Constrained solutions of the eigenvalue problem in truncated basis sets

It is shown that simple orthogonality constraints between some set of known approximate eigenfunctions and another set of functions which are to be determined as approximate eigensolutions need to be modified. The proposed modification introduces a measure of the approximate character of the known functions and leads to the reduction of the dimensionality of the eigenvalue problem for other solutions. The discussed method is fully variational and leads directly to a Hermitian eigenvalue problem. This approach is also independent of the choice of truncated basis sets for different classes of approximate solutions of the eigenvalue problem. © 1997 John Wiley & Sons, Inc.     

Nonsingular two/one-component relativistic Hamiltonians accurate through arbitrary high order in α2

A series of nonsingular two-component relativistic Hamiltonians is derived from the Dirac Hamiltonian by first performing the free-particle Foldy–Wouthuysen transformation and then a block-diagonalizing transformation. The latter is defined in terms of operators which can be determined iteratively through arbitrary order in α, leading to transformed Hamiltonians with the two-component block accurate through α^2k, k=1, 2, 3,… . These Hamiltonians give relativistic energies which differ from Dirac's energies only in terms higher than α^2k. Their relation to other nonsingular methods of relativistic quantum chemistry (the Douglas–Kroll method, the regular Hamiltonian schemes) is discussed. By removing the spin-dependent operators, the derived Hamiltonians can be written in spin-free one-component form. The computational effort involved is essentially the same as in the case of the Douglas–Kroll scheme and amounts to relatively easy modification of the core Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 225–239, 1997     

Studies on the configuration of nitrogenous stereogenic centres in adducts of rhodium(II) tetraacylates with chiral amines: the application of 1H and 13C NMR spectroscopy

The ¹H and ¹³C NMR spectra of enantiomerically pure amines (S)-N,N-dimethyl-1-phenylethylamine, (S)-N-methyl-1-phenylethylamine, (S)-N-ethyl-1-phenylethylamine and (S)-N-ethyl-N-methyl-1-phenylethylamine in the presence of a twofold molar excess of dirhodium(II) tetratrifluoroacetate and dirhodium(II) Mosher’s acid derivatives [(4S) and (4R)] were measured in CDCl₃ as a solvent. The amines having various substituents at the nitrogen atom (H, CH₃ and CH₂CH₃) formed in such conditions as an equilibrium mixture of C_SN_R and C_SN_S 1:1 adducts. The signals of both diastereoisomers were observed in NMR spectra at either room temperature (303 K) or moderately decreased temperatures (263–273 K). The rates of mutual diastereoisomer conversion were estimated by selective inversion recovery experiments and varied from less than 0.1 to ca. 10 s^?1, depending on the ligand and temperature. Analysis of ¹³C NMR data and NOE experimental data resulted in the unambiguous determination of the configuration at the nitrogen atom with respect to the carbon stereogenic centre.Modelling of adduct structures and calculations of molecular energy and NMR parameters (GIAO) using Density Functional Theory (DFT) were performed in order to support the experimental findings. The calculations were carried out using 3-21G//B3LYP (structure optimizing) and 311G(2d,p)/LanL2DZ//B3LYP theory levels (molecular energy and NMR shielding).     

Strong interactions through the XAu–Y bridge: the Au bond?

The interaction between AuOH and the lone-pair donors (HF, H₂O) is shown to result in well-bound complexes whose structure resembles that of the corresponding H-bonded systems with the gold atom replacing hydrogen. The dissociation energies are estimated to be 10.7 and 27.4 kcal/mol for HFAu–OH and H₂OAu–OH, respectively. However, the interaction between AuOH and the lone pair donors is found to involve significant charge transfer. Furthermore, the Au–O stretching frequency increases upon the complex formation. It is concluded that, in spite of certain similarity to the H-bonded species, the Au-bonded complexes should be considered as Lewis acid–base pairs.     

Gaussian geminal basis set optimization with crude SCF reference state

Gaussian geminal basis functions for second-order correlation energy calculations according to the Sinanogˇlu method are optimized with reference to rather crude SCF functions. The optimized geminal basis set is then used in a one-step calculation of the correlation energy with respect to the near-Hartree-Fock reference State. The numerical results for the beryllium atom indicate the usefulness of the proposed technique.     

CNDO calculations of diamagnetic shielding in molecules

An approximate procedure for the calculation of diamagnetic shielding in molecules is presented. The method proposed is based on the ‘complete neglect of differential overlap’ (CNDO) molecular wave functions and is formulated according to the zero differential overlap (ZDO) approximation. The results obtained with several CNDO-type wave functions for diatomic and polyatomic molecules are in very good agreement with non-empirical SCF calculations. The ¹⁴N diamagnetic shielding constants in several molecules were computed and some approximations usually adopted in the interpretation of ¹⁴N chemical shifts are critically discussed. It was shown that in some cases the observed ¹⁴N chemical shifts cannot be interpreted solely in terms of the paramagnetic contribution to the shielding constant.     

Is fullerene C60 large enough to host an aromatic molecule?

The endohedral complex of fullerene with benzene was studied with computational chemistry methods. The changes of structural parameters, such as bond lengths of host and guest and volume increments accompanying complex formation, were investigated, as well as the transfer of electron density between host and guest. The results obtained with three DFT functionals, which were recently designed for weak interactions, were compared. A three‐centered hydrogen bond between H atom of benzene and two atoms of fullerene was found. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Importance of electron correlation effects and basis set superposition error in calculations of interaction energies and interaction-induced electric properties in hydrogen-bonded complexes: a model study

A detailed study of the interaction energies and interaction-induced electric dipole properties in model linear hydrogen cyanide complexes (HCN) _m (m?=?2?C4) is carried out within the finite field HF SCF, MP2, CCSD and CCSD(T) approximations using the recently developed LPol-n (n?=?ds, fs, dl, fl) basis sets. The importance of high-order correlation effects and the basis set superposition error is evaluated. To correct for the latter is crucial for obtaining accurate interaction energy values, but the error can safely be neglected in the estimation of induced electric properties when the LPol-n (n?=?ds, fs, dl, fl) basis sets are used. Correlation effects are important in the evaluation of both the interaction energies and the induced electric properties of the systems.