The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

Some valence bond calculations for H2 with 1s and 2p basis sets

Summary The results ofab initio valence bond calculations are reported for H₂, with up to 16 nuclear centred and eight midbond 1s and 2p AOs included in them. The 24 AO calculation, with 116S=0 spin structures, gives an STO-6G energy of –1.17237 a.u., which is close to an MP4 estimate of –1.17256 a.u.     

Optimized Structures and Relative Stabilities of the Carboranes from Ab Initio Calculations

Ab initio calculations at the STO-3G level were performed on almost all of the possible isomers for the entire series of closo-carboranes, C₂B_n-2H_n, 5 ? n ? 12. Geometry optimizations using the gradient method were also included in all calculations. We report here the relative energies obtained for the various isomers as well as the optimized structures. These calculations confirm our previous predictions of relative stabilities obtained from topological charge stabilization. Comparisons of our structures with those from experimental data provide us with a measure of reliability for bond distances obtained using ab initio SCF MO calculations at the STO-3G level. Results from the geometry optimization substantiated the experimentally known fluxional behavior of the 8 and 11 atom polyhedra.     

Alkylhydrazides and their protonated forms: Physical methods andab initio calculations

The basicity of hydrazides of the highest aliphatic carboxylic acids RC(O)NHNH₂ (R = C_nH_2n+1,n = 5-12) has been studied by potentiometric titration, and IR and¹H NMR spectroscopy.Ab initio Hartree-Fork calculations using the 6–31G^* basis set with full optimization of geometry were carried out on the simplest acy1hydrazines and their possible protonated forms. Based on these calculations, and the 1R and¹H NMR spectra, the tautomerism of alkylhydrazides and the structures of their protonated forms are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2645–2649, November, 1996.     

Electronic structure of Li− and F− calculated directly in momentum space

Summary A self-consistent field method is applied to compute directly in momentum space the electronic structures of the bound anions Li^– and F^– at the Hartree-Fock level. The convergence towards the Hartree-Fock limit, starting from STO-3G, 3–21G, 3–21+G and 6–311+G AO's, is stable and monotonous. Substantial improvement in the quality of the anion orbitals is noted already after one iteration. Particularly interesting is the efficiency with which the method modifies and improves the shape of the trial functions.     

Theoretical study of reaction mechanisms for the ketonization of vinyl alcohol in gas phase and aqueous solution

Theoretical ab initio calculations are done on different mechanisms for the conversion of vinyl alcohol to acetaldehyde, both in gas phase and in solution. Several basis sets are used in order to assess the accuracy of the results in gas phase and a continuum model of the solvent is employed to mimic reactions in water solution. The results indicate a catalytic action of water in hydrated clusters in gas phase, whereas in solution, and within the error limits of our calculations, both neutral water-chain and ionic mechanisms appear to be equally probable. Finally, the action of acids or bases is tested through the analysis of the reaction of vinyl alcohol with H₃O⁺ and HO^–. The results of the calculations are shown to be in qualitative agreement with the experimental facts when 6-31++G basis set is used but not when either STO-3G or 4-31G basis sets are employed.     

Structure and stability of closo-hexaboranes and their heteroanalogs

The molecular and electronic structures of closo-hexaboranes B₆H₆ ^2–, B₆H₇ ^–, and B₆H₈ and closo-heterohexaboranes XYB₄H₄ (X = Y = CH, N; X = BH, Y = CH^–, N^–, NH, O) were studed by the ab initio (MP2(full)/6-311+G**) and density functional (B3LYP/6-311+G**) methods. The bridging H atoms in closo-hexaboranes B₆H₇ ^– and B₆H₈ can undergo facile low-barrier migrations around the boron cage (the barrier heights are about 10—15 kcal mol^–1). All heteroboranes having octahedron-like structures with hypercoordinated N and O atoms are rather stable and can be the subject of synthetic research efforts.     

Infrared and Raman Spectra,Conformational Stability,Ab Initio Calculations,and Vibrational Assignments for Cyclopropyldifluorosilane

The infrared (3200–30 cm^–1) spectra of gaseous and solid Cyclopropyldifluorosilane, c-C₃H₅SiF₂H, and the Raman spectra (3200–20 cm^–1) of the liquid with quantitative depolarization values and the solid have been recorded. Both the syn (cis) and skew (gauche) conformers have been identified in the fluid phases, but only the syn conformer remains in the solid. Variable temperature (–55 to –100°C) studies of the infrared spectra of the sample dissolved in liquid xenon have been carried out. From these data, the enthalpy difference has been determined to be 73 ± 10 cm^–1 (209 ± 29 cal mol^–1), with the syn conformer being the more stable rotamer, which is at variance with the predictions from ab initio calculations. A complete vibrational assignment is proposed for both conformers based on infared band contours, relative intensities, depolarization values, and group frequencies. The vibrational assignments are supported by normal coordinate calculations utilizing the force constants from ab initio MP2/6-31G* calculations. Utilizing the frequencies of the silicon–hydrogen sketch, the rm Si—H bond distances of 1.474 and 1.472 Å have been obtained for the syn and skew conformers, respectively. Complete equilibrium geometries have been determined for both rotamers by ab initio calculations employing the 6-31G* and 6-311 +G** basis sets at levels of restricted Hartree-Fock (RHF) and/or Moller–Plesset (MP) to second order. The potential energy terms for the conformer interconversion have been obtained from the MP2/6-31G* calculation. The results are discussed and compared to those obtained for some similar molecules.     

A density functional theory study on boundary of “superreduced” transition metal carbonyl anions [M(CO)n](M=Cr, n=5, 4, 3, z=2, 4, 6; M=Mn, n=5, 4, 3, z=1, 3, 5; M=Fe, n=4, 3, 2, z=2, 4, 6; M=Co, n=4, 3, 2, z=1, 3, 5)

A nonlocal density functional theory (DFT) method has been applied to the calculations on optimized geometry, Mulliken atomic net charges and interatomic Mulliken bond orders as well as total bonding energies (E) in the binary transition metal carbonyl anions with different reduced states [M(CO)_n]^z− (M=Cr, n=5, 4, 3, z=2, 4, 6; M=Mn, n=5, 4, 3, z=1, 3, 5; M=Fe, n=4, 3, 2, z=2, 4, 6; M=Co, n=4, 3, 2, z=1, 3, 5). For comparison of relative stability, a relative stabilization energy D is defined as D=E([M(CO)_n]^z−)−nE(CO). The calculated C–O distances are lengthened monotonously with the increase of the anionic charge, but the M–C distances are significantly lengthened only in the higher reduced states. The relative stabilization energy calculated is a considerable negative value in the lower reduced states, but a larger positive value in the higher reduced states. The DFT calculations show that with the increase of the anionic charge, the Mulliken net charges on the M, C, and O atoms all increase, however, an excess of the anionic charge is mainly located at the central metal atom. The calculated C–O Mulliken bond orders decrease consistently with the increase of the anionic charge, but the M–C bond orders exhibit an irregular behavior. However, the total bond orders calculated clearly explain the higher reduced states to be considerably unstable. From analysis of the calculated results, it is deduced that the stability of the binary transition metal carbonyl anions [M(CO)_n]^z− studied are associated with the coordination number n and the anionic charge z, further, it is possible for the anions studied to be stable if n≥z, conversely, it is impossible when n<z.     

Ab initio studies on several species of the formula X3YO and X3YOH

Ab initio molecular orbital calculations using both minimal and extended basis sets have been applied to two isoelectronic sets of molecules. One set corresponds to the 18 electron species H₃NO, H₃CO^– and H₃COH while the second set contains the 42 electron fluorinated molecules F₃NO, F₃CO^– and F₃COH. The geometries of these molecules have been optimized, using both the minimal STO-3G and the extended 4-31G basis sets. These comparative calculations reveal that the 4-31G basis produced structural parameters in much better agreement with experiment. The effect of includingd-orbitals in the basis set was also investigated. For the fluorinated oxides it has been found that the optimized 4-31G structures were only slightly altered by the addition ofd-orbitals. For H₃NO, on the other hand, the inclusion ofd-orbitals considerably shortens the N-O bond distance. Both H₃NO and CF₃OH, which are unknown experimentally, are theoretically predicted to be capable of existence. The electronic structures of these molecules have also been examined using electronic partitioning according to the Mulliken scheme.     

Spectra and Structures of Silicon-Containing Compounds. XXIV.* Raman and Infrared Spectra,r 0 Structural Parameters,Vibrational Assignment,Barriers to Internal Rotation,and Ab Initio Calculations of Ethylsilane

The infrared (3200 to 400 cm^–1) and Raman (3200 to 20 cm^–1) spectra of gaseous and solid ethylsilane, CH₃CH₂SiH₃, have been recorded. Additionally, the Raman spectrum of the liquid has been obtained with quantitative depolarization values. The SiH₃ torsional mode has been observed as sum and difference bands with the silicon-hydrogen stretching vibration. Utilizing the torsional fundamental frequency of 132 cm^–1 the threefold periodic barrier of 590 cm^–1 (7.06 kJ/mol) has been obtained. Utilizing the frequencies of the silicon-hydrogen stretches, Si-H bond distances of 1.485 and 1.484 Å have been obtained for the bonds gauche and trans to the methyl group, respectively. Using previously reported rotational constants from seven different isotopomers, the r ₀ parameters have been calculated and are compared to the corresponding r _s parameters. A complete vibrational assignment is proposed that is consistent with the predicted frequencies utilizing the force constants from ab initio MP2/6-31G(d) calculations. Both the infrared intensities as well as the Raman activities and depolarization values have been obtained from the ab initio calculations. Complete equilibrium geometries have been determined by ab initio calculations employing the 6-31G(d), 6-311 + G(d,p), and 6-311+G(2d,2p) basis sets at levels of restricted Hartree–Fock (RHF) and/or Moller–Plesset (MP) to second order. The results are discussed and the theoretical values are compared to the experimental values when appropriate.     

A charge-conserving approximation method for ab initio calculations

A new method is presented for approximate ab initio calculations in quantum chemistry. It is called CCAM (charge conserving approximation method). The calculation method does not include the use of empirical parameters. We use Slater type orbitals as basis set, replacing STO's by STO-2G functions to evaluate three- and four-center integrals and making the STO-2G two-orbital charge distributions have the same total charge as STO. The results are presented for test calculations on five molecules. In view of these results, CCAM is better than ab initio calculations over STO-6G in the results on total energies, kinetic energies and occupied orbital energies. In atomic populations, dipole moments and unoccupied orbital energies, CCAM is also satisfactory. We estimate that CCAM would be as fast as ab initio calculations over STO-2G in evaluating molecular integrals.     

Conformational Stability of Chloromethyl Silyl Chloride from Temperature-Dependent FT-IR Spectra of Krypton Solutions

The Raman spectra (3200–30 cm^–1) of liquid and solid, and infrared spectra of gaseous and solid chloromethyl silyl chloride, ClCH₂SiH₂Cl, have been recorded. Variable temperature (–105––150°C) studies of the infrared spectra of the sample dissolved in liquid krypton have been carried out. From these data, the enthalpy difference is 177 ± 35 cm^–1 (2.12 ± 0.42 kJ/mol), with the more stable form being the trans conformer, which is consistent with the prediction from ab initio calculations at both the Hartree–Fock level and with electron correlation by the perturbation method to second order. It is estimated that 56% of the sample is in the trans form at ambient temperature. A complete vibrational assignment is proposed for both the trans and gauche conformers based on infrared band contours, relative intensities, depolarization values, and group frequencies, which is supported by normal coordinate calculations utilizing the force constants from the ab initio MP2/6-31G(d) calculations. The optimized geometries have also been obtained from ab initio calculations utilizing several different basis sets with full electron correlation by the perturbation method up to MP2/6-311+G(2d,2p). The results are discussed and compared to some corresponding results for several related molecules.     

Heterocomplexes in liquid mixtures MeOH—HF

The IR spectra and densities of MeOH—HF liquid mixtures were measured for component molar ratios ranging from 12 : 1 to 1 : 3. The IR spectra of all of the solutions exhibit bands with maxima at 3500, 2600, and 1800 cm^–1 and continuous absorption (CA) in the region of 3500—1300 cm^–1. The intensities of these bands and the CA increase with an increase in the HF concentration. A similar behavior was found for the difference between the experimental solution density and the additive sum of the solution component densities. Ab initio SCF calculations of the (MeOH)_5–n (HF) _n cyclic complexes (n = 0—5) were performed using the 6-31G basis set. The observed properties of MeOH—HF liquid mixtures may be due to the formation of heterocomplexes with a stable cyclic fragment consisting of more than four MeOH and HF molecules.     

Ab. initio calculations of Cl2SO ·nAICl3 complexes (n = 1, 2)

Fragments' of the potential energy surfaces (PES) for the SOCl₂ ·nAICl₃ (n = 1, 2) complexes were calculated by theab initio MO LCAO method using the RHF approximation for the STO-3G basis set and adding a 3d-AO for the S atom, as well as by the semiempirical MNDO method. Two local minima, assigned to the donor-acceptor complex Cl₂SO+AlCl₃ (la) and to Cl₃SOAlCl₂ (1b) were located on the PES atn = 1. Two local minima corresponding to two donor-acceptor complexes Cl₂SOAl₂Cl₆ and, were also located on the PES atn = 2. An analysis of the enthalpies of cation formation in the SOC1₂ +nAICl₃ (n = 1-3) systems calculated by theab initio method shows that the enthalpy of formation of the SOCl₊ cation atn = 2 is 17 kcal mol^–1 less than that atn = 1; the structure of the Cl₂SOAlCl₂ ⁺ cation with two strong electrophilic centers at the Al and S atoms becomes more favorable energetically atn = 3. The results of calculations for Cl₂SO ·nAICl₃ complexes by the MNDO method are in agreement with those obtained by theab initio method except for the geometry of complexes containing the Cl₃SO fragment and the charge values on the S atoms.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1116–1120, May, 1996.     

Spectra and Structure of Silicon-Containing Compounds. XXV. Raman and Infrared Spectra,r 0 Structural Parameters,Vibrational Assignment,and Ab Initio Calculations of Ethyl Chlorosilane-Si-d2

The infrared (3200 to 400 cm^–1) spectra of gaseous and solid and Raman (3200 to 20 cm^–1) spectra of liquid and solid ethyl chlorosilane-Si-d₂, CH₃CH₂SiD₂Cl, have been recorded. Both the gauche and trans conformers have been identified in the fluid phases, but only the gauche conformer remains in the solid phase. Variable temperature (–105 to –150°C) studies of the infrared spectra of CH₃CH₂SiH₂Cl dissolved in liquid krypton have been carried out. From these data, the enthalpy difference has been determined to be 78±11 cm^–1 (0.93±0.13 kJ/mol), with the gauche conformer the more stable form. Utilizing the frequencies of the silicon-hydrogen stretches, from the chlorosilane-Si-d isotopomer, Si—H bond distances of 1.481 and 1.480 Å have been obtained for the gauche conformer and 1.481 Å for the trans conformer. Complete vibrational assignments are proposed for both isotopomers which are consistent with the predicted frequencies utilizing the force constants from ab initio MP2/6-31G(d) calculations. Both the infrared intensities and the Raman activities and depolarization values have been obtained from the ab initio calculations. Complete equilibrium geometries have been determined by ab initio calculations employing the 6-31(d), 6-311++G(d,p), and 6-311+G(2d,2p) basis sets with full electron correlation by the Moller–Plesset (MP) perturbation method to second order. Continuing the previously reported rotational constants from five different isotopomers and the ab initio predicted structural parameters, adjusted r ₀ parameters have been calculated, which are compared to the corresponding r _s parameters. The results are discussed and the theoretical values are compared to the experimental values when appropriate.Taken in part from the dissertation of Y. E. Nashed, which will be submitted to the Department of Chemistry in partial fulfillment of the Ph.D. degree     

Hydration of the carboxylate group: Anab initio molecular orbital study of acetate-water complexes

The hydration of the carboxylate group in the acetate anion has been investigated by performingab initio molecular orbital calculations on selected conformers of complexes with the form CH₃CO₂ ^– ·nH₂O·mH₂O, wheren andm denote the number of water molecules in the first and second hydration spheres around the carboxylate group, andn + m 7. The results of RHF/6–31G^* optimizations for all the complexes and MP2/6–31+G^** optimizations for several one-water complexes are reported. The primary consequence of hydration on the structure of the acetate anion is a decrease in the length of the C-C bond. Enthalpy and free energy changes calculated at the MP2/6–31+G^** and MP2/6–311+ +G^** levels are reported for the reactions CH₃CO₂ ^– + [H₂O] _P CH₃CO₂ ^– ·nH₂O ·mH₂O where [H₂O] _P is a water cluster containingp water molecules andp=n+m 7. The calculations show that conformers with the lowest enthalpy change on complex formation are often not those with the lowest free energy change, due to a greater entropic loss in complexes with tighter and more favorable enthalpic interactions. Hydrogen bonding of six water molecules directly to the carboxylate group in CH₃CO₂ ^– is found to account for approximately 40% of the enthalpy change and 37% of the free energy change associated with bulk solvation.     

An ab initio study of the structures and enthalpies of the hydrogen-bonded complexes of the acids H2O,H2S,HCN, and HCl with the anions OH−, SH−, CN−, and Cl−

Ab initio calculations at second-order Møller-Plesset perturbation theory with the 6-31 + G(d,p) basis set have been performed to determine the equilibrium structures and energies of a series of negative-ion hydrogen-bonded complexes with H₂O, H₂S, HCN, and HCl as proton donors and OH^–, SH^–, CN^–, and Cl^– as proton acceptors. The computed stabilization enthalpies of these complexes are in agreement to within the experimental error of 1 kcal mol^–1 with the gas-phase hydrogen bond enthalpies, except for HOHOH^–, in which case the difference is 1.8 kcal mol^–1. The structures of these complexes exhibit linear hydrogen bonds and directed lone pairs of electrons except for complexes with H₂O as the proton donor, in which cases the hydrogen bonds deviate slightly from linearity. All of the complexes have equilibrium structures in which the hydrogen-bonded proton is nonsymmetrically bound, although the symmetric structures of HOHOH^– and ClHCl^– are only slightly less bound than the equilibrium structures. MP2/6-31 + G(d,p) hydrogen bond energies calculated at optimized MP2/B-31 + G(d,p) and at optimized HF/6-31G(d) geometries are similar. Using HF/6-31G(d) frequencies to evaluate zero-point and thermal vibrational energies does not introduce significant error into the computed hydrogen bond enthalpies of these complexes provided that the hydrogen-bonded proton is definitely nonsymmetrically bound at both Hartree-Fock and MP2.     

Maximum radius of convergence perturbation theory: test calculations on Be,Ne, H<Subscript>2</Subscript> and HF

Maximum radius of convergence (MAXR _c) perturbation theory [(2000) Journal of Chemical Physics 112:6997] is tested on the beryllium and neon atoms using calculations that are truncated in high orders. Calculations are also performed on the ground-state potential-energy curves of H₂ and HF. The neon atom calculations use the 3-21G basis set with added diffuse s and p functions. All other calculations use the STO-3G minimum basis set. MAXR _c perturbation theory consistently performs well. The Epstein–Nesbet and Møller–Plesset perturbative expansions frequently diverge or exhibit slow convergence compared to the expansions obtained from MAXR _c. AcknowledgementsJ.P. Fi. acknowledges support for a grant from the Japanese Society for the Promotion of Science.Contribution to the Björn Roos Honorary Issue     

The ring-opening of an unsymmetrical tetrahedral intermediate - 2-hydroxy-1,3-oxathiolane

Ab initio calculations were performed on 2-hydroxy-1,3-oxathiolane: and the two products of its breakdown: Complete geometry optimizations were performed at minimal (STO-3G) and split-valence (3-21G) basis set levels. In addition, a single point calculation was performed at 6-31G* level withd orbitals added on sulfur only. The conformation of the oxathiolane intermediate and its stability relative to the breakdown products was investigated. The STO-3G basis set gave an envelope form while 3-21G gave the twist form of the five-membered ring as the most stable. For all three basis sets the ester product was more stable than thioester.