Molecular equilibrium geometries and vibrational frequencies by maximum overlap symmetry molecular orbital method

It is demonstrated that the maximum overlap symmetry molecular orbital method can be used for optimization of molecular geometries and calculation of vibrational frequencies by adding a two-body repulsive energy term and a modification of the Wolfsberg–Helmholz formula. The obtained equilibrium geometries and vibrational frequencies are on the whole in good accordance with experimental data, which shows that the basic idea using the method to optimize molecular geometries and to calculate vibrational frequencies is reasonable.     

Ab initio predictions of the molecular structures and harmonic vibrational frequencies of Ga2O2 isomers

The potential energy surface of Ga₂O₂ is examined at the SCF and MP2 levels employing basis set of triple- plus double polarization quality. Four stationary points located at the SCF level are characterized via their Hessian index. Electron correlation is important for the energy ordering and splitting of the isomers. For example, two minimum energy structures, a cyclicD _2h form and a linear Ga-O-Ga-O, separated by 25.69 kcal/mol at the SCF level have an energy difference of only 1.70 kcal/mol at the MP2 levels. Our computed harmonic vibrational frequency at 962 cm^–1 for the Ga-O-Ga-O minimum structure in in good agreement with the experimental predicted value of 967 cm^–1.     

An analysis of predictions by the semi-empirical MNDO molecular orbital method for some aspects of molecular energetics

Calculations using the MNDO HE molecular-orbital method predict that NH₄, PH₄ and H₃S are stable free radicals, and that local minima exist for H₃O and H₂Cl. The tendency of MNDO to overestimate the stability of such systems is traced to its neglect of overlap integrals. Results for H⁺₂ (both ground and excited states) support this conclusion. Stable radicals with formulas BeH₃ and BH₄ are also predicted. Analysis of hydrocarbon thermochemistry indicates that MNDO fails to predict the correct sign for the relative magnitude of bond interactions, whereas ab initio calculations give the correct sign and approximately the correct magnitude. Finally, it is shown that the apparent superiority of MNDO over ab initio MO calculations in predicting molecular energetics is illusory when the methods are compared on the same basis.     

Calculations of molecular vibrational frequencies using semiempirical methods

MINDO/3, MNDO, AM1, and PM3 calculations of molecular vibrational frequencies are reported for 61 molecules. All techniques were applied to both well-behaved and badly behaved systems. Overall, MINDO/3 and MNDO were found to contain rather large errors whereas AM1 and PM3 were relatively accurate. Since no technique does well for all molecules, the technique used should be chosen based on the molecular vibration of interest. In general, AM1 and PM3 together provide fairly accurate results.     

The ab initio calculated molecular structures,force fields and vibrational frequencies of some organic azides

Double zeta basis molecular calculations were carried out on the hydrazoic acid and azidomethane molecules. The molecular structures were optimized by the gradient method and the force fields were obtained by numerical differentiation of the gradient vector. The computed harmonic force fields and vibrational frequencies were compared with experimental values.     

Application of molecular orbital calculations to the bicyclo[3.2.2]nonatrienyl anion and some related ions

The stabilities and the electronic structures of (CH)₉^? and (CH)₉⁺ systems were investigated using INDO MO calculation. The total overlap populations of the C-C bonds of bicyclo[3.2.2]nonatrienyl anion indicated its high degree of conjugation, in contrast to less conjugated bicyclo[3.2.2]nonatrienyl cation. On the other hand, the (CH)₉^? intermediate of the D_3h symmetrical structure was shown to be much less conjugated than the D_3h symmetrical (CH)₉⁺ ion. It was suggested from the calculated results that the sum of the total overlap populations of all C-C bonds involved in a (CH)_n molecule could be a quantitative measure of aromaticity for the (CH)_n systems in the three-dimensional structures.     

Molecular orbital theory study on surface complex structures of phosphates to iron hydroxides: calculation of vibrational frequencies and adsorption energies

Quantum mechanical calculations were applied to resolve controversies about phosphate surface complexes on iron hydroxides. Six possible surface complexes were modeled: deprotonated, monoprotonated, and diprotonated versions of bridging bidentate and monodentate complexes. The calculated frequencies were compared to experimental IR frequency data (Persson et al. J. Colloid Interface Sci. 1996, 177, 263-275; Arai and Sparks J. Colloid Interface Sci. 2001, 241, 317-326.). This study suggests that the surface complexes change depending on pH. Four possible species are a diprotonated bidentate complex at pH 4-6, either a deprotonated bidentate or a monoprotonated monodentate complex at pH 7.5-7.9, and a deprotonated monodentate complex at pH 12.8. In addition, reaction energies were calculated for adsorption from aqueous solution to determine relative stability to form a monoprotonated monodentate complex and a deprotonated bidentate complex. According to these results, the monoprotonated monodentate complex should be favored. Vibrational frequencies of the monoprotonated monodentate and deprotonated bidentate complexes were analyzed with electronic effects on the Fe-OP and H-OP bonds.     

Scaling factors for vibrational frequencies and zero-point vibrational energies of some recently developed exchange-correlation functionals

The scaling factors for the vibrational frequencies and zero-point vibrational energies evaluated at various combinations of recently developed exchange-correlation functionals and various basis sets are reported. The exchange-correlation functionals considered are B972, B98, HCTH, OLYP, O3LYP, G96LYP, PBE0 and VSXC functionals; the basis sets employed are 3-21G, 6-31G*, 6-31G**, 6-31+G, 6-311G*, 6-311G**, 6-311G(df,p), 6-311+G(df,p), cc-pVDZ and aug-cc-pVDZ. The experimental harmonic frequencies of 122 small molecules and the zero-point vibrational energies of 39 small molecules are used to determine the scaling factors through the least-square fitting procedure. It was found that the scaling factors do not depend significantly on the basis sets considered. The vibrational frequency scaling factors evaluated by using the B98 and PBE0 functionals are recommended on the basis of smallest root mean square error. The zero-point vibrational energy scaling factors evaluated from the B972 functional with Pople's double-zeta basis set and the HCTH functional with Pople's triple-zeta basis set are recommended on the basis of smallest root mean square error.     

Molecular orbital study of molecular nitrogen fixation

The model systems of molecular nitrogen fixation [N₂ + H]?, [N₂ + H]⁺, [N₂ + H]^?, [N₂ + H₂], [N₂ + H₂]⁺, and [N₂ + H₂]^? were studied by the semiempirical INDO method. The study was based on the formal analogy between the catalytic reactions and the photochemical, radical, and ionic reactions on the other side. Symmetrical and donor-acceptor properties of necessary catalytic systems were proposed using the dependence of energy characteristics and electron structure on reaction coordinate. On the basis of this MO study we have proposed the appropriate symmetry types of catalysts for each of acceptable models of nitrogen fixation. For one of the proposed systems there was realised a model MO computation with explicit inclusion of atoms of transition metals (Fe, V).     

Interactions of metal ions with water: ab initio molecular orbital studies of structure, vibrational frequencies, charge distributions, bonding enthalpies, and deprotonation enthalpies. 2. Monohydroxides

The formation and properties of a wide range of metal ion monohydroxides, M(n)(+)[OH(-)], where n = 1 and 2, have been studied by ab initio molecular orbital calculations at the MP2(FULL)/6-311++G**//MP2(FULL)/6-311++G** and CCSD(T)(FULL)/6-311++G**//MP2(FULL)/6-311++G** computational levels. The ions M(n)()(+) are from groups 1A, 2A, 3A, and 4A in the second, third, and fourth periods of the Periodic Table and from the first transition series. Geometrical parameters, vibrational frequencies, atomic charge distributions, orbital occupancies, and bonding enthalpies are reported. The M(n)(+)-O distances are shorter in the hydroxides than in the corresponding hydrates (published previously as Part 1, Inorg. Chem. 1998, 37, 4421-4431) due to a greater electrostatic interaction in the hydroxides. The natural bond orbitals for most of the first-row transition metal ion hydroxides do not contain a formal metal-oxygen bonding orbital; nevertheless the atomic charge distributions show that for both n = 1 and 2 a significant amount of electron density is consistently transferred from the hydroxide ion to the bound metal ion. Deprotonation enthalpies for the hydrates have been evaluated according to the simple dissociation process, M(n)(+)[OH(2)] --> M(n)(+)[OH(-)] + H(+), and also via proton transfer to another water molecule, M(n)(+)[OH(2)] + H(2)O --> M(n)(+)[OH(-)] + H(3)O(+). The drastic reduction in these deprotonation enthalpies as H(2)O molecules are sequentially bonded in the first coordination shell of the metal ion (amounting to 71, 64, 85, and 91 kcal/mol for the bonding of six water molecules to Mg(2+), Ca(2+), Mn(2+), and Zn(2+), respectively) is found to be due to the greater decrease in the bonding enthalpies for the hydroxides relative to the hydrates. Proton transfer to bases other than water, for example side chain groups of certain amino acids, could more than offset the decrease in deprotonation energy due to the filling of the first coordination shell. Linear relationships have been found between the pK(a) values for ionization of the Mg(2+), Ca(2+), Mn(2+), Fe(2+), Co(2+), Ni(2+), Cu(2+), and Zn(2+) aquo ions, and Delta for the bonding of the first water molecule, for the bonding of the hydroxide ion, and for proton dissociation from the monohydrate. Similar relationships have also been found between the pK(a) values and the reciprocal of the M-O bond lengths in both the monohydrates and hydroxides. Thus the ionization of metal hydrates in water echoes the properties of the monomeric species M(n)(+)[OH(2)].     

Molecular orbital studies of some transition metal complexes

A set of molecular orbital calculations based on a particular semi-empirical method, has been undertaken on a homologue series of bis(-2-methylallyl)transition metal (Ni, Co, Fe, Cr) complexes (abbreviated as ML₂). Arguments are found for predicting the stability of the NiL₂ system, which is the only one that could be synthetized.

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Zusammenfassung Eine Reihe von semiempirischen MO-Rechnungen wurde für die homologe Reihe von bis(-2-methylallyl) Metallkomplexen (Ni, Co, Fe, Cr) durchgeführt. Gründe für die Stabilität der Ni-Verbindung, die als einzige synthetisiert wurde, werden angeführt.

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Résumé Un ensemble de calculs par une méthode semi-empirique particulière d'orbitales moléculaires a été effectué sur une série homologue de complexes bis (-2-méthylallyl)-métal de transition (Ni, Co, Fe, Cr): ML₂.Certains arguments sont trouvés en faveur de la stabilité du système NiL₂, le seul à avoir été synthétisé.

     

Effects of rapid intramolecular vibrational redistribution on molecular spectra at microwave frequencies

Some molecules with more than 10 atoms and more than two torsional degrees of freedom have state densities sufficient for rapid (10¹⁰ s^?1) intramolecular vibrational redistribution at energies as low as 0.25 kcal/mol. Predicted features of low-resolution microwave (LRMW) band spectra of rapidly relaxing polar prolate molecules are discussed and compared with LRMW spectra of ethyl esters.     

Reciprocity in the degeneracies of some tetra-atomic molecular ions

Various ab initio computations, as, e.g., in G. J. Hala?sz and A?. Vibo?k, Int. J. Quantum Chem. 111, 342 (2011), have shown that in molecules of the type (HCCH)(+), when the extremal H atoms are distorted from a linear form but maintain a planar geometry, a pair of conical intersections (ci) occur at such positions that the ratios of the distortional coordinates of the two atoms are in the two ci's reciprocals of each other. These computations have here been extended to locate the ci's also for HCNH. The two groups of results are explained by simple analytic perturbational expressions for the energy differences of the lowest adjacent electronic states, with inclusion of excited state effects.     

The vibrational frequencies of HNO

Electronic and vibrational emission spectra have been produced by the reaction of H atoms with NO, and studied under moderate resolving power. Preliminary rotational analyses of some of the bands give ν″₁=2684_.7 cm^?1, ν″₂=1565_.3 cm^?1 and ν″₃=1500_.4 cm^?1. The values for ν″₁ and ν″₃ are considerably different from early published values.     

Molecular orbital calculation of spin-orbit splittings in some halogeno-compounds

CNDO and INDO calculations incorporating the spin—orbit operator in the Hamiltonian have been carried out to obtain the spin—orbit splittings of ionization potentials of some halogen compounds. Two sets of spin—orbit coupling constants were tested. The calculated splittings are compared with photoelectron spectroscopy experimental results from the literature.     

Semi-empirical molecular orbital calculations on some tautomers of cytosine

The stability of a series of cytosine tautomers has been investigated using both all valence electron and -electron SCF methods. The effect of general and selective scaling of the bond lengths was studied in the CNDO/2 calculations. The enol tautomer of cytosine exceeded the keto form in stability in these calculations. -electron SCF CI calculations were performed on the cytosine tautomers using two different parameterization schemes. The calculated transitions obtained for the enol form showed a close proximity to that of the keto and imino structures. Comparison was made with the experimental electronic spectrum in water and acetonitrile. No clear distiction between the keto and enol forms could be made on the basis of these calculations.

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Zusammenfassung Die StabilitÄt einer Reihe von Cytosin-Tautomeren wurde mit einer Allvalenzelektronen- und mit einer -Elektronen-SCF-Methode untersucht. Die Auswirkung einer allgemeinen als auch selektiven Skalierung der BindungslÄngen wurde bei den CNDO2-Berechnungen untersucht. Das Enoltautomere des Cytosins übertrifft nach diesen Rechnungen die Ketoform an StabilitÄt. Bei den -Elektronen-SCF-CI-Rechnungen wurden zwei Methoden der Parametrisierung angewandt. Die für die Enolform berechneten übergÄnge zeigten eine gro\e Ähnlichkeit zu denjenigen der Keto- und Iminostrukturen. Die berechneten Werte wurden mit dem experimentellen Spektrum von Cytosin in Wasser sowie Acetonitril verglichen. Auf Grund der Berechnungen konnte keine klare Unterscheidung zwischen der Keto- und der Enolform getroffen werden.

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Résumé Etude de la stabilité d'une série de tautomères de la cytosine par les méthodes SCF à électrons de valence et à électrons . L'effet d'ajustement global ou selectif des longueurs de liaison a été étudié dans le cadre CNDO/2. Le tautomère énolique de la cytosine s'avère dans ces calculs plus stable que la forme cétonique. Des calculs d'électrons SCF CI ont été effectués sur les tautomères de la cytosine en utilisant deux schémas différents pour la paramétrisation. Les transitions calculées obtenues pour la forme énolique montrent une grande analogie avec celles des structures cétoniques et iminiques. La comparaison a été faite avec le spectre électronique expérimental dans l'eau et l'acétonitrile. Aucune distinction claire entre les formes cétoniques et énoliques n'a pu Être faite à partir de ces calculs.

     

Van der Waals interaction and hydrogen bond effects on molecular vibrational frequencies

The frequency shift of an AZ two-atomic fragment upon molecule transfer from gas to solution or matrix is investigated. The nearest neighbour ligands are considered to form a cluster. The coupling of the ν_s(AZ) mode with the cluster low-frequency oscillators (ν_Q) is taken into account. One such oscillator can be the ν_σ(AZ…B) intermolecular stretching frequency oscillator in the H-bonded or charge transfer complex. A general expression for the ν_s(AZ) frequency shift (Δω) is obtained, which allows for both the usual van der Waals interaction and the (ν_s, ν_σ) and (ν_s, ν_Q) mode couplings. When the former prevails, the relative frequency shift Δω/ω_f is invariant to the Z → Z* (e.g., H → D) isotopic substitution. When the mode coupling prevails, the quantity Δω/ω²_f is invariant what is typical for H bonds. If the H-bonded or charge transfer complexes are absent, the frequency shift Δω is proportional to α(ϱ_AZ + ϱ_L)⁻⁶ where α is the polarizability of the ligand, ϱ_AZ and ϱ_L are the van der Waals radii of AZ and ligand, respectively. The additional ν_s(AH) frequency shift upon transfer of the AH…B complex from the gas to solution seems to be caused by (ν_s, ν_Q) mode coupling.     

Spectral studies and molecular orbital PPP-calculations of some azo-dyes

The UV, IR and 1H-NMR spectra of some 4-(R-phenyl azo) 1-hydroxy 2-naphthoic acid derivatives are studied. The effects of substituent groups and the solvent polarity on electronic spectral, IR bands and 1H-NMR proton chemical shifts are considered, the molecular orbital calculations obtained are rationalized quantitatively with that obtained practically using the PPP-model with configuration interaction (CI).     

A molecular orbital treatment of the electronic spectra of some tryptamines

The electronic absorption spectra of tryptamine, 5-methoxytryptamine, 6-fluorotryptamine, N-acetyl-5-hydroxytryptamine, gramine, and melatonin were investigated. The observed transitions were π–π*, and the values of band maxima and intensity reflected an extent of interaction between the indole ring and the alkylamine side chain. Molecular orbital calculations at the level of INDO /S –CI were performed on all the studied molecules. State functions and transition energies were calculated. The correspondence between the experimental and theoretical results was satisfactory. © 1992 John Wiley & Sons, Inc.