Effects of finite size nuclei in relativistic four-component calculations of hyperfine structure

The effect of a finite size model for both the nuclear charge and magnetic moment distributions on calculated EPR hyperfine structure have been studied using a relativistic four-component method based on density functional theory. This approach employs a restricted kinetically balanced basis (mDKS-RKB) and includes spin-polarization using noncollinear spin-density exchange-correlation functionals in the unrestricted fashion. Benchmark calculations have been carried out for a number of small molecules containing Zn, Cd, Ag, and Hg. The present results are compared with those obtained at the Douglas-Kroll-Hess second order (DKH-2) method. The dependence of the results on the quality of the orbital and auxiliary basis sets has been studied. It was found that some basis sets contain irregularities that deteriorate the results. Especial care has to be taken also on the construction of the auxiliary basis for fitting the total electron and spin-densities.     

Molecular mechanical calculations of the molecular structure of eight-coordinate europium complexes

Molecular mechanics methods were applied to the determination of the structure of eight-coordinate europium complexes: tris(acetylacetonato)Eu(III) trihydrate, tris(acetylacetonato) (1,10-phenanthroline)Eu(III), and tetrakis(benzoylacetonato)Eu(III). Optimization of MM2 force-field parameters and improvement of the calculation method were carried out using models of the complexes based on X-ray structural investigations. Steric ligandligand interactions in the first coordination sphere were treated as dominant for the lanthanide complexes. The major contributions to the energy are those of nonbonded 1,3-interactions between the atoms directly bound to the europium atom. The results of the calculations agree well with the crystal structures of the mentioned complexes.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1555–1559, September, 1993.     

Molecular structure calculations: a unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

We elaborate on the theory for the variational solution of the Schro?dinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schro?dinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H(2) (+) and H(2), three bound states of the positronium molecule, Ps(2), and the ground and two excited states of the (7)Li atom.     

Molecular structure and electronic spectrum of taspine: Semiempirical calculations

AM1 calculations show that taspine has the three energy-minima along the rotation-like nuclear displacement of the dimethylaminoethyl group. They correspond to two enantiomeric structures and a Cs structure, which have nearly equal energies. The energy barrier between the enantiomeric structures and the Cs structure is calculated to be about 1 kcal/mol. The small barrier readily causes an intramolecular interconversion of the two enantiomers through the Cs structure and thus results in the optical inactivity of taspine. CNDO/S calculations show that the electronic spectra of the enantiomer and the Cs structure are quite similar. These calculated spectra are in good agreement with the observed electronic spectra.     

Molecular structure of 1,2,3-triethyldiaziridine: Gas-phase electron diffraction and theoretical calculations

For the first time, the equilibrium molecular structure and conformational composition (6 to 8 conformers) of 1,2,3-triethyl-diaziridine in the gas phase were determined by gas-phase electron diffraction. Using 1D and 2D ¹H and ¹³C NMR spectro-scopy, it was shown that in a CDCl₃ solution under normal conditions on the NMR time scale, the molecule exists only as one conformer. The enthalpy of formation Δ_fH ⁰₂₉₈ of the studied molecule in the gas phase was calculated by the method of atomization reactions and is equal to 92.2 ± 1.7 kJ mol⁻¹.     

Molecular structure of ethynylbenzene from electron diffraction and ab initio molecular orbital calculations

The molecular structure and benzene ring distortions of ethynylbenzene have been investigated by gas-phase electron diffraction and ab initio MO calculations at the HF/6-31G^* and 6-3G^** levels. Least-squares refinement of a model withC _2v, symmetry, with constraints from the MO calculations, yielded the following important bond distances and angles:r _g(C _i -C _o )=1.407±0.003 Å,r _g(C _o -C _m )=1.397±0.003 Å,r _g(C _m -C _p )=1.400±0.003 Å,r _g(Cr _i -CCH)=1.436 ±0.004 Å,r _g(C=C)=1.205±0.005 Å, C _o -C _i -C _o =119.8±0.4°. The deformation of the benzene ring of ethynylbenzene given by the MO calculations, including o-C_i-C_o=119.4°, is insensitive to the basis set used and agrees with that obtained by low-temperature X-ray crystallography for the phenylethynyl fragment, C₆H₅-CC-, in two different crystal environments. The partial substitution structure of ethynylbenzene from microwave spectroscopy is shown to be inaccurate in the ipso region of the benzene ring.     

Molecular structure of 5-fluorouracil from gas-phase electron diffraction data and quantum-chemical calculations

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Molecular structure and electronic spectrum of ellagic acid: Semiempirical molecular orbital calculations

The molecular structure of ellagic acid has been optimized by using PM3 semiempirical MO method. Ellagic acid has been calculated to be planar with the molecular symmetry of C_2h. The lactone carbonyl groups are not tilted from the molecular plane. CNDO/S MO method has been used to interpret the experimental uv-vis spectroscopic data. The results of the PM3 and CNDO/S calculations have been in good agreement with the experimental data.     

Molecular orbital calculations for the HF crystal

CNDO based molecular orbital calculations are reported for solid HF and compared with results from a recent structural determination. It is found that theoretical structure is not in good agreement with that observed experimentally at 4 K.     

Relativistic band structure calculations

The inclusion of relativistic effects in band theory is discussed. Examples showing how these affect optical properties, Fermi surface properties, and cohesive properties are shown. With respect to the latter, it is pointed out that the mass–velocity and Darwin shifts are most important, whereas the SO coupling can be omitted since it does not shift the bands (quenching of angular momentum). The band theoretical aspects are presented in the terminology of the LMTO -ASA method which offers a physical transparent picture of the formation of bands. The volume and energy dependences of the spin-orbit splittings are explained in this picture. As examples are considered calculations for W, Xe, Au, and the copper halides.     

Molecular structure and conformations of benzenesulfonamide: gas electron diffraction and quantum chemical calculations

The molecular structure and conformational properties of benzenesulfonamide, C6H5SO2NH2, were studied by gas electron diffraction (GED) and quantum chemical methods (MP2 and B3LYP with different basis sets). The calculations predict the presence of two stable conformers with the NH2 group eclipsing or staggering the SO2 group. The eclipsed form is predicted to be favored by about 0.5 kcal/mol. According to GED, the saturated vapor over solid benzenesulfonamide at a temperature of 150(5) degrees C consists of the eclipsed conformer. The GED intensities, however, possess a very low sensitivity toward the vapor composition, and contributions of the anti conformer of up to 75% (at the 0.05 level of significance) or up to 55% (at the 0.25 level of significance) cannot be excluded. The molecule possesses C(sS) symmetry with the S-N bond perpendicular to the ring plane.     

Molecular structure and rotational isomerism in glyoxylicacid from microwave spectroscopy and ab initio calculations

An improved substitution structure for glyoxylic acid in the hydrogen bonded trans-1 form is presented. By means of microwave double resonance spectroscopy, the trans-2 form, with a zig-zag chain of atoms HOCCH, was identified. Using trans-2 dipole moment components calculated by ab initio SCF theory, the energy of the trans-2 form is found to be 1.2 ± 0.5 kcal mole^?1 higher than that of the trans-1 form. The ab initio energy difference (?1.0 kcal mole^?1) has the wrong sign.     

Molecular structure of caffeine as determined by gas electron diffraction aided by theoretical calculations

The molecular structure of caffeine (3,7-dihydro-1,3,7-trimethyl-1H-purine-2,6-dione) was determined by means of gas electron diffraction. The nozzle temperature was 185 °C. The results of MP2 and B3LYP calculations with the 6-31G⁷ basis set were used as supporting information. These calculations predicted that caffeine has only one conformer and some of the methyl groups perform low frequency internal rotation. The electron diffraction data were analyzed on this basis. The determined structural parameters (r_g and ∠_α) of caffeine are as follows: <r(NC)_ring> = 1.382(3) Å; r(CC) = 1.382(←) Å; r(CC) = 1.446(18) Å; r(CN) = 1.297(11) Å; <r(NC_methyl)> = 1.459(13) Å; <r(CO)> = 1.206(5) Å; <r(CH)> = 1.085(11) Å; ∠N₁C₂N₃ = 116.5(11)°; ∠N₃C₄C₅ = 121. 5(13)°; ∠C₄C₅C₆ = 122.9(10)°; ∠C₄C₅N₇ = 104.7(14)°; ∠N₉–C₄=C₅ = 111.6(10)°; <∠NCH_methyl> = 108.5(28)°. Angle brackets denote average values; parenthesized values are the estimated limits of error (3σ) referring to the last significant digit; left arrow in parentheses means that this parameter is bound to the preceding one.     

Molecular structure of noradrenaline according to gas-phase electron diffraction data and quantum chemical calculations

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Molecular structure of carphedon as studied by gas electron diffraction and quantum chemical calculations

The gas-phase structure and conformational properties of carphedon (C₁₂H₁₄N₂O₂, phenylpiracetam, 2-oxo-4-phenyl-1-pyrrolidineacetamide) have been determined by gas electron diffraction (GED) and quantum chemical calculations (B3LYP and MP2 with 6-31G and cc-pVDZ basis sets). Since quantum chemical calculations demonstrate that the orientation of the acetamide group is fixed by a strong intramolecular N–H(amide)···O(pyrrolidone) hydrogen bond, the number of possible conformers is reduced considerably. Depending on the conformation of the pyrrolidine ring, envelope with out-of-plane C4 atom and acetamide group on the same side of the plane (“+”) or envelope with C4 and acetamide group on opposite sides (“?”), and on the orientation of the phenyl ring, axial (Ax), or equatorial (Eq), four relevant conformations, Ax?, Ax+, Eq?, and Eq+, exist. According to both quantum chemical methods (B3LYP and MP2 with cc-pVDZ basis sets) these four conformers differ by less than 2 kcal/mol in free energies. However, the two methods predict different relative free energies. The GED data were analyzed with different models. With a single-conformer model the best fit of the experimental GED intensities (agreement factor R _f = 4 %) is obtained with the Ax+ conformer. Using a two-conformer model the fit improves considerable for a 50(11):50(11) mixture of Ax? and Eq+ conformers (R _f = 2.7 %). No further improvement is obtained with a three-conformer model and large uncertainties for relative contributions occur. The geometric parameters of gaseous carphedon are compared with those in the crystal phase, where two molecules are connected by two intermolecular N–H···O hydrogen bonds, and with gas-phase values of piracetam.     

Molecular conformations and relative stabilities can be as demanding of the electronic structure method as intermolecular calculations

We have performed a variety of high-level electronic structure calculations on two moderately sized organic molecules and found considerable sensitivity of the intramolecular potential energy surface to the method employed. The gas-phase structure of tyrosine-glycine varies qualitatively between B3LYP and MP2 optimizations, producing different close contacts between the tyrosine ring and the glycine moiety. The relative energies of the 2-(acetylamino)benzamide conformations found in its two polymorphs can vary by over 20 kJ mol-1 between MP2 and B3LYP calculations, using the same basis set. It is shown by a novel analysis that the intramolecular equivalent of basis set superposition error competes with the errors in the intramolecular dispersion in causing this sensitivity.     

Molecular MC–SCF calculations

A practical method for finding multi-configurational SCF wave functions is proposed. The basic equation is equivalent to the Brillouin theorem; comparison with the usual SCF equations obtained through effective hamiltonians gives an interpretation of the offdiagonal Lagrange multipliers. Numerical applications to Formaldehyde in a minimum Slater-type orbital basis with four different variational wave functions are reported. The molecular orbitals found in these calculations are localized on the chemical bonds. The largest contributions to the energy are obtained from π-π and dispersion-type σ-π correlation.     

Molecular orbital calculations on polythiophenes containing heterocyclic substituents: effect of structure on electronic transitions

Molecular orbital calculations have been performed on thiophene oligomers bearing heterocyclic substituents at the third position in order to understand the interplay of effects such as the nature of substituent, skeletal substitution pattern, heteroatom identity, etc. on electronic transitions. The geometry optimization was carried out using the semiempirical AM1 method, and the electronic transitions predicted for the oligomers were extrapolated for polymers using an oligomeric approach. The experimentally determined optical transitions were found to follow the predicted trend of electronic transitions of monomers and polymers.