First and second-order properties of charge-localized and Frost-localized orbitals

Two methods of localization of Frost-model molecular orbitals are considered, both of which are extremely easy to apply, requiring the evaluation of only one-election integrals. The chargelocalization criterion can be used with any single-determinant wavefunction, but when applied to the Frost model it yields similar orbitals to those got by orthonormalizing the basis of floating spherical gaussians, while maintaining their localized feature. Properties of charge-localized orbitals are calculated for NH₃, H₂O, CH₄, C₂H₆.     

The Mechanism of Transformation of Triethylsilane by Collision-Free IR Multiphoton Excitation of Its Molecules

The mechanism of IR multiphoton dissociation of triethylsilane (TES) in the collision-free mode was studied. The principal unimolecular reactions are the C–Si and C–C bond rupture. The reactions of molecular elimination of CH₄, C₂H₄, and C₃H₆do not play a substantial part in the mechanism of chemical transformations of TES. The spontaneous fragmentation of C₂H₅and (C₂H₅)₂Si(CH₂)H radicals produced by C–Si and C–C bond rupture, respectively, was shown to be feasible.     

On the use of local basis sets for localized molecular orbitals

Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li₂, HF, H₂O, NH₃, CH₄ and C₂H₆.     

The use of population localised orbitals to interpret molecular orbital calculations

An efficient and general method is derived to calculate population localised molecular orbitals (LMO's) from a given SCF eigenvector matrix, by reduction to an eigenvalue problem. Applications to both localised molecules (NH₃ and C₂H₂) and delocalised ones (B₂H₆, C₆H₆ and butadiene) are discussed in some detail. It is shown that unequal occupation of atomic energy levels leads to non-orthogonal LMO's. The consequences of non-orthogonal atomic hybrid orbitals are discussed, formulas for their overlap in terms of atomic occupation numbers are derived and it is shown that the occupation numbers are connected to LMO atomic orbital coefficients by various sum rules.     

Localized molecular orbitals for polyatomic molecules

Molecular wavefunctions have been generated by the PRDDO (Partial Retention of Diatomic Differential Overlap) method for the monocyclic aromatic rings containing six π-electrons (C₄H ₄ ^?2 , C₅H ₅ ^? , C₆H₆, C₇H ₇ ⁺ , and C₈H ₈ ⁺² ) and ten π-electron species (C₈H ₈ ^?2 , C₉H ₉ ^? , C₁₀H₁₀). The eigenvalue spectra of the canonical molecular orbitals are presented. Localized molecular orbitals (LMO's) generated using the Boys criterion are reported for localizations involving all occupied molecular orbitals (complete localizations) and localizations of the π orbitals only. We find evidence for σ-π separation in the complete localizations for some of these molecules even though the Boys criterion is often biased against such results. We demonstrate for C₆H₆ and find for the other molecules that the π-orbital localizations are indeterminate (i.e. there are an infinite number of equally satisfactory LMO structures between two limiting extremes). This result may be viewed as a corollary of Hückel's (4n+2) rule for aromaticity.     

On a definition of bond energies based on localized molecular orbitals

A theoretical model is presented for defining bond energies based on localized molecular Orbitals. These bond energies are obtained by rearranging the total SCF energy including the nuclear repulsion term to a sum over orbital and orbital interaction terms and then to total orbital terms, which can be interpreted as the energies of localized orbitals in a molecule. A scaling procedure is used to obtain a direct connection with experimental bond dissociation energies. Two scale parameters are employed, the C-C and the C-H bond dissociation energy in C₂H₆ for A-B and C-H type bonds, respectively. The implications of this scaling procedure are discussed. Numerical applications to a number of organic molecules containing no conjugated bonds gives in general a very satisfactory agreement between experimental and theoretical bond energies.     

Molecular properties from coupled-cluster Brueckner orbitals

We investigate to which extent a single determinant made up from orbitals obtained by a Brueckner coupled-cluster doubles calculation is able to reproduce correlated one-electron properties. It is shown that dipole and quadrupole moments and radial expectation values compare quite well with BCCD finite-field results for a test selection of nine molecules enclosing HF, H₂O, NH₃, CO, N₂, NO⁺, HCN, CuH and CH₃OH and three rare-gas atoms He, Ne and Ar. Furthermore, we find that even second-order properties such as dipole and quadrupole polarizabilities are reproduced fairly well when determined as first derivatives of the corresponding Brueckner orbital expectation values.     

Kinetics of reactions between methoxycarbonyl,methyl, and methoxy radicals formed in flash photolysis of dimethyl oxalate in gas phase

Flash photolysis of dimethyl oxalate produced the radicals CH₃, CH₃O, and COOCH₃. Thermally equilibrated methoxycarbonyl radicals did not decompose during radicalradical reactions in the presence of 40-torr cyclohexane in the temperature range 298–448 K. Cyclohexyl radicals were also generated during the flash photolysis of the reaction mixture. Rate coefficients of radical–radical reactions were calculated from the amounts of stable products determined by gas chromatography: CO, CO₂, CH₄, C₂H₄, C₂H₆, CH₂O, CH₃OH, CH₃OCH₃, HCOOCH₃, CH₃COOCH₃, CH₃OCOOCH₃, CH₃C₆H₁₁, and CH₃OC₆H₁₁. Calculations were performed using an iterative computer integration program. Absolute values of rate coefficients were based on the rate coefficient of the reaction between methyl radicals, k₁ = 2.7 × 10¹⁰ dm³ mol^?1 s^?1, measured with the same equipment. The rate coefficients for reactions (5)–(8) are:      

Relative rate constants for the reactions of trichloropropenyl radical. Application of the two-parameter Taft equation

The relative rate constants for the hydrogen atom abstraction by CCl₃CH?CH· radical from CH₂Cl₂, CHCl₃, CH₃COCH₃, CH₃CN, C₆H₅CH₃, C₆H₅OCH₃, CH₃CHO, and CH₃OH in the liquid phase at 20°C have been measured. It was shown that these reaction rate constants are correlated by the two-parameter Taft equation with ρ* = 0.726 ± 0.096, r* = 1.22 ± 0.16. A relationship between r* and bond dissociation energy D(R? H) has been found for the abstraction reactions of different free radicals.     

Density localization of atomic and molecular orbitals

Density localized molecular Orbitals are computed for the molecules LiH, LiF, BF, BN, CO, C₂H₂, CH₄, NH₃, H₂O, and HF. The density localization method is based on the minimization of the sum of the interorbital density overlap integrals. The results of this method are compared to the results of the energy localization method of Edmiston and Ruedenberg and the localization procedures of Boys and of Magnasco and Perico. The agreement among the results obtained by these four methods is in general good. With a few exceptions the localized molecular orbitals agree with the classical chemical concepts.

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Zusammenfassung Dichtelokalisierte Molekülorbitale sind berechnet worden für die Moleküle LiH, LiF, BF, BN, CO, C₂H₂, CH₄, NH₃, H₂O und HF. Die Dichtelokalisierungsmethode beruht auf der Minimisierung der Summe der Dichteüberlappungsintegrale zwischen verschiedenen Orbitalen. Die Ergebnisse dieses Verfahrens werden verglichen mit den Resultaten der Energielokalisierungsmethode von Edmiston und Ruedenberg und den Verfahren von Boys und von Magnasco und Perico. Die übereinstimmung zwischen den verschiedenen Methoden ist im allgemeinen gut. Mit einigen Ausnahmen werden die klassischen chemischen Vorstellungen von Elektronenpaaren reproduziert.

     

Analytical optimization of orbital exponents in Gaussian-type functions for molecular systems based on MCSCF and MP2 levels of fully variational molecular orbital method

We have analyzed the basis function series in molecular systems by optimization of orbital exponents in Gaussian-type functions (GTFs) including the electron correlation effects with multiconfiguration self-consistent field (MCSCF) and M?ller?CPlesset second-order perturbation (MP2) methods. First, we have derived and implemented the gradient formulas of MCSCF and MP2 energies with respect to GTF exponent, as well as GTF center and nuclear geometry, based on the fully variational molecular orbital (FVMO) method. Second, we have applied these electron-correlated FVMO methods to H₂, LiH, and hydrocarbon (CH₄, C₂H₆, C₂H₄, and C₂H₂) molecules. We have clearly demonstrated that the optimized exponent values with electron-correlated methods are different from those with simple Hartree?CFock method, since adequate basis functions for adequate virtual orbitals are indispensable to describe the accurate wave function and geometry for electron-correlated calculations.     

A radial probability density function for analysis of canonical molecular orbitals

A one‐dimensional probability density function, analogous to the atomic radial density for the hydrogen atom, r²R_nl(r), is defined for an arbitrary three‐dimensional density. It is obtained numerically by taking the derivative of a cumulative probability distribution with respect to the cubic root of the volume enclosed by each in a series of isosurfaces. Each point in the function is associated with a unique isosurface, and the isosurface associated with the maximum of the defined function represents the most probable isosurface with respect to the putative radius. This function therefore provides an objective selection criterion for a single isosurface to represent a three‐dimensional density. This technique is applied to set of canonical molecular orbitals. The selected threshold value varies from orbital to orbital, but the enclosed probability falls in the range of 20% to 55% for the reported orbitals. In all cases, the enclosed probability is much smaller than the common choices found in the literature. The concomitant smaller volume often makes possible a more localized interpretation and helps to clarify the conventional delocalized interpretation of molecular orbitals. For example, the isosurface plots selected by this method distinguish the formally bonding orbital in He₂ from the true bonding orbital in H₂. Examples from N₂, F₂, HF, H₂O, C₂H₆, and Ni(CO)₄ are also presented. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 310–321, 2000     

Localized orbitals based on the fermi hole

The Fermi hole provides a direct (non-iterative) method for tansforming canonical SCF molecular orbitals into localized orbitals. Except for simple overlap integrals required to maintain orthogonality, this method requires no integrals over orbitals or basis functions. This method is demonstrated by application to a furanone (C₄H₄O₂), methylacetylene, and boron trifluoride. The results of these calculations are compared to those determined by the orbital centroid criterion of localization.     

An application of the method of conjugate gradients to the calculation of minimal basis set localized orbitals

Using an STO -3G basis set, energy localized molecular orbitals (LMO ) were determined for the ten electron series HF, H₂O, NH₃, and CH₄ as well as for CH₃OH and C₂H₂F₂. The method of conjugate gradients is shown to be a viable alternative to other non-eigenvalue methods. The characterization of the LMO in terms of first and second moment measures indicates that the STO -3G basis set LMO may be accurately correlated to larger sp basis set LMO . Also, it is shown that the first and second moment measures display a good linear correlation with the classical concept of electronegativity.     

Calculation and properties of non-orthogonal,strictly local molecular orbitals

A general procedure to calculate non-orthogonal, strictly local molecular orbitals (NOLMOs) expanded using only a subset of the total basis set is presented. The energy of a single determinant wave function is minimised using a Newton-Raphson approach. Total energies and barriers to internal rotation for CH₄, NH₃, H₂O, CH₃CH₃, CH₃NH₂, CH₃OH, NH₂NH₂, NH₂OH and HOOH, and certain properties of the NOLMOs present in these molecules, are investigated using the 4-31G basis set.     

The use of transition-state theory to extrapolate rate coefficients for reactions of oh with alkanes

A method is described for extrapolating existing experimental data on the reactions of OH radicals with alkanes to higher temperatures using conventional transition-state theory. Expressions are developed for the estimation of the structural properties of the activated complex necessary for calculating ΔS^± and ΔH^±. The vibrational frequencies and internal rotations of the activated complex are given by those of the reacting alkane or the analogous alcohol and a set of additional internal modes that is the same for all OH + alkane reactions considered. Differences between primary, secondary, and tertiary hydrogen attack are discussed, and the validity of representing the activated complexes of all OH + alkane reactions by a fixed set of vibrational frequencies and other internal modes is evaluated. Calculations are presented for the reaction of OH with CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, i-C₄H₁₀, c-C₄H₈, c-C₅H₁₀, c-C₆H₁₂, (CH₃)₂CHCH(CH₃)₂, (CH₃)₃CCH(CH₃)₂, (CH₃)₄C, and (CH₃)₃CC(CH₃)₃, and the results are compared with experiments.     

Gasometric determination of alkyl radicals in polyalkylsiloxanes and silicofunctional organic silicon compounds

Summary We have worked out a gasometric method for determination of alkyl radicals (CH₃, C₂H₅) in polyorganosiloxanes and silicofunctional organic silicon compounds, based on their splitting as the corresponding hydrocarbons (CH₄, C₂H₆) by alkali. The accuracy of the method is 1–2%.     

An MS Xα and ETS study of the influence of “d” orbitals on the electron affinities of thio-substituted benzenes

The electron transmission spectra of the o,o′-dimethyl substituted benzenes 2,6-(CH₃)₂C₆H₃-XR (X = O,S, NR: R = H, CH₃) show that the substituents adopt a planar (R = H) or rotated (R = CH₃) conformation depending upon their size and they suggest that in the sulphur derivatives the ²B₁ H anion states are stabilized by S3d orbital participation. MS Xα calculations performed on both the planar and orthogonal forms of the model systems p-(XH)₂-C₆H₄ (X = O, S) support this hypothesis and assign the extra resonance present in the ET spectra of the thio derivatives to electron capture into [ σ_S-R* MOS. strongly mixed with sulphur 3d orbitals ( = 33% d character).     

Construction of molecular orbitals localized on polyatomic fragments

A simple method of localizing molecular orbitals on polyatomic molecular fragments is proposed; the method allows one to separate orbitals in the structural units of extended molecules. The method is illustrated by semiempirical calculations of the binuclear bridged complexes [(NH₃)₅Rupy-(C₂H₂)_n-py-Ru(NH₃)₅]⁵⁺ (n = 0,1,2,3). One of possible application is construction of orbital bases for calculations by the configuration interaction method with limited sets of active MOs. Translated fromZhumal Strukturnoi Khimii, Vol. 39, No. 4, pp. 571–578, July–August, 1998.     

Minor processes in the photolysis of azomethane at low pressure: An upper limit for the rate of the unimolecular elimination of H2 from vibrationally excited ethane

The photolysis of azomethane in the near UV has been studied at room temperature and pressures from 10 mtorr to 10 torr. The main products, C₂H₆ and N₂, accounted for more than 99% of the reaction. Minor hydrocarbon products observed were (with quantum yields) C₃H₈ (3.5 × 10^?3), C₂H₄ (3.2 × 10^?4), CH₄ (3 × 10^?3), and n-C₄H₁₀ (trace). Quantum yields of H₂ of 4 × 10^?5 and 2 × 10^?5 were measured at azomethane pressures of 0.1 and 1.0 torr, respectively. The minor hydrocarbon products can be accounted for by reactions of CH₃ and C₂H₅ radicals following hydrogen abstraction from azomethane by CH₃. The H₂ product observed represents an upper limit for the H₂ elimination from vibrationally excited C₂H₆ formed by CH₃ combination in the system, corresponding to a rate of elimination ca. 5 × 10^?5 times the competing rate of dissociation to 2CH₃. Assuming a frequency factor of 10¹³ s^?1 for the H₂ elimination, a lower limit of about 90 kcal mol^?1 was estimated for the energy barrier.