Estimation of dissociation energy of alkali diatomics using an extended Linderberg relation

The ground state wave function of a model potential consisting of a zero-range square well joined to a Coulomb tail is used in a two equivalent centre problem to evaluate the overlap integral (S) and the resonance integral (β). It is shown that an extended Linderberg relation of the form β = K/R (dS/dR) is generally well obeyed. The extended relation has been used within a LCAO framework to obtain dissociation energies of the homonuclear diatomic molecules of the alkali atoms.     

Generalized 1/Z expansion for heteronuclear molecules

We have first studied empirical regularities in various series of heteronuclear diatomic molecules between the energy E, the total number of electrons N, the equilibrium distance R_e and Z? = (Z₁Z₂)^1/2 where Z₁e and Z₂e are the nuclear charges in the diatom. In particular, for various alkali halide series, R_e²|E|/N^5/3 is shown to correlate rather simply with Z?R_e³. Some theoretical basis is afforded by generalizing the 1/Z expansion used early by the writers in work on homonuclear diatomics. Finally, when Z₂/Z₁ → ∞, a model is presented which predicts a finite asymptotic bond length and this prediction is confronted with available experimental data for both heteronuclear diatoms and for the polyatomic series CH₄ to SnH₄.     

The variation of spectroscopic properties with numbers of electrons

A formalism that describes the variation of the spectroscopic properties, D_e, R_e, and k_e, of homonuclear, diatomic molecules, with the number of molecular electrons has been developed. The theory describes the interrelation of these properties and predicts “critical” behavior in sequences of “isonuclear” and neutral molecules. Detailed calculations are possible with the help of experimental data in lieu of a deeper, dynamical theory of molecular behavior with respect to electron number. The present work points the way toward a first-principle's theory. © 1992 John Wiley & Sons, Inc.     

用量子化学参数研究烯烃聚合物定量构效关系

以密度泛函理论(DFT)方法所得的烯烃聚合物结构单元的物性参数如总能量E_t、内能E_in、等容比热C_V、熵S、四极矩Q_ii、偶极矩 µ、平均极化率α及原子最大负电荷q^－等8个量子化学参数, 用逐步回归法分别建立了这些参数与摩尔体积V_{298 K}, 摩尔等张体积P_s、摩尔吸收常数色散分量F_d、摩尔折射率R_LL、摩尔抗磁磁化率χ、摩尔粘度温度函数H_vsum、摩尔Rao函数U_R及摩尔Hartmann函数U_H的结构-性能定量关系 (QSPR) 模型, 其测试集的决定系数R²分别是: V_{298 K} 为0.989, P_s为0.982, F_d为0.975, R_LL为0.997, χ为0.988, H_vsum为0.914, U_R为0.988及U_H为0.972. 结果表明, 用这些量子化学参数所建立的聚合物QSPR模型能用于聚合物性能的预测.     

The MTXαR method. The determination and use of “molecular” α values in molecular multiple scattering Xα calculations

A semiempirical approach is used to fix the α value for use in the extraatomic regions in multiple-scattering (MS Xα) calculations which retain the muffin-tin treatment of the potential. Such a “molecular” α value for an atom is determined by requiring the corresponding homonuclear diatomic molecule to have its minimum at the experimentally determined equilibrium separation; hence they are called α _R. Molecular α _R values are determined for the ground state Li₂ and F₂ molecules and are tested in a calculation of the ground state LiF potential curve. We find a binding energy at the calculated equilibrium separation to be within 1% of the experimental value. The LiF curve based entirely on the ordinary atomic α values is substantially inferior. The present MT Xα _R approach appears to be competitive with others which are intended to improve the muffin-tin version of MS Xα calculations.     

Anharmonicity of a molecular oscillator

The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations ( Q ) and the electronic degrees of freedom as represented by the chemical potential (μ) at constant number of electrons (N). The coupling parameters have well‐founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron‐nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d³E/d Q ³ ≠ 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the “strong harmonic” oscillator, when for the force constant k both a = (?k/? Q )_N = 0 and λ = (?k/?N) _Q = 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

An Exchange Charge Model for Covalent Bonds in Simple Homonuclear Diatomic Molecules

The point charge in Parr's simple bond charge model is replaced by the exchange charge, which can be evaluated according to a simple ab initio method. The calculated exchange charge correlate well with the experimental values of force constants and dissociation energies for homonuclear diatomic molecules H₂, Li₂, F₂, Na₂ and Cl₂.     

Electron attachment to homonuclear diatomic molecules

The electron propagator method is applied to the calculation to the electron affinities of some first- and second-row homonuclear diatomic molecules Li₂, Be₂, C₂, F₂, Na₂, Si₂, and Cl₂. Perturbation theory is applied through second order to analyze the results in order to determine the relative importance of correlation and relaxation effects in the binding of the additional electron. © 1993 John Wiley & Sons, Inc.     

Calculation of normal vibrations as applied to the study of properties of inorganic compounds

Using the Morse potential and spectroscopic constants it has been shown for diatomic molecules that the force constant of the bond (Kq) is proportional to its dissociation energy (D) so that Kq can be regarded as a measure of the bond strength. An analysis of K_MA of a series of complexes clearly indicates the correlation between the force constants K_MA and the MA bond length, thermodynamic constants of the MA bond dissociation, and reaction rates of the MA bond rupture.     

A poisson equation for vibrational potentials of diatomic molecules

A Poisson equation for nuclear motions in diatomic molecules is derived. The working formula is whereV _α ² is the Laplacian operator for the position of nucleusα, W is the Born-Oppenheimer molecular energy, is the atomic number ofα, and ? _β (α) is the electronic charge density evaluated atα due to orbitals centered onβ. Harmonic, anharmonic and quartic equilibrium force constants are calculated using Hartree-Fock molecular and atomic electronic charge densities, for a number of first and second row diatomic molecules. A charge-model field gradient formula for harmonic force constants $$k_e = {3 \mathord{\left/ {\vphantom {3 {R_e^3 ,}}} \right. \kern-\nulldelimiterspace} {R_e^3 ,}}$$ wherek _e is the force constant andR _e the equilibrium internuclear distance, which offers general improvement over a similar formula due to Bratoz, is presented.     

Bonding criteria for diatomic molecular orbitals and inter-relations among them

Bonding criteria for molecular orbitals in diatomic molecules are discussed. An orbital force criterion is shown to have several conceptual and practical advantages, providing a basis for the investigation of inter-relations among many of the commonly employed criteria.It is found that interconsistency among those criteria is guaranteed, within the framework of Koopmans' Theorem, if the orbital energies are monotonic in the range (R _e, ).The application of the orbital force criterion to the second row homonuclear diatomics exhibits reasonable chemical trends concerning the valence-shell orbitals, as well as indications of a slightly antibonding nature of the inner orbitals.Based on a section of a thesis to be submitted by Y.T. to the Senate of the Technion-Israel Institute of Technology, in partial fulfilment of the requirements for the D.Sc. degree     

Improved interaction potential for alkali halide molecules

An improved interaction potential has been devised for diatomic alkali halide molecules. This potential, in addition to similar attraction terms as in the Rittner potential, includes a new exponential for the short-range repulsion. The constant m in the exponential is seen to be well expressible in terms of the parameters of the Rittner potential. The new potential is also correlated with different properties, as for example, effective charges, effective radii, effective principal quantum numbers, etc., of the combining ions. Various spectroscopic constants, viz., the ionic dissociation energy D_i, the vibrational–rotational coupling constant α_e, the vibrational anharmonicity constant ω_ex_e, as well as two second-order spectroscopic constants γ_e and β_e have been calculated for this and for the Rittner potential. From comparisons between these two potentials, the new one has been observed better than the other.     

Attractive-dominant and repulsive-dominant hydrocarbon reactions

The difference between the expectation values of the total electronic kinetic energy operator (ΔE_K), and the operators accounting for the Coulombic interactions between the electrons and nuclei (ΔV_en), between all pairs of electrons (ΔV_ee), and between all pairs of nuclei (ΔV_nn) for the product and reactant species in a wide variety of hydrocarbon reactions are calculated using single determinant basis set data reported in the literature. Following Allen, their contributions to ΔE_T, the difference between the corresponding total molecular energies and thus the reaction heat, are grouped together as a repulsion energy term, ΔE_rep = ΔE_K + ΔV_ee + ΔV_nn, and an attraction energy term ΔE_attr = ΔV_en. For all but 2 of the 71 individual reactions considered in this paper, the experimental reaction heat at 0°K corrected for zero-point energy contributions, (ΔH)_zpe, is the result of near compensation between far larger ΔE_rep and ΔE_attr terms, in sharp contrast to the much smaller ΔE_rep and ΔE_attr terms which are characteristic of many molecular rotation processes. By matching the sign of (ΔH)_zpe with that of ΔE_rep or ΔE_attr, as the case may be, the reactions are classified as attractive-dominant or repulsive-dominant (46 in the former class and 23 in the latter), a property which is independent of the direction in which the reaction is written. The sign and magnitude of ΔV_ee, ΔV_nn, and ΔV_en and reaction category are discussed in relation to the various kinds of structural change involved in going from reactants to products. For the vast majority of reactions, the numerical relationship ΔV_ee ≈ ΔV_nn has been found to hold to within a few percent.     

A Systemic DFT Study on Several 5<Emphasis Type="Italic">d</Emphasis>-Electron Element Dimers: Hf<Subscript>2</Subscript>, Ta<Subscript>2</Subscript>, Re<Subscript>2</Subscript>, W<Subscript>2</Subscript>, and Hg<Subscript>2</Subscript>

Eleven kinds of density functionals in conjunction with three different basis sets are employed to investigate the homonuclear 5d-electron dimers: Hf₂, Ta₂, Re₂, W₂ and Hg₂. The computed bond lengths, vibrational frequencies and dissociation energies of these molecules are used to compare with available experimental data to find the appropriate combination of functional and basis set. The different functionals and basis sets favor different ground electronic state for Hf₂ and Re₂ molecules, indicating that these two dimers are sensitive to the functionals used. The molecular properties of Hg₂ dimer depend strongly on both functionals and basis sets used. It is found that the BP86 and PBEPBE functionals are generally successful in describing the 5d-electron dimers. For the ground states of these dimers, the bonding patterns are determined by natural bond orbital (NBO) analysis. Natural electron configurations show that the 6s and 5d orbitals in the bonding atoms hybrid with each other for the studied dimers except for Hg₂.     

Electrostatic potential–density relationships in molecules

In this work, we present Hartree–Fock and density functional theory nuclear electrostatic potential–density relationships for several homonuclear diatomic molecules. The results of our calculations are encouraging with relatively low errors in the energies. Implications for the application of this work to novel molecular energy equations as well as the need for further improvement of these newly proposed relationships in molecules have been addressed. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Solid state interaction between V2O5 and MoO3: specific features related to minor vanadia transfer

Vanadia transport, which is a minor reaction flux in the solid state reaction between V₂O₅ and MoO₃, was studied using chemical and neutron activation analyses and electron spectroscopy for chemical analysis. It was found that negligible quantities of vanadia were transferred in a molybdena briquette during the reaction. Vanadia was presumably localized in thin external layers of molybdena grains. The reaction potential difference U _r across a Pt|MoO₃|V₂O₅|Pt cell was studied. It was shown that in this cell U _r was produced at the molybdena briquette and was due to vanadia transport. The U _r value changed with time in two stages. The reaction potential difference U _r was constant (or diminished slightly) at the first stage and dropped abruptly at the second stage. The duration of the first stage depended on the initial thickness of the MoO₃ briquette: the thicker the briquette, the longer the U _r value was nearly constant. Causes and probable mechanisms of U _r generation are discussed in different terms: chemical reaction, variation of a _{O 2} at the boundary between the reaction product and initialoxides, or surface spreading of the minor (V₂O₅ or V₉Mo₆O₄₀) diffusant. The last mechanism, which received the least study in the general case, was shown to be the most probable one for the reaction at hand. Electronic Publication     

Relation of the force constant of a bond to the electric field at a nucleus

The change in the electric field at a nucleus in a molecule due to bond stretch is related to the force constant of the stretched bond. The validity of this relationship using approximate wave functions at the SCF and MP2 levels of theory is tested for the diatomic molecules H₂, HF, CO, and N₂. The effect of basis set variation on H₂ is also investigated. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1664–1667, 1997     

A configuration interaction study of the four lowest 1∑+ states of the LiH molecule

A configuration interaction study was completed on the ¹∑⁺ states of the LiH molecule using a nonorthogonal one-electron basis in elliptical coordinates. A few wave functions with highly optimized parameters were obtained for the X¹∑⁺ and A¹∑⁺ states and combined to construct a larger wave function which gave improved results for both states over a wide range of R values. The third and fourth roots are also reported since the wave function is extensive enough to give good upper bounds for the two states. Calculations were completed for 34 values R in the range 1 ≤ R ≤ 10 bohr (b). The calculated X¹∑⁺ curve has a minimum at Re = 3.060b (3.015b), with E(Re) = ?8.0556 Hartree (H) (?8.0704), μ(Re) = ?5.89 debye (d) (?5.88d) and μ/(R dμ/dR)|_Re = 1.75 (1.80 ± 0.3). For the A¹∑⁺ state, Re = 4.928b (4.906b), E(Re) = ?7.9372H(?7.9496H), μ(Re) = +3.96d and μ/(R dμ/dR)|_Re = ?-0.471. The values in parentheses are experimental results for comparison. The numerical vibrational and rotational analysis agreed well with experiment for both states. The A¹∑⁺ state exhibited a pronounced negative anharmonicity. Both states show strong interaction of three zeroth-order configurations, the nature of which changes considerably with R. The thus far unobserved second excited state has two minima, a metastable one at R = 3.70b and another at R ≈ 10.00b. The third excited state also appears to have a minimum at R ≈ 7.00b.     

The true diatomic potential as a perturbed Morse function

The problem of representing a diatomic (true) Rydberg-Klein-Rees potential U^t by an analytical function U^a is discussed. The perturbed Morse function is in the form U^a = U^M + ∑b_nyⁿ, where the Morse potential is U^M = Dy², y = 1 ?exp(?;a(r ? r_e)). The problem is reduced to determination of the coefficients b_n so U^a(r) = U^t(r). A standard least-squares method is used, where the number N of b_n is given and the average discrepancy ΔU = |(U^t ? U^a)/U^t| is observed over the useful range of r. N is varied until ΔU is stable. A numerical application to the carbon monoxide X¹∑ state is presented and compared to the results of Huffaker¹ using the same function with N = 9. The comparison shows that the accuracy obtained by Huffaker is reached in one model with N = 5 only and that the best ΔU is obtained for N = 7 with a gain in accuracy. Computation of the vibrational energy E_v and the rotational constant B_v, for both potentials, shows that the present method gives values of ΔE and ΔB that are smaller than those found by Huffaker. The dissociation energy obtained here is 2.3% from the experimental value, which is an improvement over Huffaker's results. Applications to other molecules and other states show similar results. © 1995 by John Wiley & Sons, Inc.     

Simplifications of spin-rotation parameters for homonuclear diatomic molecules

Spin-rotation parameters for homonuclear diatomic molecules are simplified and applied to the np ³Π_u Rydberg series of H₂. A model of spin-rotation is derived by dividing the electron distribution into core- and Rydberg-like terms.