Equilibrium Geometric Parameters Research Articles

Theoretical study of stationary points of the MgSiO 3 molecule

Structural properties of energetically low-lying stationary points of the MgSiO 3 molecular system have been investigated by theoretical density functional techniques. A large number of singlet and triplet structures representing local minima of the neutral MgSiO 3 molecule are completely characterised. The energetically lowest of these minima is a singlet state of planar kite-shaped C 2v symmetry. The system equally possesses a variety of stable charged species of which the respectively lowest in energy is presented. We report energies, equilibrium geometric parameters, selected harmonic vibrational wave numbers along with corresponding absorption coefficients. Stability and geometric aspects are compared to the molecules Si 2O 3 and Mg 2O 3, as well as to the isoelectronic Al 2O 3 molecular system.

A density functional study of small (AlN) x clusters: structures, energies, and frequencies

Structural properties of energetically low-lying stationary points of small aluminium/nitrogen clusters with unity stoichiometric ratio (AlN) x ( x=1,2,4,6,12) have been investigated by theoretical density functional techniques employing the Becke–Perdew-86 gradient corrected exchange correlation functional. A large number of singlet and triplet stationary points representing local minima and transition structures of (AlN) x are completely characterised. We report energies, equilibrium geometric parameters, selected harmonic vibrational wave numbers along with corresponding absorption coefficients. Stability and geometric aspects of (AlN) 12 are discussed in detail by introducing a measure of sphericity.

The vibrational energy pattern in propyne ( 12CH 312C 2H)

The results of ab initio calculations at the MP2 level of theory are presented, which provide refined equilibrium geometrical parameters and better characterization of the vibrational normal modes in propyne (CH 3C 2H). These results help performing the vibrational analysis of the high resolution Fourier transform absorption spectrum of this molecule which has been recorded between 2000 and 10 200 cm −1. The vibrational assignment criteria also include, in particular, the detailed identification of the band shape based on the observed rotational structure that is resolved for most bands. Some 46 bands are observed and their band shape identified in most cases. Among the bands newly reported, some 14 are vibrationally assigned, three of them tentatively. The relative intensity of all observed bands is estimated from the spectra. Approximate ζ rotational constants are obtained for ν 3+ ν 6 (0.074) and 2 ν 1+ ν 8 (0.38). The results are merged with those of the previous literature, leading to list the origin of 118 vibrational bands, from which an extensive set of vibrational constants is extracted. Two polyad quantum numbers emerge from the vibrational energy pattern: N sb=3 v 1+ v 3+2 v 5+ v 9 and N s= v 1+ v 3, supported by the ν 1 with ν 3+ ν 5 and ν 1 with ν 3+2 ν 9 anharmonic resonances.

Effect of finite domain-wall width on the domain structures of epitaxial ferroelectric and ferroelastic thin films

A theory of domain (twin) structures, which takes into account the finite width of domain walls, is developed for epitaxial ferroelectric and ferroelastic thin films. The theory is based on the dislocation–disclination modeling of the sources of mechanical stresses in polydomain films. Calculations are performed for an orthorhombic or tetragonal film grown on a dissimilar orthorhombic, tetragonal, or cubic substrate. The case of a laminar 90° domain structure with the walls inclined at 45° to the film/substrate interface (c/a/c/a structure in tetragonal films) is considered. A simple dislocation–disclination model is constructed for the junctions of thick domain walls with the film/substrate interface. Using this model, the stress fields in the film and substrate and the associated elastic energy are evaluated. By minimizing the total energy of the material system at a fixed domain-wall width, the equilibrium geometric parameters of a periodic 90° domain structure are calculated. Then the range of stability of this structure in epitaxial films is determined as a function of the wall width. The mechanical restoring forces, which hinder cooperative translational vibrations of thick 90° walls near their equilibrium positions, are also calculated. On this basis, the domain-wall contributions to the dielectric and piezoelectric responses of prepolarized ferroelectric films are evaluated at different wall widths. Finally, the influence of the film straining by the substrate on the equilibrium domain-wall width is analyzed. An increase of the wall width in an epitaxial thin film relative to that in a bulk crystal is predicted.

Equilibrium conformation of dimethylaminodichlorophosphine molecule: the use of the results of quantum-chemical calculations and spectroscopic measurements in the analysis of gas-phase electron diffraction data

Geometric parameters and force fields of two stable isomers of dimethylaminodichlorophosphine molecule, a gauche-conformer with C1 symmetry (A) and anti-conformer with C s symmetry (D), resulting from internal rotation about the P—N bond, were calculated in the RHF/6-31G* approximation. Using the scaled quantum-chemical force field for the most stable conformer A, the first reliable interpretation of the vibrational spectra of the light and perdeuterated isotopomers of dimethylaminodichlorophosphine was obtained. The root-mean-square vibrational amplitudes, harmonic and anharmonic vibrational corrections, and centrifugal distortion corrections were also calculated. Structural analysis of electron diffraction data was performed with consideration of nonlinear kinematic effects at the first-order level of perturbation theory. The experimental values of the equilibrium geometric parameters were estimated. The results obtained suggest a nonplanar equilibrium configuration of the amino group in the dimethylaminodichlorophosphine molecule.

Isomerism and Vibrational Spectra of Alkali Metal Perrhenates: Ab Initio CISD+Q Calculations

The equilibrium geometric parameters, isomerization energies, force fields, vibrational frequencies and intensities in the IR spectra of MReO4 molecules (M = Li, Na, K) are calculated by the configuration interaction method including all singly and doubly excited configurations with Davidson's correction for quartic excitations in expanded basis sets using effective relativistic core potentials. The calculations indicate that the chemical bonds between the metal atoms and the ReO4 anion group are highly polar. It is found that the MReO4 molecule has two isomers. The basic isomer with C2v symmetry has bidentate b coordination of the M+ cation to the ReO 4 - anion. The excited isomer is of C3v symmetry and corresponds to monodentate m coordination of M+. The low relative energies of the m isomers (17-29 kJ/mole) and the low energy barriers to the intramolecular m→b rearrangements (5-11 kJ/mole) indicate that MReO4 molecules are structurally nonrigid systems where the M–XO4 chemical bonds are “polytopic.” The results of calculations are compared with the available literature data on the structure and vibrational spectra of MReO4 molecules.

Electronic structure investigation of the Al 4O 4 molecule

Structural properties of energetically low-lying isomers of the isolated Al 4O 4 molecular system have been investigated by theoretical ab initio techniques within the Hartree–Fock (HF) and second-order Møller–Plesset (MP2) frozen core level of approximation and density functional methods (DFT) employing the Becke-3–Perdew-86 (B3P86) hybrid functional. In total, nine local minima representing six Al 4O 4 isomers of various spin multiplicities are completely characterised. The two energetically lowest of these stationary points, a singlet of planar D 2 h and a triplet of cubic T d symmetry, are furthermore sifted by considering other choices of exchange (B, B3) and correlation (LYP, PW91) functionals as well as higher levels of theory (G2/MP2, G2, and CCSD(T), D 2 h only). We report energies, equilibrium geometric parameters, selected harmonic vibrational wavenumbers along with corresponding absorption coefficients and compare the different computational approaches.

The structure of CX2YNO (X, Y=F, Cl) molecules in the ground and lowest excited singlet electronic states

Ab initio quantum-chemical calculations of equilibrium geometric parameters, vibrational frequencies, and potentials of internal rotation for CCIF2NO and CCl2FNO molecules in the ground (S0) and lowest excited singlet (S1) electronic states were performed. The results of calculations were compared with experimental data. A new interpretation of experimental spectra of the CCIF2NO molecule was suggested.

Ab initio study of the molecular structure, isomerism, and vibrational spectra of MAF4. (M = Li, Na, K; A = Al, Ga)

The equilibrium geometrical parameters, force constants, vibration frequencies, IR intensities, and isomerization and dissociation energies of MAF4 molecules are calculated by Hartree-Fock and second-order Moller — Plessett perturbation theory methods in the Li (9s3pld/4s3pld), Na, Al (12s8pld/6s4pld), K (14s11p3d/9s8p3d), F (9s5pld/4s2pld), and Ga (13s10p5d/6s5p2d) bases of grouped Gaussian functions. The calculations show that the structures corresponding to the bi-(b) and tridentate (t) coordinations of the M+ cation by the AF 4 - anion are isomers. The b configuration is energetically most favorable for LiAF4 molecules. The b and t structures of NaAF4 have close energies, and the t configuration is basic for KAF4 molecules. Simple empirical relations between the molecular constants in the series LiAF4→NaAF4→KAF4 are found and the molecular parameters of RbAF4 and CsAF4 are estimated. A combined analysis of the ab initio and experimental data available in the literature for MAF4 molecules is carried out. A number of bands observed in the IR spectrum of the matrix-isolated MAlF4 molecules are assigned to their tridentate isomer.

Ab initio study of the structure, force fields, and vibrational spectra of alkali metal tellurites

The equilibrium geometrical parameters, force fields, vibration frequencies, and intensities in the IR molecular spectra of M2TeO3 (M-Li, Na, K) are found by the Hartree — Fock ab initio method in the bases complemented with polarization and diffusion functions using relativistic effective core potentials. The relative energies of alternative molecular configurations and the energies of the dissociation M2TeO3→ M2O + TeO2 are refined using Moller — Plessett second-order perturbation theory. It is found that the chemical bond in these molecules can be approximated by the scheme (M+)2[TeO3]2- The equilibrium nuclear configuration has Cs symmetry and corresponds to the bis-bidentate coordination of M+ cations by the pyramidal anion [TeO3]2-. The mono-bidentate structures of Cs symmetry correspond to the saddle points on the potential energy surface of the molecules. The calculated IR molecular spectrum of K2TeO3 agrees with the experimental spectrum obtained by the matrix isolation method by J. Ogden et al. [J. Chem. Soc. Dalton Trans., 1957 (1997)]. Based on the results of the previous ab initio studies of alkali metal sulfites and selenites, the barrier of the intramolecular rearrangement (bb)→(mb)→(bb)’ was found to lower in the series Li2XO3→Na2XO2→K2XO3 (X = S, Se, Te) and M2TeO3→M2SeO3→M2SO3. The degree of deformation of the XO fragment in the M2XO3 molecules decreases when the M atom is replaced by its heavier analog (Li→Na→K).

Ab initio study of molecular structure and internal rotation in methyldicyanophosphine and methyldiisocyanophosphine. The Raman spectrum of methyldicyanophosphine and its interpretation with the use of scaling ofab initio force fields

The equilibrium geometric parameters and structures of transition states of internal rotation for the molecules of methyldicyanophospine MeP(CN)2 and its isocyano analog MeP(NC)2 were calculated by the RHF and MP2 methods with the 6–31G* and 6–31G** basis sets. At the MP2 level, the total energy of cyanide is −35 kcal mol−1 lower than that of isocyanide and the barriers to internal rotation of methyl group for MeP(CN)2 and MeP(NC)2 are 2.2 and 2.7 kcal mol−1, respectively. For both molecules, the one-dimensionalab initio potential functions of internal rotation approximated by a truncated Fourier series were used to determine the frequencies of torsional transitions by solving direct vibrational problems for a non-rigid model. The Raman spectrum of crystalline MeP(CN)2 was recorded in the range 3500–50 cm−1. The vibrational spectra of this compound were interpreted by scalingab initio force fields calculated by the RHF and MP2 method. The vibrational spectrum of methyldiisocyanophosphine was predicted with the use of the obtained scale factors.

Ab initio study of the molecular structures, force fields, and vibrational spectra of alkaline metal fluoride dimers MM′F2 (M, M′=Li, Na, K)

Ab initio calculations of the equilibrium geometrical parameters, force constants, and IR vibration frequencies and intensities of Li2F2, Na2F2, K2F2, LiNaF2, LiKF2, and NaKF2 are reported. The calculations use the Hartree-Fock-Roothaan method and second-order Moller-Plesset perturbation theory along with configuration interaction theory including singly and doubly excited configurations and corrections for quartic excitations with basis sets of grouped Gaussian functions: Li — (9s3p1d/4s3p1d), Na — (12s8p1d/6s4p1d), K — (14s11p3d/9s8p3d), F — (9s5p1d/4s2p1d). According to the results of calculations, the equilibrium structures of the molecules are planar cyclic structures of D2h (for M2F2) and C2v (for MM′F2) symmetries. The linear configurations M-F-M′-F (of C∞v symmetry) are 70–190 kJ/mole less stable than the cyclic ones; for all molecules except M-F-K-F, these configurations correspond to local minima on the potential energy surface. The role of correlation effects in ab initio calculations of the geometry, force fields, and IR characteristics of molecules with highly polar chemical bonds is discussed. The theoretical force fields of the molecules are represented in canonical form in a system of redundant natural vibrational coordinates. The force fields of MM′F2 molecules are studied. The results of the ab initio calculations are compared with the experimental structural data and vibrational spectra available in the literature.

Ab initio relativistic pseudopotential study of small silver and gold sulfide clusters (M2S)n, n=1 and 2

Small semiconductor silver and gold sulfide clusters (Ag2S)n and (Au2S)n, n=1,2, are studied by valence ab initio calculations with the inclusion of electron correlation at the second-order perturbation theory (MP2) and coupled-cluster [CCSD and CCSD(T)] levels. Various relativistic and nonrelativistic pseudopotentials are employed to describe the effects of core electrons. Correlation and relativistic effects are essential in determining the geometry and relative stability of monomer and dimer structures. Relativistic effects result in a notable decrease in the calculated interatomic distances, which is especially significant in the case of gold sulfide structures (up to 10%). Correlation effects markedly increase the stability of compact structures with an increased number of relatively short M…M contacts (M…M distances of about 280–330 pm). Excluding the correlation of lower-lying valence orbitals (sulfur 3s and silver 4d or gold 5d) results in completely opposite predictions. This fact suggests that the effects of d–d and d–outer valence (metal ns and sulfur 3p) electron correlation give rise to attractive short-range interactions of intramolecular van der Waals type, which determine the increased stability of more compact cluster structures. However, large-core pseudopotentials strongly exaggerate this effect in the case of gold and give results rather different from those obtained with more valid and accurate small-core pseudopotentials. It is shown that the reason for this deficiency lies in the nature of pseudopotentials themselves rather than in basis-set shortcomings. The atomization and dissociation energies, equilibrium geometrical parameters, dipole moments, and Mulliken populations are calculated and discussed.

Conformational investigation of alpha,beta-dehydropeptides. IX. N-Acetyl-(E)-alpha,beta-methylamide: stereoelectronic properties from infrared and theoretical studies.

The Fourier transform infrared spectra of Ac-(E)-deltaAbu-NHMe were analyzed to determine the predominant solution conformation(s) of this (E)-alpha,beta-dehydropeptide-related compound and the electron density perturbation in its amide groups. The measurements were performed in dichloromethane and acetonitrile in the region of mode vs (N-H), amide I, amide II and vs (C(alpha)=Cbeta). The equilibrium geometrical parameters, calculated by a method based on the density functional theory with the B3LYP functional and the 6-31G* basis set, were used to support spectroscopic interpretation and gain some deeper insight into the molecule. The experimental and theoretical data were compared with those of three previously described molecules: isomeric Ac-(Z)-deltaAbu-NHMe, Ac-deltaAla-NHMe, which is deprived of any beta-substituent, and saturated species Ac-Abu-NHMe. The titled compound assumes two conformational states in equilibrium in the DCM solution. One conformer is extended almost fully and like Ac-deltaAla-NHMe is C5 hydrogen-bonded. The other adopts a warped C5 structure similar to that of Ac-(Z)-deltaAbu-NHMe. The C5 hydrogen bond, unlike the H-bond in Ac-deltaAla-NHMe, is disrupted by acetonitrile. The resonance within the N-terminal amide groups in either of the (E)-deltaAbu conformers is not as well developed as the resonance in Ac-Abu-NHMe. However, these N-terminal groups, compared with the other unsaturated compounds, constitute better resonance systems in each conformationally related couple: the C5 hydrogen-bonded Ac-(E)-deltaAbu-NHMe/Ac-deltaAla-NHMe and the warped C5 Ac-(E)-deltaAbu-NHMe/Ac-(Z)-deltaAbu-NHMe. The resonance within the C-terminal groups of the latter couple apparently is similar, but less developed than the resonance in Ac-Abu-NHMe. The electron distribution within the C-terminal group of the hydrogen-bonded C5 (E)-deltaAbu conformer apparently is determined mainly by the electron influx from the C(alpha)=Cbeta double bond.

Conformational investigation of alpha,beta-dehydropeptides. VIII. N-acetyl-alpha,beta-dehydroamino acid N'-methylamides: conformation and electron density perturbation from infrared and theoretical studies.

The Fourier transform infrared spectra are analyzed in the regions of Vs(N-H), amide I, amide II and Vs(C alpha = C beta) bands for a series of Ac-delta Xaa-NHMe, where delta Xaa = delta Ala, (Z)-delta Abu, (Z)-delta Leu, (Z)-delta Phe and delta Val, to determine the predominant solution conformation of these alpha,beta-dehydropeptide-related molecules and the electron distribution perturbation in their amide bonds. The measurements were performed in dichloromethane (DCM). To confirm and rationalize the assignments, the spectra of the respective series of saturated Ac-Xaa-NHMe, recorded in DCM, and the spectra of these two series of unsaturated and saturated compounds, recorded in acetonitrile, were examined. To help interpret the spectroscopic results, the equilibrium geometrical parameters for some selected amides were used. These were optimized with ab initio methods in the 6-31G** basis set. Each of the dehydroamides studied adopted a C5 structure, which in Ac-delta Ala-NHMe is fully extended and accompanied by the strong C5 hydrogen bond. Interaction with the C alpha = C beta bond lessened the amidic resonance within each of the flanking amide groups. The N-terminal C = O bond was noticeably shorter, both amide bonds were longer than the corresponding bonds in the saturated entities and the N-terminal amide system was distorted. Ac-delta Ala-NHMe constituted an exception. Its C-terminal amide bond was shorter than the standard one and both amide systems were prototypically planar.

An ab initio study of the structure, dissociation energy, and heat of formation of Na2S

The equilibrium geometries and fundamental frequencies of Na2S are calculated at HF, MP2(FC, FU), and MP3 with the 6–31G(d) basis set and at HF and MP2(FC, FU) with the 6–31G(d) basis set, respectively. The total energy at MP2(FU)/6–31G(d)-optimized geometry is computed at MP4 with 6–311G(d, p), 6–311 + G(d, p), and 6–311G(2df, p), at QCISD(T)/6–311G(d, p), and at MP2/6–311G(3df, 2p) levels, respectively. The dissociation energy, the atomization energy, and the heat of formation for Na2S are evaluated using the G1 and G2 models. The calculated results indicated that Na2S in its ground state was a bent structure (C2v). Electron correlation corrections on the bending angle are very significant. The equilibrium geometrical parameters are Re(Na-S) = 2.45 Å and ∠Na-S-Na = 111.13° at the MP2(FU)/6–31G(d) level. The theoretically estimated dissociation energy, total atomization energy, and heat of formation are 67.07, 117.55, and 0.35 kcal mol−1, respectively, at 298.15 K. © 1997 John Wiley & Sons, Inc.

Ab initio investigation of tautomeric stability, molecular structure, and internal rotation of methylphosphonic dicyanide, methoxydicyanophosphine, and their isocyano analogs

The equilibrium geometric parameters and structures of the transition states of internal rotation for MeP(O)(CN)2, McOP(CN)2, and their isocyano analogs, MeP(O)(NC)2 and MeOP(NC)2, have been calculated by theab initio SCF method and with inclusion of electron correlation effects according to the second-order Muuller-Plesset perturbation theory (MP2). At both levels the 6-31G* basis set has been used. The estimation of relative stability of these tautomeric forms depends largely on the calculation level. The total energies of the cyanides calculated by the MP2 method are 25–30 kcal mol−1 lower than those of the corresponding isocyanides. The oxo-tautomeric forms containing four-coordinate phosphorus are 15–25 kcal mol−1 more stable than the three-coordinate phosphorus aci-derivatives. The internal rotation potential curves of the aci-forms are characterized by a deep minimum for thetrans-arrangement of the methoxy group and phosphorus lone electron pair. Two additional less clearly pronounced minima are located symmetrically on both sides of the weak maximum, which corresponds to thecis-arrangement. The equilibrium oxo-form structures have a staggered configuration of the methyl group with respect to the phosphorus atom bonds.

The self-consistent nonorthogonal group function approach in reduced basis frozen-core calculations

The orthogonal group function approach, as based on the Huzinaga equation, is extensively applied in reduced basis frozen-core calculations. Although the theory is developed for orthogonal electronic groups, the use of reduced basis sets prevents strict orthogonality and the formalism is complemented to take, partially, into account nonorthogonality (projection factors, projection energy). In the present article, an alternative to this approach, based on the nonorthogonal formalism, is proposed. An orbital equation is derived from the Adams-Gilbert equation and the energy is evaluated according to a recent proposal based on the power-series expansion of the overlap energy. A comparative overview of the orthogonal and nonorthogonal formalisms is presented and the results of reduced basis frozen-core calculations as obtained with the two methods are compared. It is found that the nonorthogonal formulation predicts equilibrium geometrical parameters in some cases similarly and, in other cases, slightly better than does the orthogonal one. Based on this observation and on the fact that the nonorthogonal formulation is exempt from empirical parameters (projection factors), it is concluded that the nonorthogonal formalism represents an appealing alternative in reduced basis frozen-core calculations. © 1996 John Wiley & Sons, Inc.

Energetics and geometry of 90° domain structures in epitaxial ferroelectric and ferroelastic films

Statics of 90° domain structures formed in a thin tetragonal film epitaxially grown on a cubic substrate is studied theoretically on the basis of a rigorous solution of the associated elasticity problem. Inhomogeneous internal stresses existing in the strained polydomain epitaxy are calculated by the method of fictitious dislocations distributed along domain boundaries and the film/substrate interface. The calculation properly takes into account the influence of the film free surface on the field of internal stresses. For both possible periodic laminar structures, the energies of elastic strain fields existing in the film and the substrate are evaluated. These results are used to compute the equilibrium geometric parameters of periodic domain structures that minimize the total internal energy of a polydomain epitaxy. The dependencies of the equilibrium parameters on the film thickness and the relative misfit strain between the substrate and film are described. By comparing the minimum internal energies associated with various domain configurations, a diagram of equilibrium domain patterns is developed. In the range of relative misfit strains lower than some critical value, two threshold film thicknesses exist, separating three stability regions of domain patterns which correspond to a monovariant film and two periodic domain structures. In the rest of the diagram, a pattern consisting of equivalent domains with the tetragonal axes parallel to the interface is stable, irrespective of the film thickness.

Ab initio calculations on the geometry and OH vibrational frequency shift of cyclic water trimer

The equilibrium geometrical parameters R OO θ and χ of cyclic water trimer have been determined at the counterpoise corrected SCF+MP2 level in the ESPB basis within pseudo-C 3v symmetry. The final structure has short ( R OO=2.85 Å) and strongly bent (θ=20°) hydrogen bonds. The non-bonded OH bonds are directed by χ=48° out of the OOO plane. The interaction energy (Δ E) is −14.7 kcal mol −1 and the corresponding D 0=10.2 kcal mol −1. The likely error bars on these results are discussed. The second order polarization interactions in the trimer are markedly non-additive. The total non-additivity contributes −2.0 kcal mol −1 to the final Δ E, and it is responsible for a shortening of R OO by 0.07 Å. Its largest effect (about −70 cm −1) is in the H-bonded OH vibrational frequency shift Δν OH, which at the equilibrium geometry is calculated to be −230 cm −1. The shift is markedly sensitive to the angle χ, and vibrational averaging along this coordinate is expected to reduce Δν. The results therefore support Nelander's reassignment of the IR and Raman gas phase OH spectra, which implies Δν OH≈ −175 cm −1.