Relation between molecular and atomic correlation energies via overlap population

A relationship is explored between correlation energies of light diatomic molecules, both hetero and homo, correlation energies of the constituent atoms and the overlap population S. While S is quantitatively sensitive to the choice of basis set, it is demonstrated that the general trends revealed are largely independent of such a choice. A weak residual dependence on molecular chemical potential is also indicated by the present study.     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of the Li2 molecule

It is usually very difficult to directly obtain molecular dissociation energy D_e and all accurate high-lying vibrational energies for most diatomic electronic states using modern experimental techniques or quantum theories, and it is also very difficult to give accurate analytical expression for diatomic molecular dissociation energy. This study proposes a new analytical formula for obtaining accurate molecular dissociation energy based on the LeRoy and Bernstein's energy expression in dissociation limit. A set of full vibrational energy spectra for some electronic states of Li₂ molecule are studied using the algebraic method (AM) suggested recently, and the corresponding accurate molecular dissociation energies are evaluated using the proposed new formula and high-lying AM vibrational energies. The results show that the AM spectra and the new theoretical dissociation energies agree very well with experimental data, and thereby providing a new physical approach to generating accurate dissociation energies for electronic states of diatomic molecules.     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N<Subscript>2</Subscript> molecule

It is usually very difficult to directly obtain molecular dissociation energy D _e and all accurate high-lying vibrational energies for most diatomic electronic states using modern experimental techniques or quantum theories, and it, is also very difficult to give accurate analytical expression for diatomic molecular dissociation energy. This study proposes a new analytical formula for obtaining accurate molecular dissociation energy based on the LeRoy and Bernstein’s energy expression in dissociation limit. A set of full vibrational energy spectra for some electronic states of N₂ molecule are studied using the algebraic method (AM) suggested recently, and the corresponding accurate molecular dissociation energies are evaluated using the proposed new formula and high-lying AM vibrational energies. The results show that the AM spectra and the new theoretical dissociation energies agree excellently with experimental data, and thereby providing a new physical approach to generating accurate dissociation energies for electronic states of diatomic molecules.     

On one-electron basis set extrapolation of atomic and molecular correlation energies

It is well known that the convergence of correlation energies in atomic and molecular calculations is relatively slow and that calculations aimed at high accuracy must explicitly make corrections for this. In this work we consider 1e ^? basis set extrapolation as a means of obtaining high accuracy. The correlation consistent basis sets of Dunning et al. have provided a convenient platform for extrapolation, with the independent variable being X?=?D,?T,?Q,?5,?…?. There has been much debate in the literature about the functional form to use for the extrapolation, with contention between the ‘theoretically justified’ (X?+?1)^?3 form and empirical forms based on exponentials or variable powers. We will dissect the theoretical justification of the (X?+?1)^?3 form by considering MP2 calculations on He and Ne as a function of the maximum angular momentum (?) in the basis using basis sets having converged radial extent. Calculations with ? up to 14 were carried out for Ne. It is shown that while the asymptotic form of (??+?1)^?3 is clearly reached, higher order terms are very important in the range of ? normally used in molecular calculations. We also use similar analysis techniques for an open shell atom and a small molecule. The functional form for the dependence of molecular properties with ? is complex and it is safer to extrapolate fitting parameters than energies.     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N_2 molecule

1 IntroductionAccurate results of high-lying vibrational energies and molecular dissociation energy De of diatomic electronic states are very important for thermodynamics, molecular spec- troscopy, reactive scatterings, and the collision physics of ultracold atoms. For example, the binding energy of the highest bound vibrational state to the ground vibrational state determines the s-wave scattering length. This in turn determines the low- energy (pre- dominantly s-wave) atomic elastic-scatteri…     

Atomic additivity of the correlation energy in molecules—an ab initio MP4 and G3 study

It is shown that the closed shell valence electron molecular correlation energy of organic molecules in their ground states is a homogeneous multilinear function of the numbers of neutral atoms in their canonical hybridization state. The additivity is a robust feature, which holds for MP2(fc), MP3(fc) and MP4(fc) model calculations. The latter results obtained on a test set of 91 widely different organic molecules, exhibiting a whole gamut of electronic structure patterns, are excellent as evidenced by the absolute average deviation from the additivity values (AAD) of only 1.4 kcal mol^?1 and R ² = 0.999 93. The maximum absolute deviation (MAD) is 5.3 kcal mol^?1. The additivity formula for the total molecular electron correlation retrieved from G3 calculations also has an excellent performance (AAD = 1.2 kcal mol^?1, R ² = 0.999 98 and MAD = 7.2 kcal mol^?1). If it is taken into account that the additivity formulae require only back of the envelope calculations, these results are remarkable indeed, in particular since the G3 correlation energies span a very large range from 180.7 (methane) to 1642.8 (hexafluorocyclopropane) kcal mol^?1. Comparison of the exact electron correlation energies in free atoms with the corresponding average correlation energies in molecules reveals that a substantial increase in the latter provides an important contribution in overcoming a very strong Coulomb repulsion between the nuclei. It is shown that the additivity formulae are useful in detecting some special molecular features such as strong resonance and anti-aromaticity.     

双原子分子振动能谱与离解能的精确研究

代数方法(AM)的建立解决了实验方法和精确量子力学理论方法难以获得双原子分子的包含最高振动能级在内的所有高阶振动能级的精确数值这一问题.基于LeRoy与Bernstein的工作,孙卫国等又建立了精确计算双原子分子离解能的新解析表达式.应用新公式和代数方法(AM),研究了一些双原子分子部分电子态的振动能谱和分子离解能,获得了与实验值符合非常好的理论结果.该方法在理论上提供了获得双原子分子完全振动能谱和精确分子离解能的物理新方法.     

Size effects on cation heats of formation. IV. Methyl and ethyl substitutions in methyl,methylene, acetylene and ethene

An empirical relation between the heat of formation of molecular ions and cation size is used to study the effects of methyl and ethyl substitution of hydrogen atoms on the cations of the C_nH_m hydrocarbons methyl, methylene, acetylene and ethene. The results provide tests of the graphical method, revealing regularities and irregularities in the empirical size relation used, as well as its value as a predictive tool for determining cation and neutral heats of formation. Of the 36 C_nH_m cations studied, only 5 have heats of formation listed in the renowned ATcT tables. Some C_nH_m cation heats of formation are questioned or eliminated, mainly in cases where multiple choices are available in the literature. Proposals are made for investigating or re-investigating the ionisation energies and the heats of formation of several of the molecules studied where no data previously exist or where our analysis suggests that more reliable values are needed. The relative effects of methyl and ethyl substitution on the thermodynamic stability of the series of alkyl-substituted C_nH_m cations are discussed.     

Microsolvation effects on the electron binding energies of halide anions

Ab initio electron propagator calculations in the partial third order (P3) and P3+ approximations were performed to obtain vertical electron detachment energies (VEDEs) of fluoride and chloride clusters with one through three molecules of water. Larger clusters of F^? and Cl^? with six water molecules were also treated with and without the polarisable continuum model (PCM). For the smaller clusters, good agreement between calculated VEDEs and peak positions in photoelectron spectra is achieved. Large shifts in VEDEs are observed for both hexameric fluoride–water and chloride–water complexes when the PCM is applied. Significant changes in coordination geometries about the chloride anion also occur in this model. In all fluoride complexes, Dyson orbitals for the lowest VEDEs are delocalised over oxygen atoms. On the contrary, for the case of chloride–water clusters, the Dyson orbitals corresponding to the lowest VEDEs are localised on the anion.     

Fast and accurate modeling of molecular atomization energies with machine learning

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr?dinger equation is mapped onto a nonlinear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross validation over more than seven thousand organic molecules yields a mean absolute error of ～10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.     

Bond-order correlation energies for small Si-containing molecules compared with ab initio results from low-order Møller–Plesset perturbation theory

The present study of small molecules containing silicon was motivated by (a) the considerable interest currently being shown in the kinetics and reactivity of such molecules, and (b) the biotechnological potential of silicon-derivate surfaces as substrates for the adsorption of, for instance, amino acids and proteins. Therefore, we have studied by (i) a semi-empirical approach and (ii) an ab initio procedure employing low-order Møller–Plesset perturbation theory, the molecular correlation energies of some neutral closed and open shell silicon-containing molecules in the series SiX _n Y _m . Procedure (i) is shown to have particular merit for the correlation of the ionic members studied in the above series, while the ab initio procedures employed come into their own for neutral species.     

Estimates of energies of core exchange

Energies of core exchange, δ, for some first row elements have been estimated from thermodynamic data and experimental core electron binding energies. Values of energies of core exchange extend the equivalent cores method to allow the calculation of absolute binding energies as well as shifts. In some cases it is possible to estimate the differences in binding energy without requiring heats of formation of gaseous cations. The values of δ obtained from LCAO-MO-SCF calculations show similar trends although the absolute values may differ by a few electron volts.     

A simple model for scalar relativistic corrections to molecular total atomisation energies

ABSTRACT

Scalar relativistic corrections to atomisation energies of first- and second-row molecules can be rationalised in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas–Kroll–Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies.     

On the contribution of triply-excited and quadruply-excited configurations to electron correlation energies in closed-shell systems

The contribution made by triply-excited and quadruply-excited configurations to electron correlation energies in closed-shell systems is examined in detail. Many-body perturbation theory is used to calculate the contribution of these configurations to the correlation energies in 25 atoms and molecules. Calculations are performed for the nitrogen, carbon monoxide and carbon monosulphide molecules for a range of nuclear geometries.     

Accurate vibrational energy spectra and dissociation energies of some diatomic electronic states

An algebraic method (AM) used to study the full vibrational spectra of diatomic systems, and an analytical formula used to calculate accurate molecular dissociation energies are applied to study the full vibrational spectra and molecular dissociation energies of some electronic states of homonuclear and heteronuclear diatomic molecules and diatomic ions. Studies show that the AM method and the analytical expression are reliable and economical physical methods for studying full vibrational spectra and molecular dissociation energies of diatomic electronic systems theoretically. They are particularly useful for those diatomic systems whose high-lying vibrational energies may not be available.      

Accurate studies on dissociation energies of diatomic molecules

The molecular dissociation energies of some electronic states of hydride and N2 molecules were studied using a parameter-free analytical formula suggested in this study and the algebraic method (AM) proposed recently. The results show that the accurate AM dissociation energies DeAM agree excellently with experimental dissociation energies Deexpt, and that the dissociation energy of an electronic state such as the 23△g state of 7Li2 whose experimental value is not available can be predicted using the new formula.     

用分子子图法计算硝基呋咱化合物的生成热

用新的分子子图法计算硝基呋咱类化合物的生成热 ,将呋咱基团视为母体 ,即基子图项 ;硝基、叠氮基、甲基、氰基拆分为一个个原子 ,从原子的角度来分分子子图 ,将碳、氢、氧、氮原子视为取代基 ,即亚子图项 .同时考虑呋咱基团的个数 ,考虑 1位、2位、3位、4位上碳、氢、氧、氮原子及双键、叁键对生成热的影响 ,还考虑不饱和度、总硝基个数、环的个数 (除呋咱环 )、氮氮及氮氧双键的个数对生成热的影响 .用这种新的分子子图编码方法 ,对硝基呋咱化合物的生成热进行了拟合和预估 ,取得了满意的结果 ,其回归方程的相关系数达到了 0 .995 4 .     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of halogen molecule

This paper obtains accurate vibrational spectroscopic constants and full vibrational energy spectrum by the algebraic method (AM) for some electronic states of halogen diatomic molecules.Motivated by the recent success of obtaining the dissociation energies of Li 2 molecule by using a new analytical formula,it further extends the formula to study the dissociation energies of halogen diatomic molecules.The results show that the AM spectrum and the theoretical dissociation energies agree well with RKR data and experimental data respectively.     

Accurate vibrational energy spectra and dissociation energies of some diatomic electronic states

An algebraic method (AM) used to study the full vibrational spectra of diatomic systems, and an analytical formula used to calculate accurate molecular dissociation energies are applied to study the full vibrational spectra and molecular dissociation energies of some electronic states of homonuclear and heteronuclear diatomic molecules and diatomic ions. Studies show that the AM method and the analytical expression are reliable and economical physical methods for studying full vibrational spectra and molecular dissociation energies of diatomic electronic systems theoretically. They are particularly useful for those diatomic systems whose highlying vibrational energies may not be available.     

New correlation potential for the local-spin-density functional formalism I. Total energies and ionization potentials in free atoms

Based on the recently proposed Vosko-Wilk-Nusair interpolation formulae for the correlation energy density of the spin-polarized homogeneous electron liquid, a new parametrized form for the correlation potential for the self-consistent local-spin-density calculations of atoms, molecules and solids is proposed. The total energies and first ionization potentials for a few light atoms are calculated. The influence of the improved spin-polarization dependence on the calculated quantities is investigated, too. The calculated ionization potentials are in good agreement with observed values and are better (in average by 0.3 eV) than the values predicted by the hitherto most commonly used correlation potentials within the local spin density approximation.