catalyzed dehydrogenation of ammonia–borane for chemical hydrogen storage

The mechanism for catalytic dehydrogenation of ammonia–borane (AB = H 3N–BH 3), a promising candidate for chemical hydrogen storage, by the Ni(NHC) 2 complexes was studied by using density functional theory at the non-empirical meta-GGA level, Tao–Perdew–Staroverov–Scuseria (TPSS) functional, with all-electron correlation-consistent polarized valence double-zeta (cc-pVDZ) basis set. The mechanism for both the first and the second H 2 release from AB was studied for the first time. Several unusual aspects of this catalytic mechanism were revealed through our calculations. First, the first H 2 release begins with proton transfer from nitrogen to the Ni bound carbene carbon, forming a new C–H bond, instead of the previously hypothesized direct B–H or N–H bond activation. Second, this new C–H bond is activated by the metal, transferring the H to Ni, then forming the H 2 molecule by transferring another H from B to Ni, rather than β-H transfer. Third, the second H 2 release from H 2N–BH 2 begins with the breaking of a 3-center, 2-electron Ni–H–B bridging structure with the assistance of the unsaturated carbene carbon atom to form a B–C bond. Fourth, a nearly rhombic N 2B 2H 6 structure is formed to help the regeneration of the catalyst Ni(NHC) 2. These reaction pathways explain the importance of NHC ligands in this catalytic process and yield lower energy barriers than those mechanisms that begin with N–H or B–H activations catalyzed by the metal atoms. The predicted reaction mechanism which features unexpected ligand participation points the way to finding new catalysts with higher efficiency, as partial unsaturation of the M–L bond may be essential for low energy H transfers.

Multireference many-electron correlation energies from two-electron reduced density matrices computed by solving the anti-Hermitian contracted Schrödinger equation

Two-electron reduced density matrices (2-RDMs) have recently been directly calculated by solving the anti-Hermitian contracted Schr\"odinger equation (ACSE) to obtain $95$--$100\phantom{\rule{0.3em}{0ex}}%$ of the ground-state correlation energy of atoms and molecules with the accuracy increasing with the size of the one-electron basis set [Mazziotti, Phys. Rev. Lett. 97, 143002 (2006).] In this paper, the ACSE method is extended to treat strong multireference correlation effects that are often important at nonequilibrium molecular geometries. While previous ACSE calculations have employed an initial 2-RDM from the Hartree-Fock method, we initialize the solution of the ACSE with a 2-RDM guess from a multiconfiguration self-consistent field calculation. Applications are made to multireference correlation in the potential energy surfaces of the molecules $\mathrm{HF}$, ${\mathrm{H}}_{2}\mathrm{O}$, and ${\mathrm{C}}_{2}$ in polarized valence double-zeta basis sets while ${\mathrm{N}}_{2}$ is treated in polarized valence double- and triple-zeta basis sets. Accurate ground-state energies and 1-RDM occupation numbers are obtained at both equilibrium and nonequilibrium geometries where the energies are within a few millihartrees of those from full configuration interaction.

The Fluorobenzene−Argon S1 Excited-State Intermolecular Potential Energy Surface

We evaluate the first excited-state (S1) intermolecular potential energy surface for the fluorobenzene-Ar van der Waals complex using the coupled cluster method and the augmented correlation-consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. To calculate the S(1) interaction energies, we use ground-state interaction energies evaluated with the same basis set and the coupled cluster singles and doubles (CCSD) including connected triple excitations [CCSD(T)] model and interaction and excitation energies evaluated at the CCSD level. The surface minima are characterized by the Ar atom located above and below the fluorobenzene ring at a distance of 3.5060 A with respect to the fluorobenzene center of mass and at an angle of 5.89 degrees with respect to the axis perpendicular to the fluorobenzene plane. The corresponding interaction energy is -425.226 cm(-1). The surface is used in the evaluation of the intermolecular level structure of the complex, and the results are compared to the experimental data available and to those found in previous theoretical papers on ground-state potentials for similar complexes.

The p-Difluorobenzene−Argon S1 Excited State Intermolecular Potential Energy Surface

The first excited state (S1) intermolecular potential energy surface for the p-difluorobenzene-Ar van der Waals complex is evaluated using the coupled-cluster method and the augmented correlation consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. In order to calculate the S1 interaction energies we use the ground state surface evaluated with the same basis set and the coupled-cluster singles and doubles [CCSD] including connected triple excitations [CCSD(T)] model, and interaction and excitation energies evaluated at the CCSD level. The surface minima are characterized by the Ar atom located above and below the p-difluorobenzene center of mass at a distance of 3.4736 A. The corresponding interaction energy is -435.233 cm-1. The surface is used in the evaluation of the intermolecular level structure of the complex.

Potential-energy surface and van der Waals motions of p-difluorobenzene-argon cation

The structure and dynamics of the van der Waals complex of argon with the p-difluorobenzene cation are investigated using the ab initio theory. The restricted open-shell Møller-Plesset second-order perturbation method combined with the augmented correlation-consistent polarized valence double-zeta basis set is employed to determine the electronic ground-state potential-energy surface of the cationic complex. This surface is extremely flat in a wide region of the configuration space of the Ar atom which moves almost freely over the monomer ring. However, it is bound to the monomer stronger in the cationic than in the neutral complex. Its binding energy is calculated to be 621 cm(-1) at a distance of 3.445 A from the monomer center. The calculated dissociation energy of 572 cm(-1) agrees perfectly with the experimental value of 572+/-6 cm(-1) [S. M. Belm, R. J. Moulds, and D. Lawrence, J. Chem. Phys. 115, 10709 (2001)]. The effect of a strong coupling of large-amplitude intermolecular motions on the character of van der Waals vibrational states is investigated. The vibrational structure of the spectrum of the complex is explained and its earlier assignment is partly corrected.

Application of variational reduced-density-matrix theory to the potential energy surfaces of the nitrogen and carbon dimers

The acceleration of the variational two-electron reduced-density-matrix (2-RDM) method, using a new first-order algorithm [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], has shown its usefulness in the accurate description of potential energy surfaces in nontrivial basis sets. Here we apply the first-order 2-RDM method to the potential energy surfaces of the nitrogen and carbon dimers in polarized valence double-zeta basis sets for which benchmark full-configuration-interaction calculations exist. In a wave function formalism accurately stretching the triple bond of the nitrogen dimer requires at least six-particle excitations from the Hartree-Fock reference. Furthermore, cleaving the double bond of C2 should produce a "non-Morse"-like potential curve because the ground state near equilibrium (X 1sigma(g)+) has an avoided crossing with the second excited state (B' 1sigma(g)+) and a level crossing with the first excited state (B 1delta(g)). Because the 2-RDM method variationally optimizes the energy over correlated 2-RDMs on the two-electron space without parametrization of the many-electron wave function, it captures multireference correlations that are difficult to describe with approximate wave functions. The 2-RDM method yields for N2 a potential energy surface with features and spectroscopic constants that are more accurate than those from single-reference methods and similar in accuracy to multireference techniques, and it describes the non-Morse-like behavior of C2 which is not captured by single-reference methods.

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order Møller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order Møller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.

Direct ab initio dynamics study on the rate constants and kinetics isotope effects of CH3O+H→CH2O+H2 reaction

We present a direct ab initio dynamics study of thermal rate constants of the hydrogen abstraction reaction of CH(3)O+H-->CH(2)O+H(2). The unrestricted Becke's half-and-half hybrid functional using the Lee-Yang-Parr correlation functional with Dunning's correlation consistent polarized valence double-zeta basis set, the unrestricted quadratic configuration interaction calculation including single and double substitutions with Dunning's correlation consistent polarized valence double-zeta basis set, and the unrestricted quadratic configuration interaction calculation including single and double substitutions with a triples contribution with Dunning's correlation consistent polarized valence triple-zeta basis set methods were employed to optimize the structures and to calculate frequencies for all stationary points. Minimum energy paths were obtained by the unrestricted Becke's half-and-half hybrid functional using the Lee-Yang-Parr correlation functional and the unrestricted quadratic configuration interaction calculation including single and double substitutions with the same Dunning's correlation consistent polarized valence double-zeta basis set levels of theory. No barrier is found at the unrestricted Becke's half-and-half hybrid functional using the Lee-Yang-Parr correlation functional with Dunning's correlation consistent polarized valence double-zeta basis set level of theory in contrast to a small barrier of 1.43 kcal mol(-1) at the unrestricted quadratic configuration interaction calculation including single and double substitutions with Dunning's correlation consistent polarized valence double-zeta basis set level of theory. In particular, the barrier vanishes as the energies along the minimum energy path MEP are refined at the unrestricted quadratic configuration interaction calculation including single and double substitutions with a triples contribution with Dunning's correlation consistent polarized valence triple-zeta basis set level of theory. Smaller barriers of 0.47 and 0.17 kcal mol(-1) were obtained at the unrestricted quadratic configuration interaction calculation including single and double substitutions with a triples contribution with Dunning's correlation consistent polarized valence triple-zeta basis set and the unrestricted quadratic configuration interaction calculation including single and double substitutions with a triples contribution with Dunning's correlation consistent polarized valence triple-zeta basis set based on the geometries at the unrestricted quadratic configuration interaction calculation including single and double substitutions with Dunning's correlation consistent polarized valence triple-zeta basis set levels of theory, respectively. The forward rate constants are evaluated with the canonical variational transition state theory in the temperature range of 300-2500 K. The calculated forward rate constants at the unrestricted quadratic configuration interaction calculation including single and double substitutions with a triples contribution with Dunning's correlation consistent polarized valence triple-zeta basis set based on the geometries at the unrestricted quadratic configuration interaction calculation including single and double substitutions with Dunning's correlation consistent polarized valence double-zeta basis set level of theory are in good agreement with the available experimental data. The kinetic isotope effects are estimated.

The chlorobenzene-argon ground state intermolecular potential energy surface.

Using the coupled cluster singles and doubles including connected triple excitations model with the augmented correlation consistent polarized valence double zeta basis set extended with a set of 3s3p2d1f1g midbond functions, we evaluate the ground state intermolecular potential energy surface of the chlorobenzene-argon van der Waals complex. The minima of 420 cm(-1) are characterized by Ar atom position vectors of the length 3.583 A, forming an angle of 9.87 degrees with respect to the axis perpendicular to the chlorobenzene plane. These results are compared to those obtained for similar complexes and to the experimental data available. From the potential the three-dimensional vibrational eigenfunctions and eigenvalues are calculated and the results allow to correct and complete the experimental assignment.

Quantum chemical ab initio calculations of correlation effects in complex polymers: poly(para-phenylene).

Different quantum chemical approaches to the ground state correlation energy per unit cell of infinite poly(para-phenylene) (PPP) chains are presented. PPP is an organic polymer with interesting optical properties, due to its conjugated, aromatic pi system. The inclusion of correlation effects is crucial for a sound quantum chemical description of such a system. The correlation calculations were performed on the coupled cluster with single and double excitations (CCSD) level of theory using Dunning's spd correlation consistent polarized valence double-zeta basis sets. The correlation energy per unit cell is determined by means of the incremental method, which comprises series of CCSD calculations with partial excitation spaces. The resulting correlation energy per unit cell of PPP is -21.797 eV and compares well with that obtained by a simple but much more demanding cluster convergence approach (-21.775 eV). In addition, the accuracy and performance of the incremental scheme is discussed with respect to full CCSD benchmark calculations on PPP oligomers. Two variants are considered, the conventional one based on bond-type local units, and an extended one based on natural chemical subunits. Whereas it is difficult to reach "chemical" accuracy with the first variant, the second variant allows an accurate and efficient treatment with only a few individual CCSD calculations for a polymer with an aromatic pi system such as PPP.

Fluorobenzene-argon ground-state intermolecular potential energy surface.

The ground-state intermolecular potential energy surface for the fluorobenzene-argon van der Waals complex is evaluated using the coupled-cluster singles and doubles including connected triple excitations model, with the augmented correlation consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. In the surface minima the Ar atom is located above and below the fluorobenzene plane at a distance of 3.562 A from the fluorobenzene center of mass and at an angle of 6.33 degrees with respect to the axis perpendicular to the fluorobenzene plane. The corresponding binding energy is 391.1 cm(-1). Both these results and the eigenvalues obtained from the potential compare well with the experimental data available.

Efficient calculation of electron paramagnetic resonance g-tensors by multireference configuration interaction sum-over-state expansions, using the atomic mean-field spin–orbit method

Using the multireference configuration interaction method due to Grimme and Waletzke, combined with the atomic mean-field approximations for the efficient calculation of spin–orbit matrix elements, the g-tensors in second-order perturbation theory have been calculated for the main group radicals CO+, CN, BO, BS, MgF, AlO, O2, HCO, H2O+, NO2, CO2−, NF2, NO22−, O3−, ClO2, and H2CO+, and for the transition metal compounds ZnH, ZnF, and TiF3, using explicit sum-over-state expansions for up to 20 excited states. In most cases, a valence triple-zeta basis set with polarization functions has been employed. It is shown that the addition of diffuse functions to this basis set does not improve the g-tensor results, and in several instances leads to slower convergence of the sum-over-state expansion. The calculated g-tensors are in good agreement with experimental values, and with our previous multireference configuration interaction results available for 9 of the 19 radicals. Our results are shown to be equivalent to, or better than, values obtained by other theoretical methods. Examples of radicals for which g-tensor calculations presented problems in the past are AlO and TiF3. For AlO, we obtain Δg⊥=−1530 ppm (parts per million), compared with an experimental value of −1900 ppm in Ne matrix. Using the SVP (valence double-zeta plus polarization) basis set, Δg⊥ of TiF3 is calculated to be −115.3 ppt (parts per thousand), compared with experimental values of −111.9 and −123.7 ppt.

Ab initio Study of the Geometrical and Electronic Structures of Sc(MDA)2 and Sc(MDA)3 Molecules

The geometrical parameters, force fields, and vibrational spectra of various geometrical configurations of Sc(MDA)2 and Sc(MDA)3 molecules were calculated using the restricted Hartree—Fock method taking into account electron correlation by second–order Moller–Plesset perturbation theory. The calculations were performed using effective pseudopotentials for describing atomic cores and valence double zeta basis sets supplemented by polarization functions. It was shown that the configurations of D 3 [Sc(MDA)3] and D 2h [Sc(MDA)2] symmetry correspond to the minimum on the potential energy surface of the ground electronic state. The configurations of D 3h symmetry for Sc(MDA)3 and D 2d for Sc(MDA)2 correspond to first–order saddle points. The ground electronic states of Sc(MDA)2 and Sc(MDA)3 molecules are the states of 2 A g and 1 A 1 symmetries, respectively. For both configurations (D 2h and D 2d of the Sc(MDA)2 molecule, the energies of vertical electron transitions were calculated using the CASSCF method. The formation of chemical bonding in the compounds considered was analyzed. It was shown that the Sc–O bond is predominantly ionic and the π conjugation is characteristic only of the oxygen–carbon skeleton of the chelate fragment. The results obtained are compared with literature experimental and theoretical data for related compounds.