Calculation of bond dissociation energies of diatomic molecules using bond function basis sets with counterpoise corrections

Bond function basis sets combined with the counterpoise procedure are used to calculate the molecular dissociation energies D_e of 24 diatomic molecules and ions. The calculated values of D_e are compared to those without bond functions and/or counterpoise corrections. The equilibrium bond lengths r_e and harmonic frequencies o_e are also calculated for a few selected molecules. The calculations at the fourth-order Møller-Plesset approximation (MP 4) have consistently recovered about 95–99% of the experimental values for D_e; compared to as low as 75% without use of bond functions. The calculated values of r_e are typically 0.01 Å larger than the experimental values, and the calculated values of o_e are over 95% of the experimental values. © 1996 John Wiley & Sons, Inc.     

A first‐principles study of diatomic NiAl: Ground state,structure, and spectroscopic constants

A computational study of diatomic NiAl is reported. Molecular properties evaluated include the equilibrium bond length (r_e), equilibrium stretching frequency (ω_e), doublet‐quartet energy splitting, and nickel‐aluminum bond strength. Several interesting conclusions have resulted from this research. First, convergence in calculated properties is smoother with recently reported correlation consistent basis sets than earlier basis sets for Ni and Al. Second, with the exception of bond strength, basis set limit properties extrapolated using correlation basis sets are in agreement with reported data. Third, this research suggests that caution may be needed with regard to the use of DFT for developing interatomic potentials for larger scale simulations. For example, B97‐1 showed better agreement with reported r_e for ²NiAl than B3LYP. However, the situation was reversed for the calculation of ω_e. With respect to bond strength, the situation is unclear due to the scatter among experiment and calculations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Molecular orbital study of the Q–e scheme in free radical copolymerization

Molecular orbital calculations were used to study free radical polymerization. Calculations show that the monomer is activated during the reaction and the pi bond becomes a diradical. The radical on the carbon that is about to form the new bond is called the e radical in this article. The other is the Q radical. For different monomers it is shown indirectly that changes in the energies of formation of the Q and e radicals are related to changes in the Q and e terms in the empirical Q–e scheme of Alfrey and Price. The polar effect in the Q–e scheme involves the e-radical, unpaired electron density. Specifically, the Q–e sum (e_x + e_y) is correlated with the e radical spin density. Also the e term is correlated with the electron density on the unsubstituted carbon of the monomer. The relationship of the Q radical to the adjacent substituent is shown by correlating ln Q values with the energy of addition of a hydrogen atom to a monomer. These relationships give theoretical meaning to the Q–e terms and allow calculation of Q and e values from molecular orbital properties for small monomers.     

An energy criterion for determiningd orbital contribution to adsorbate bonding to a transition metal: CO/Fe12

Summary A new criterion is presented for determining the contribution of a particular class or group of orbitals to a chemical bond. The new criterion is the diatomic energy contribution of particular orbitals to a bond. In neglect to differential overlap methods the total energy may be decomposed entirely into monoatomic and diatomic terms. The contribution of the electrons ind orbitals to the diatomic energy terms, which are responsible for holding a molecule together, have been calculated for an Fe-Fe bond of Fe₁₂ and for the Fe-C bond of CO absorbed at an on-top site of an Fe₁₂ cluster. This direct measure of thed electron contribution to the total energy indicates that thed orbitals are responsible for only a small contribution to the Fe-Fe binding energy and to the binding energy for absorbed CO. This occurs, despite there being larged orbital attractive diatomic energy terms, because a careful analysis indicates repulsive terms balance the attractive terms.     

Electron–Electron interaction energy in homonuclear diatomic molecules

The derivative of the electron–electron potential energy U_ee with respect to internuclear separation R is studied for light homonuclear diatomic molecules at equilibrium. It is readily related to nuclear–nuclear potential energy U_nn, the force constant K, and the electron–nuclear potential energy U_en. An approximate expression, based on the simplest form of density functional theory, is then used to eliminate dU_en/dR|_Re. The result thus obtained for dU_ee/dR|_Re transcends an earlier proposal of Kryachko by including a term 2/3R_eK, with K the force constant. Numerical tests at SCF–RHF level are presented for nine homonuclear diatomic molecules.     

Large electron correlation effect leading to BeBe bond

The bonding of the beryllium diatomic molecule (Be₂) in the ground state is exclusively made from the electron correlation effect. Unlike the ordinary van der Waals bond, where the electron correlation of the dispersion type makes weak bond energy (D_e) at large bond distance (R_e), the BeBe bond is surprisingly strong with D_e = 830 cm^?1 and R_e = 245 pm. This paper presents in an analytical way the different electron correlation effects with the corresponding spectroscopic data.     

Theoretical investigations on thallium halides: Relativistic and electron correlation effects in T1X and T1X3 compounds (XF,C1, Br,and I)

Relativistic and electron correlation effects in thallium halides TlX and TlX₃ (X?F, Cl, Br, and I) are investigated by extensive ab initio configuration interaction calculations. Spin–orbit coupling is included at the Hartree–Fock level for the diatomic TlBr and TlI. At the best level of treatment of electron correlation (quadratic configuration interaction), the calculated molecular properties are in good agreement with experimental results, i.e., for the diatomic thallium halides deviations from experimental values are <0.06 Å for bond distances, <0.14 mdyn/Å for force constants, <35 kJ/mol for dissociation energies, and <0.3 D for dipole moments. The convergence of the Møller–Plesset series up to the fourth order is discussed. Two alternative structures of TlI₃ are compared. At the Møller–Plesset level of theory, the trigonal planar structure with thallium in the oxidation state + 3 is the preferred gas phase arrangement compared with the bent arrangement containing a linear I unit and thallium in the oxidation state + 1, the difference being ca. 95 kJ/mol. Vibrational frequencies are predicted for all trigonal planar thallium(III) halides. © 1993 John Wiley & Sons, Inc.     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. I. Li2, Be2, B2, and C2

Electron localizability indicators based on the parallel‐spin electron pair density (ELI–D) and the antiparallel‐spin electron pair density (ELIA) are studied for the correlated ground‐state wavefunctions of Li₂, Be₂, B₂, and C₂ diatomic molecules. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two functionals. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for Li₂, B₂, and C₂ the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Effect of crosslinking density on biaxial relaxation of SBR by using reduced variables

Use of reduced variables to account for the effect of crosslinking density ν_e in a styrene–butadiene rubber (SBR) system is demonstrated for general biaxial stress states. Recently published results from stress relaxation tests on five SBR vulcanizates crosslinked to different degrees by tetramethylthiuram disulfide were superposed by using ν_e as a reduction variable. The equilibrium shear modulus G_e calculated from the master relaxation curve at long reduced times was in satisfactory agreement with other results for SBR. The time-axis shifts were related in a linear logarithmic manner to the crosslinking density but had a slope slightly less than values previously reported for elastomer systems.     

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.     

A comparative study of O2, CO,and NO binding to iron–porphyrin

Minimum-energy structures of O₂, CO, and NO iron–porphyrin (FeP) complexes, computed with the Car–Parrinello molecular dynamics, agree well with the available experimental data for synthetic heme models. The diatomic molecule induces a 0.3–0.4 Å displacement of the Fe atom out of the porphyrin nitrogen (N_p) plane and a doming of the overall porphyrin ring. The energy of the iron–diatomic bond increases in the order Fe(SINGLE BOND)O₂ (9 kcal/mol) < Fe(SINGLE BOND)CO (26 kcal/mol) < Fe(SINGLE BOND)NO (35 kcal/mol). The presence of an imidazole axial ligand increases the strength of the Fe(SINGLE BOND)O₂ and Fe(SINGLE BOND)CO bonds (15 and 35 kcal/mol, respectively), with few structural changes with respect to the FeP(CO) and FeP(O₂) complexes. In contrast, the imidazole ligand does not affect the energy of the Fe(SINGLE BOND)NO bond, but induces significant structural changes with respect to the FeP(NO) complex. Similar variations in the iron–imidazole bond with respect to the addition of CO, O₂, and NO are also discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 31–35, 1998     

Shallow and deep trap states of solvated electrons in methanol and their formation,electronic excitation,and relaxation dynamics

We present condensed-phase first-principles molecular dynamics simulations to elucidate the presence of different electron trapping sites in liquid methanol and their roles in the formation, electronic transitions, and relaxation of solvated electrons (e_met⁻) in methanol. Excess electrons injected into liquid methanol are most likely trapped by methyl groups, but rapidly diffuse to more stable trapping sites with dangling OH bonds. After localization at the sites with one free OH bond (1OH trapping sites), reorientation of other methanol molecules increases the OH coordination number and the trap depth, and ultimately four OH bonds become coordinated with the excess electrons under thermal conditions. The simulation identified four distinct trapping states with different OH coordination numbers. The simulation results also revealed that electronic transitions of e_met⁻ are primarily due to charge transfer between electron trapping sites (cavities) formed by OH and methyl groups, and that these transitions differ from hydrogenic electronic transitions involving aqueous solvated electrons (e_aq⁻). Such charge transfer also explains the alkyl-chain-length dependence of the photoabsorption peak wavelength and the excited-state lifetime of solvated electrons in primary alcohols.

Condensed-phase first-principles molecular dynamics simulations elucidate the presence of different electron trapping sites in liquid methanol and their roles in the formation, electronic transitions, and relaxation of solvated electrons.     

The bonding in second row transition metal dihydrides,difluorides and dichlorides

Summary The dihydrides, the difluorides and the dichlorides of the second row transition metal atoms from yttrium to palladium have been studied with methods including electron correlation of all valence electrons. Comparisons are made to the previously studied corresponding diatomic systems. It is found that the general trends of the binding energies of the second hydride and halide remain the same as in the diatomic hydrides and halides. The second ligand binding energies for the dihalides thus vary much more than for the dihydrides. This is due to important attractive effects between the halide lone-pairs and empty 4d-orbitals to the left and strong repulsions towards occupied 4d-orbitals to the right. For some systems the second ligand binds much more than the first ligand, as for RuF₂ where the difference is 34.3 kcal/mol, whereas for other systems the reverse is true, as for PdCl₂ where the first ligand binds more than the second with 20.4 kcal/mol. The results can be explained by strong ligand field effects and differences in the atomic spectra.     

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.     

Inexpensive vibrational anharmonicities from estimated derivatives: Diatomic molecules

Four alternatives are compared for estimating vibrational anharmonicity constants without explicitly calculating the expensive fourth derivatives of the potential curves. In the first, semiempirical approach, fourth derivatives for 53 diatomic molecules are estimated from ab initio second and third derivatives by using the Morse model potential. Vibrational anharmonicities ω_ex_e are then computed from the third and fourth derivatives. The second approach invokes a purely empirical linear correlation between ω_ex_e and the harmonic frequencies ω_e. The third and fourth empirical approaches suppose that the effective harmonic and anharmonic force constants are proportional (with an additive constant in the fourth approach). Experimental values for ω_ex_e are compared with empirical predictions and with semiempirical estimates based upon Hartree–Fock (HF), Møller–Plesset (MP2), and local, nonlocal, and hybrid density-functional theories (DFT), using the small 6-31G* basis set. Ab initio values of ω_e and bond lengths r_e are also compared against experiment. The (U)MP2 results are the worst and include several anomalies. The other semiempirical methods yield results of comparable accuracy for ω_ex_e of hydrides, although the DFT methods are markedly better for ω_e and r_e and for ω_ex_e of nonhydrides. The empirical estimates are nearly as good as the semiempirical ones. We conclude that: (1) both empirical and semiempirical approximations are useful for predicting stretching anharmonicity constants ω_ex_e to precisions of σ≈5 cm⁻¹ for hydrides and σ≈1.5 cm⁻¹ for nonhydrides; and (2) MP2 theory is relatively unreliable for such calculations. In addition, we find the following tests to be useful when evaluating the reliability of vibrational constants calculated at the UMP2 level: (a) the calculated values of ω_e and ω_ex_e should not deviate substantially from the empirical relations; (b) harmonic frequencies and intensities calculated at the MP2 level should be smaller than those calculated at the corresponding HF level; (c) a large distance-dependence of the spin contamination, d〈S²〉/dR≳0.05 Å⁻¹, suggests that calculated constants are too large. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1315–1324, 1998     

Empirical model of orbital relaxation and interatomic distances in molecules with polar chemical bonds

Orbital relaxation is treated as one of the reasons for shortening of chemical bonds with respect to the sum of the covalent radii of interacting atoms. The C-O, Si-O, Si-C, Si-H, Si-F, and Si-Cl bond lengths in organic and inorganic silicon compounds and of E-H and E-F bonds in diatomic hydrides and absolute-valent fluorides (E is a second-period element) are considered in terms of a simple empirical model of orbital relaxation. In all cases under study, orbital relaxation is an important factor affecting the length of the chemical bond. Translated fromZhumal Struktumoi Khimii, Vol. 38, No. 3, pp. 438–446, May–June, 1997.     

Soft Coulomb hole method applied to molecules

The soft Coulomb hole method introduces a perturbation operator, defined by ?e/r₁₂ to take into account electron correlation effects, where ω represents the width of the Coulomb hole. A new parametrization for the soft Coulomb hole operator is presented with the purpose of obtaining better molecular geometries than those resulting from Hartree–Fock calculations, as well as correlation energies. The 12 parameters included in ω were determined for a reference set of 12 molecules and applied to a large set of molecules (38 homo‐ and heteronuclear diatomic molecules, and 37 small and medium‐size molecules). For these systems, the optimized geometries were compared with experimental values; correlation energies were compared with results of the MP2, B3LYP, and Gaussian 3 approach. On average, molecular geometries are better than the Hartree–Fock values, and correlation energies yield results halfway between MP2 and B3LYP. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Ab initio study of the positronation of the CaO and SrO molecules including calculation of annihilation rates

Ab initio multireference single‐ and double‐excitation configuration interaction calculations have been performed to compute potential curves for ground and excited states of the CaO and SrO molecules and their positronic complexes, e⁺CaO, and e⁺SrO. The adiabatic dissociation limit for the ²Σ⁺ lowest states of the latter systems consists of the positive metal ion ground state (M⁺) and the OPs complex (e⁺O^?), although the lowest energy limit is thought to be e⁺M + O. Good agreement is found between the calculated and experimental spectroscopic constants for the neutral diatomics wherever available. The positron affinity of the closed‐shell X ¹Σ⁺ ground states of both systems is found to lie in the 0.16–0.19 eV range, less than half the corresponding values for the lighter members of the alkaline earth monoxide series, BeO and MgO. Annihilation rates (ARs) have been calculated for all four positronated systems for the first time. The variation with bond distance is generally similar to what has been found earlier for the alkali monoxide series of positronic complexes, falling off gradually from the OPs AR value at their respective dissociation limits. The e⁺SrO system shows some exceptional behavior, however, with its AR value reaching a minimum at a relatively large bond distance and then rising to more than twice the OPs value close to its equilibrium distance. © 2012 Wiley Periodicals, Inc.