Calculated Equilibrium Geometries Research Articles

Energetic stability, equilibrium geometry, and electronic properties of Bi-inducedSi(001)−(2×n)surfaces

We have performed ab initio theoretical investigations of the equilibrium geometry, energetic stability, and electronic properties of the Bi covered $\mathrm{Si}(001)\text{\ensuremath{-}}(2\ifmmode\times\else\texttimes\fi{}n)$ surface. We have examined the currently proposed $(2\ifmmode\times\else\texttimes\fi{}n)$ phases, with $n$ between 2 and 15, formed by Bi dimer blocks separated by a missing dimer line (MDL). It is pointed out that the formation of defect-free MDLs plays an important role in determining the energetic stability of the $(2\ifmmode\times\else\texttimes\fi{}n)$ phases. Our total energy results suggest an upper as well as a lower limit for the number of Bi dimers in the Bi dimer block of the $(2\ifmmode\times\else\texttimes\fi{}n)$ structure. Our calculated equilibrium geometries compare very well with recent experimental measurements. Furthermore, our theoretically simulated scanning tunneling microscopy (STM) images of the occupied states reveal formation of bright Bi dimer blocks separated by MDLs, in confirmation with experimentally obtained STM pictures.

Ab initio calculation of accurate dissociation energy, potential energy curve and dipole moment function for the A 1 Σ + state 7 LiH molecule

The reasonable dissociation limit of the A1Σ+ state 7LiH molecule is obtained. The accurate dissociation energy and the equilibrium geometry of this state are calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space for the first time. The whole potential energy curve and the dipole moment function for the A1Σ+ state are calculated over a wide internuclear separation range from about 0.1 to 1.4 nm. The calculated equilibrium geometry and dissociation energy of this potential energy curve are of Re=0.2487 nm and De=1.064 eV, respectively. The unusual negative values of the anharmonicity constant and the vibration-rotational coupling constant are of ωeχe=–4.7158cm−1 and αe=–0.08649cm−1, respectively. The vertical excitation energy from the ground to the A1Σ+ state is calculated and the value is of 3.613 eV at 0.15875 nm (the equilibrium position of the ground state). The highly anomalous shape of this potential energy curve, which is exceptionally flat over a wide radial range around the equilibrium position, is discussed in detail. The harmonic frequency value of 502.47cm−1 about this state is approximately estimated. Careful comparison of the theoretical determinations with those obtained by previous theories about the A1Σ+ state dissociation energy clearly shows that the present calculations are much closer to the experiments than previous theories, thus represents an improvement.

Ab initio interaction and spectral properties of CO+–He

In this contribution, ab initio methods have been used to study the open-shell CO+–He van der Waals (vdW) complex in both the ground and the first Π excited electronic state. Calculations were performed at the UCCSD(T) level of theory in the framework of the supermolecule approach using the cc-pVTZ basis set complemented with a set of standard bond functions in the middle of the vdW bond. Calculations predict a most-stable equilibrium conformation with β e=45°, R e =2.85 A and D e =275 cm−1 for the ground CO+(X2Σ)–He(1S) state and β e=90°, R e =2.70 A and D e =218 cm−1 for the excited CO +(A2Π)–He(1S) state. The dipole moment μ and independent components of the field polarizability α of the CO +–He vdW complex have been studied at the calculated equilibrium geometry of these states. The vertical excitation energies from the ground CO+(X 2Σ)–He(1S) to the excited CO+(A2Π)–He (1S) electronic state and corresponding shifts in the fluorescent spectrum with respect to the isolated CO+ molecule are also presented

Evolution of the electronic structure of Be clusters

Using a modified symbiotic genetic algorithm approach and many-body interatomic potential derived from first principles, we have calculated equilibrium geometries and binding energies of the ground-state and low-lying isomers of Be clusters containing up to 41 atoms. Molecular-dynamics study was also carried out to study the frequency of occurrence of the various geometrical isomers as these clusters are annealed during the simulation process. For a selected group of these clusters, higher-energy isomers were more often found than their ground-state structures due to large catchment areas. The accuracy of the above ground-state geometries and their corresponding binding energies were verified by carrying out separate ab initio calculations based on molecular-orbital approach and density-functional theory with generalized gradient approximation for exchange and correlation. The atomic orbitals were represented by a Gaussian 6-311G** basis, and the geometry optimization was carried out using the GAUSSIAN 98 code without any symmetry constraint. While the ground-state geometries and their corresponding binding energies obtained from ab initio calculations do not differ much from those obtained using the molecular-dynamics approach, the relative stability of the clusters and the energy gap between the highest occupied and the lowest unoccupied molecular orbitals show significant differences. The energy gaps, calculated using the density-functional theory, show distinct shell closure effects, namely, sharp drops in their values for Be clusters containing 2, 8, 20, 34, and 40 electrons. While these features may suggest that small Be clusters behave free-electron-like and, hence, are metallic, the evolution of the structure, binding energies, coordination numbers, and nearest-neighbor distances do not show any sign of convergence towards the bulk value. We also conclude that molecular-dynamics simulation based on many-body interatomic potentials may not always give the correct picture of the evolution of the structure and energetics of clusters although they may serve as a useful tool for obtaining starting geometries by efficiently searching a large part of the phase space.

Theoretical Studies of Inorganic Compounds. 341) Energy Decomposition Analysis of E–E Bonding in Planar and Perpendicular X2E−EX2 (E = B, Al, Ga, In, Tl; X = H, F, Cl, Br, I)

AbstractThe nature of E–E bonding in group 13 compounds X2E–EX2 (E = B, Al, Ga, In, Tl; X = H, F, Cl, Br, I) has been investigated by means of an energy decomposition analysis (EDA) at the BP86/TZ2P level of theory. The calculated equilibrium geometries of all molecules B2X4−Tl2X4 have a perpendicular (D2d) geometry. The largest energy barriers for rotation about the E‐E bond are predicted for the hydrogen species B2H4−Tl2H4. The EDA shows that the rotational barriers of B2X4−Tl2X4 may not be used for an estimate of the hyperconjugative strength in the D2d structures except for the tetrahydrides. The values for the planar (D2h) transition states reveals that π conjugation of the halogen lone‐pair electrons stabilizes the transition states. The bonding analysis shows that hyperconjugation in B2I4 is stronger than in B2H4 although the latter compound has a higher rotational barrier than the former. In B2F4, hyperconjugative stabilization of the perpendicular structure and conjugative stabilization of the planar structure nearly cancel each other yielding a nearly vanishing rotational barrier. The heavier analogues Al2X4−Tl2X4 have low rotational barriers and rather weak hyperconjugative interactions. The larger rotational barriers of the hydrogen systems Al2H4−Tl2H4 compared with the tetrahalogen compounds is explained with the cooperation of the relatively large hyperconjugation in the perpendicular form and the relatively weak conjugation in the planar transition structures. The EDA also indicates that the electrostatic (ΔEelstat) and molecular orbital (ΔEorb) components of the E–E bonding are similar in magnitude.Thecalculated B‐B bond dissociation energies of B2X4 (De = 93.0–108.4 kcal/mol) show that the bonds are rather strong. The heavier analogues Al2X4−Tl2X4 have weaker bonds (De = 16.6–61.7 kcal/mol). In general, the X2E‐EX2 bond dissociation energies follow the trend for atoms E: B ≫ Al > Ga > In > Tl and for atoms X: H > F > Cl > I.

The Fock-Space Coupled-Cluster Method in the Calculation of Excited State Properties

Our recently developed intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculation of equilibrium geometries, harmonic frequencies and adiabatic excitation energies for some excited states of N2 and CO. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and reference spaces are employed permitting a comparison of calculated properties with experimental data.

The (Chloromethyl)dihalosilanes X2HSiCH2Cl (X = F, Cl, Br, I): Synthesis, Multinuclear NMR Spectroscopy and Rotational Isomerism Examined by Raman Spectroscopy

Abstract(Chloromethyl)diphenylsilane Ph2HSiCH2Cl (1) was prepared from Ph2SiHCl and LiCH2Cl, in situ, and was then treated with CF3SO3H/LiCl and CF3SO3H/LiBr to give the (chloromethyl)dihalosilanes Cl2HSiCH2Cl (2) and Br2HSiCH2Cl (3). I2HSiCH2Cl (4) was formed quantitatively in a protodearylation reaction between liquid hydrogen iodide and 1. Fluorination of 4 with ZnF2 gave F2HSiCH2Cl (5), albeit in low yields. Compounds 1−5 were characterised by multinuclear NMR spectroscopy (29Si, 13C, 19F) and vibrational spectroscopy. The temperature‐dependent vibrational Raman spectra of 2, 3 and 4 prove that they are mixtures of gauche and anti rotamers in the liquid state. Enthalpy differences, ΔH (Hanti − Hgauche), were determined for the liquids by applying the van’t Hoff relation, with the gauche rotamer being lower in energy for 3 and 4, and the anti rotamer for 2. The vibrational spectra were assigned with the help of ab initio calculations of equilibrium geometries and harmonic fundamental frequencies. Harmonic symmetry force constants and potential energy distributions were calculated from the ab initio Hessian matrices. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2004)

Nonempirical Investigation of Equilibrium Geometry and Electronic Structure of Kynurenine and 3-Hydroxykynurenine Molecule

By Hartree-Fock-Roothaan method with complete geometry optimization in the basis 6-31G* ab initio calculations of equilibrium geometry and electronic structure were performed for kynurenine C10H12N2O3 and 3-hydroxykynurenine C10H12N2O3 molecules in the singlet ground state and the first triplet excited state. The molecules in the triplet state can react at the oxygen of the carbonyl group adjacent to the aromatic ring by quite different pathway compared to the molecules in the ground singlet state.

DFT study of electronic structure and geometry of anionic copper clusters

Calculations of equilibrium geometry, vertical detachment energies (VDE) and transition energies ( T e) from the electronic ground state to excited states of Cu n − clusters ( n=2–10) have been carried out within DFT model with the new functional developed recently [J. Mol. Struct. (Theochem) 664–665 (2003) 291]. The results of calculations have been compared with observed photoelectron spectra (PHES). The method provides a good agreement between calculations and experiment. For anionic Cu 2–10 − clusters, the difference between calculated and experimental values of VDE and T e for the most stable isomers does not exceed 0.21 eV. The assignment of previously unknown Cu 6 −, Cu 8 −, Cu 9 − and Cu 10 − structures has been made by both total energy calculations and comparison of experimental and calculated PHES. The electronic sructure, geometry and energetic characteristics of low-lying isomers have been studied.

Infrared and Raman spectra, ab initio calculations, barriers to internal rotation, and vibrational assignment of 4-fluoro-2-pentyne

The infrared spectra (3500–50 cm −1) of the gas and solid and the Raman spectra (3500–50 cm −1) of the gas, liquid and solid have been recorded for 4-fluoro-2-pentyne, CH 3C≡CCHFCH 3. Equilibrium geometries and energies have been determined by ab initio (HF and MP2) and hybrid density functional theory (DFT) by the method B3LYP calculations with a number of basis sets. A vibrational assignment is proposed based on the force constants, relative intensities, depolarization ratios from the ab initio and DFT calculations and rotational–vibrational band contours obtained by using the calculated equilibrium geometries. The methyl group attached to the C≡C triple bond exhibits almost completely free rotation and this is accompanied by the observation of Coriolis sub-band structure on two of the near degenerate methyl vibrations. The Coriolis coupling constants have values of 0.181±0.033 and −0.137±0.078 for the stretch and deformation, respectively. Torsional transitions of the other methyl group are evident in the far infrared spectrum from which a barrier to internal rotation of 1465±30 cm −1 is derived which agrees well with the theoretically predicted barrier value. The results are compared to the corresponding quantities of some similar molecules.

CCSD(T) calculations of equilibrium geometries and spectroscopic constants for the diatomics S2, NF, NS, and their ions

Abstract To assist the modeling of the SF6 + N2 arc plasma, a sophisticated CCSD(T)/cc-pVQZ ab initio approach was used to obtain equilibrium geometries of S2, NF, NS, SF, F2 and their singly charged cations and anions, and the CCSD(T)/cc-pwCVXZ (X=D, T, and Q) strategy was employed to estimate their energetic parameters (total and dissociation energies, ionization potentials, and electron affinities) at the complete basis set (CBS) limit. The CBS values of spectroscopic constants of NF−, SF−, and S2− are also given. The data obtained are highly accurate (for example, the mean absolute error in the internuclear separations is 0.532 pm), which warrants their use also as reliable estimates of unavailable experimental values.

Atomic structure and energetic stability of the Bi-covered InAs(110) surface

We have performed ab initio calculations of the atomic structure and energetic stability of the Bi-covered InAs(110) surface. The calculations were performed within the density-functional theory, using norm-conserving fully separable ab initio pseudopotentials. Two experimentally proposed structural models have been considered: (1×1)-ECLS and (1×2). Our total energy calculations indicate that the formation of the (1×2) model is energetically more favourable than the (1×1) model by 41 meV/(1×2). The calculated equilibrium geometries, for the InAs(110)-Bi(1×1) and -Bi(1×2) surfaces, show in general a good agreement with the experimental x-ray measurements carried out by Betti et al.

Al(111)-(3×3)R30:On-top versus substitutional adsorption for Rb and K

The atomic structure and energetics of the on-top and substitutional phase of the Al(111)-$(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30:$Rb adsorbate system have been studied employing density-functional-theory total-energy calculations. Since the energy difference between the two phases is extremely small $(\ensuremath{\approx}20\mathrm{meV})$ extensive checks with respect to the choice of the exchange-correlation functional (local density and generalized gradient approximations) and the construction of the Rb pseudopotential have been performed. All tests clearly show the substitutional adsorption site to be energetically favorable. Equivalent calculations performed for K revealed a clear chemical trend in the adsorption energetics for Na, K, and Rb: The energy gain between the substitutional and the on-top configuration decreases with increasing atomic radius of an alkali atom. The calculated equilibrium geometries are in good agreement with previously reported experimental data.

Ab initio calculations of equilibrium geometries and vibrational excitations of helical ethylene-glycol oligomers: application to modeling of monolayer infrared spectra

The density functional theory methods are used to calculate the equilibrium molecular structures and vibrational spectra of helical H(CH 2CH 2O) n H (OEG) oligomers ( n=4–7) at a level of precision that has not been accomplished before. The largest deviation between experimentally observed frequencies, obtained from infrared reflection–absorption spectra of OEG-monolayers on gold, and calculated, single molecule frequencies (unscaled), is slightly above 2%. Moreover, the most intense peak in the CH 2-stretching region at about 2890 cm −1, commonly regarded as a trademark of the OEG helical conformation, is reassigned in this study to the asymmetric CH 2-stretching mode.

A geminal model chemistry

We modify the existing model of the antisymmetrized product of strongly orthogonal geminals to define a size consistent variational theory free from any adjustable parameters apart from the usual choice of a basis set. The new theory is only slightly more computationally expensive than Hartree–Fock, gives an exact solution for an ensemble of noninteracting singlet two electron systems, and is applicable to open- and closed-shell systems. We use it to calculate equilibrium geometries, vibrational frequencies, and dipole moments of diatomic molecules from G2/97 database. We find excellent agreement with experimental values for covalently bound molecules, and overstretched bonds of molecules formed by atoms with extreme electronegativity.

Infrared and Raman spectra, conformational stability, ab initio calculations of structure, and vibrational assignment of 2-hexyne

The infrared spectra (3500–50 cm −1) of the gas and solid and the Raman spectra (3500–50 cm −1) of the liquid and solid have been recorded for 2-hexyne, CH 3–CC–CH 2CH 2CH 3. Variable temperature studies of the infrared spectrum (3500–400 cm −1) of 2-hexyne dissolved in liquid krypton have also been recorded. Utilizing four anti/ gauche conformer pairs, the anti( trans) conformer is found to be the lower energy form with an enthalpy difference of 74±8 cm −1 (0.88±0.10 kJ/mol) determined from krypton solutions over the temperature range −105 to −150 °C. At room temperature it is estimated that there is 42% of the anti conformer present. Equilibrium geometries and energies of the two conformers have been determined by ab initio (HF and MP2) and hybrid DFT (B3LYP) methods using a number of basis sets. Only the HF and DFT methods predict the anti conformer as the more stable form as found experimentally. A vibrational assignment is proposed based on the force constants, relative intensities, depolarization ratios from the ab initio and DFT calculations and on rotational band contours obtained using the calculated equilibrium geometries. From calculated energies it is shown that the CH 3 group exhibits almost completely free rotation which is in agreement with the observation of sub-band structure for the degenerate methyl vibrations from which values of the Coriolis coupling constants, ζ, have been determined. The results are compared to similar properties of some corresponding molecules.

Coupled cluster calculations of equilibrium geometries, harmonic vibrational frequencies and the barrier height of ethane

The equilibrium geometries, harmonic vibration frequencies, and the rotational barrier of C 2H 6 have been calculated using CCSD(T) level of theory in combination with correlation-consistent basis sets of Dunning. The best estimate values of r e(CH), r e(CC) and θ e(HCH) are 1.0895, 1.5240 Å and 107.66°, which are in close agreement with the experimental equilibrium geometry of 1.089±0.005 Å for r e(CH), 1.524±0.003 Å for r e(CC), and 106.9±0.5° for θ e(HCH). The structure and harmonic vibrational frequencies for the CH 4 molecule have also been analyzed.

Zero electron kinetic energy photoelectron spectroscopy and density functional calculations of Al–P(CH3)3 and Al–As(CH3)3

Aluminum-trimethylphosphine and trimethylarsine have been prepared by pulsed laser vaporization. Their electronic spectra have been obtained for the first time, using pulsed field ionization zero electron kinetic energy (ZEKE) photoelectron spectroscopy. The ZEKE spectra reveal the information about adiabatic ionization energies, intermolecular and ligand vibrations, and charge effects on molecular geometries. In coordination with the experimental measurements, density functional theory has been used to calculate equilibrium geometries, vibrational frequencies, and bond dissociation energies for the neutral and ionic complexes. The calculations predict that ionization causes the most significant geometry changes in the Al–P–C or Al–As–C angles, in agreement with the experimental observations. The aluminum ion and atom bind phosphorus more strongly than arsenic in these species.

Theory of H − in SiO 2

We present an ab initio molecular orbital study of H in SiO 2 with special emphasis on H −. We have calculated equilibrium geometries, vibrational spectra, binding energies and electrical levels. For the electrical levels, we have included long-range polarization effects in three approximations. We compare our results to those of Yokozawa and Miyamoto and others. We find that H 0 is unstable in SiO 2. However, we find that, rather than disproportionate, it prefers to dimerize. We also predict that H 0 is a deep electron trap. Finally, we find that long-range polarization effects are crucially important for obtaining even qualitatively correct values for electrical levels.

Infrared and Raman spectra, ab initio calculations of structure and vibrational assignment of 1-fluoro-2-butyne

The infrared spectra (3500–50 cm −1) of the gas and solid and the Raman spectra (3500–50 cm −1) of the liquid and solid have been recorded for 1-fluoro-2-butyne, CH 3CCCH 2F. Equilibrium geometries and energies have been determined by ab initio and hybrid DFT methods using a number of basis sets. A vibrational assignment is proposed based on the force constants, relative intensities, depolarization ratios from the ab initio and DFT calculations and on vibrational–rotational band contours obtained using the calculated equilibrium geometries. From calculated energies it is shown that the CH 3 group exhibits almost completely free rotation which is in agreement with the observation of Coriolis sub-band structure in two of the degenerate methyl vibrations. The results are compared to the corresponding quantities for some similar molecules.