Diatomic Energy Research Articles

A genetic algorithm to build diatomic potentials

Through the last years, several types of numerical and combinatorial optimization algorithms have been used as useful tools to minimize functional forms. Generally, when those forms are non-linear or occur in problems without a specific optimization method, stochastic methods based on search algorithms have shown good results due to its smaller susceptibility to be trapped in a local minimum. Besides that, they can easily be implemented to work with other techniques, in this class of algorithms, the genetic ones have received special attention because they are a robust optimization tool. An algorithm can be named genetic when it uses some kind of codification to transform a set of possible solutions of a given problem in a population that will evolve subject to operators inspired, or not, by mechanisms of natural selection. In other words, they work with a population of solutions to obtain better solutions in the next generation. To do this, they use only information of cost and prize. In this work, we propose a genetic algorithm optimization technique (GAOT) to fit diatomic potential energy curves. In order to show this method, we obtain the analytical functions of the H 2 + and Li 2 systems using ab initio energy calculations with Rydberg trial functions. The diatomic vibrational energy spectra is determined from these potentials and the results are compared with other methods. This study shows that the quality of the GAOT fitting is as good as the best optimization techniques recommended to fit diatomic systems. This technique is very important because it arises as a new option to fit potential energy curves for diatomic reactions.

Connection between parameters of the Murrell–Sorbie and Fayyazuddin potentials

A connection between the Murrell–Sorbie and the Fayyazuddin potential energy functions were established by obtaining conversion matrices that convert the former's parameters into the latter and vice versa. This was attained by rearranging the Fayyazuddin potential into another, but equivalent, form comparable to the Murrell–Sorbie function with the aid of series expansion. A list of 71 sets of Fayyazuddin diatomic parameters were generated by applying one of the conversion matrices on the Huxley–Murrell data [J. Chem. Soc. Faraday Trans. II 79, 323 (1983)]. Verification of the developed conversion matrices was performed by plotting the Murrell–Sorbie and the Fayyazuddin functions using the Huxley–Murrell data and the converted data, respectively. Potential energy plots of typical (OSi) and extreme (FO, BeS and HH) diatomic parameters exhibit very good agreement between the two potential functions considered, thereby confirming the conversion matrices’ validity. Slight discrepancies of the plotted diatomic energy curves further suggest the comparative suitability of the Fayyazuddin potential for curve-fitting harder, rather than softer, bonds.

Energy partitioning schemes

The paper gives an overview, generalization and systematization of the different energy decomposition schemes we have devised in the last few years by using both the 3-D analysis (the atoms are represented by different parts of the physical space) and the Hilbert space analysis in terms of the basis orbitals assigned to the individual atoms. The so called "atomic decomposition of identity" provides us the most general formalism for analyzing different physical quantities in terms of individual atoms or pairs of atoms. (The "atomic decomposition of identity" means that we present the identity operator as a sum of operators assigned to the individual atoms.) By proper definitions of the atomic operators, both Hilbert-space and the different 3-D decomposition schemes can be treated on an equal footing. Several different but closely related energy decomposition schemes have been proposed for the Hilbert space analysis. They differ by exact or approximate treatment of the three- and four-center integrals and by considering the kinetic energy as a part of the atomic Hamiltonian or as having genuine two-center components, too. (Also, some finite basis correction terms may be treated in different manners.) The exact schemes are obtained by using the "atomic decomposition of identity". In the approximate schemes a projective integral approximation is also introduced, thus the energy components contain only one- and two-center integrals. The diatomic energy contributions have also been decomposed into terms of different physical nature (electrostatic, exchange etc.) The 3-D analysis may be performed either in terms of disjunct atomic domains, as in the case of the AIM formalism, or by using the so called "fuzzy atoms" which do not have sharp boundaries but exhibit a continuous transition from one to another. The different schemes give different numbers, but each is capable of reflecting the most important intramolecular interactions as well as the secondary ones--e.g. intramolecular interactions of type C-H[...]O.

Theoretical modeling of molecular interactions of iron with asphaltenes from heavy crude oil

The interaction of metallic iron with a model asphaltene molecule in the presence of water and electron-donor additives was modeled by using a quantum mechanics parametric method, CATIVIC. Results of Fe–asphaltene interactions show the formation of bonds on aromatic rings and directly on heteroatoms and so a decrease of C C, N C, and S C bond energies (bond activations) and the formation of metal–asphaltene complexes. Values of diatomic energies (DE), equilibrium bond distances (EBD), and diatomic bond energies (DBE) show that the most significant bonds arise when the interaction is directly on heteroatoms (N, S) and the highest activation is in the C S bonds. Electronic charge transfer occurs from the metal to hydrocarbon, except when interaction is on the N atom. Important metal O bond is observed when water interacts with Fe–asphaltene complex, leading to some activation of O H bonds. Negative charge on the system, in the presence of H 2O, will decrease Fe O and Fe N bonds and will reinforce Fe S ones. Comparison with previous work shows that, in general, hydrogenation and carbon–heteroatom bond activations due to metal interaction in the presence of water follow the trend: nickel > iron.

Theoretical study of dimeric dioxo-μ-oxo and oxo-bis (μ-oxo) of molybdenum complexes used in catalytic oxidations reactions

In this work dimeric complexes, dioxo-μ-oxo and oxo-bis (μ-oxo) of molybdenum, were theoretically modeled to try to understand reactivity for hydrocarbon oxidation. The first complex, dioxo (μ-oxo) thiocyanatomolybdenum (VI) bearing a 4,4′-di-ter-butyl-2,2′-bipyridine ligand (complex 1) in trans conformation exhibits a high oxidizing ability, giving as product a dimeric complex oxo-bis (μ-oxo) thiocyanatomolybdenum (V) with the same ligands (complex 2) in cis conformation. Calculations were perfomed by using CATIVIC, a parametric quantum chemistry method for catalytic reactions. Furthermore, new geometries were created, using the CATIVIC graphic interface, starting with complex 1 to transform it to cis conformation (complex 3). Molecular parameters for Mo were estimated from diatomic molecules and molecular properties, such as charges, interatomic distances, bond orders, and diatomic energies of selected bonds, and atoms were calculated for these complexes. In addition, LUMO characteristics were evaluated and discussed. Results suggest the feasibility of complex 1 transformation through a bridge Mo O bond rotation to form complex 3 that is energetically less stable than complex 1 in 21 kcal/mol. Results of bond strength indicate a high lability of the bipyridine ligand and a high LUMO density of states in cis conformation. Preliminary steps of the mechanism for the formation of a highly active site that explains the oxidizing ability of complex 1 is given by considering the rotation through a bridging Mo O bond to form a cis complex 3 and then a Mo N bond breaking. Vacancy creation could be considered as a previous step to the formation of active sites for catalytic oxidation.

Evidence for a simple scaling law relating neutral and cation diatomic bond energies

In the past, much chemical research has been motivated and directed by the discovery of empirical scaling laws. Today, such laws still have import, most notably as guideposts for developing better and more efficient methods of approximation in theoretical chemistry. In the course of a project examining neutral and singly-ionized cation bond energies, we have found evidence for a simple scaling law relating diatomic cation and neutral bond strengths: the loss of a valence electron from a ‘generic’ diatomic has little effect on the bond energy (i.e. D e(AB +)≅1.1 D e(AB)). Further, we find that this result varies only marginally over the population of all covalent bonds, including both singly and multiply bonded diatomics. Here, we present the evidence for this scaling law, and explore its qualitative implications for molecular structure.

Exchange methods in Kohn–Sham theory

Differences between exchange methods in exchange-only Kohn-Sham theory are highlighted by calculations of diatomic molecule total energies, uncoupled isotropic NMR shieldings, and HOMO-LUMO eigenvalue differences. Optimised effective potential (OEP) and Wu-Yang (WY) results are very similar. Localised Hartree-Fock (LHF) and Krieger-Li-Iafrate (KLI) results are close to one another, but are different to OEP and WY. Becke 1988 exchange (B88X) is different again. Shieldings reduce from OEP/WY to LHF/KLI to B88X, which is consistent with an observed reduction in HOMO-LUMO gaps. LHF, KLI, and B88X shieldings and HOMO-LUMO gaps are closer to near-exact, correlated values, than are the OEP values. These variations arise entirely due to differences in the one-electron exchange potentials, which is clearly evident in potential difference plots, relative to OEP, for the N2 molecule. Density difference plots are also presented, which exhibit a spatial correlation with the potential differences. HOMO and LUMO probability density difference plots show a contraction of the LUMO relative to OEP, which is consistent with the NMR and HOMO-LUMO findings. Plots are also presented for near-exact, correlated Kohn-Sham calculations. The features are qualitatively similar to those observed in the LHF, KLI, and B88X plots, highlighting correlated character in these approximate exchange-only calculations.

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N2 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 N 2 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.

Can resonances occur in the photodissociation continuum of a diatomic molecule? The role of potential discontinuities

Continuum resonances are standard fare in the instructional literature for quantum mechanics, where they arise from the continuity conditions imposed on one-dimensional wavefunctions for piecewise-constant potential energy functions. Such resonance structure weakens progressively as the discontinuity in the potential is smoothed, showing that the structure is specifically attributable to the discontinuity. Since diatomic molecular potential energy curves seldom vary rapidly on the distance scale of the period of the wavefunction, such continuum resonances are not expected in absorption continua. A historically interesting prediction of such structure in the Schumann–Runge continuum (B ← X) of O2 is attributed to the inadvertent incorporation of discontinuity in the B-state potential curve employed in the computations.Key words: quantum mechanics, continuum resonance, diatomic absorption, photodissociation continuum, numerical methods.

RKR-type inversion of the diatomic energy shifts due to breakdown of the Born–Oppenheimer approximation

The principal effects of the breakdown of the Born–Oppenheimer approximation on the vibration–rotation energies of a diatomic molecule can be represented by the expectation values of terms to order (me/Mi) in the effective Hamiltonian, where me is the electron mass and Mi is the mass of atom i. This paper examines the possibility of inverting these expectation values to obtain the correction functions as functions of the internuclear distance r, using a generalization of the semiclassical Rydberg–Klein–Rees method. It is shown that the correction functions are not completely determinable from the inversion, and the form of the determinable combinations is obtained.Key words: diatomic molecules, vibration–rotation energies, isotope effects, Born–Oppenheimer breakdown, Rydberg–Klein–Rees method.

An exact chemical decomposition scheme for the molecular energy

A very simple scheme is proposed to present the SCF molecular energy exactly as a sum of one- and two-center (mono- and diatomic) energy components, accounting for the bond formation, non-bonded repulsion, promotion etc. effects on the chemical energy scale. Generalization to the correlated case is expected to be straightforward.

Performance of Ornstein–Uhlenbeck diffusion quantum Monte Carlo for first-row diatomic dissociation energies and dipole moments

In this paper, calculation of nine first-row diatomic dissociation energies (De) and six first-row heterodiatomic equilibrium dipole moments (μe) highlights the strength of Ornstein–Uhlenbeck diffusion quantum Monte Carlo with the fixed-node approximation. By combining explicitly correlated wave functions based on spherical Gaussian-type orbitals and geminals obtained by an optimization of energy functional, it was possible to achieve satisfied agreement with experiment in most cases. Calculations on the molecules LiH, Li2, BH, BF, HF, LiF, CO, N2, and F2 are presented. This work gives an accuracy that is comparable to or better than previous theoretical estimates. We also compare the performance of three different approximations in estimating dipole moments of molecules.

Theoretical calculations of silica supported Mo 2( η3-C 3H 5) 4 species

Two models are studied for the anchored system Mo 2( η 3-C 3H 5) 4/SiO 2: united model (UM) and separated model (SM). Total energies, bond orders, diatomic energies, and parametric diatomic binding energies of selected bonds were calculated for Si 8O 24H 16, Mo 2( η 3-C 3H 5) 4, and Mo 2( η 3-C 3H 5) 4/Si 8O 24H 16 systems, using a CNDO–UHF parametrical method. From the energetic viewpoint, UM is more stable than SM to explain the immobilizing of Mo 2( η 3-C 3H 5) 4 on silica. It is observed Mo–H interaction that leads to C–H activation. These results support several features of the generally accepted mechanism for olefin metathesis. An interpretation of these theoretical results was carried by comparing with PAS–FTIR, 1H and 13C solid-state NMR, and XPS trends.

Physical analysis of the diatomic "chemical" energy components

The recent “chemical energy component analysis” permits the total energy of a molecule to be presented approximately but to good accuracy as a sum of atomic and diatomic energy contributions. Here the diatomic energy components are further decomposed into terms of different physical origin: electrostatics (in point-charge approximation and the distributed charge corrections), exchange effects, diatomic overlap and atomic basis extension terms. This analysis may provide us with a deeper insight into the factors influencing both the chemical bonds and the nonbonded interatomic interactions.

Interatomic exchange energy components

AbstractThe diatomic energy components obtained in the framework of the recent chemical energy component analysis can be further decomposed into terms of different physical origins, reflecting electrostatic, exchange, overlap, etc., effects. The proper definition of the interatomic exchange energy component represented a nontrivial task, however. Here, we considered two possible definitions of that quantity. The first is introduced following the definition of the intermolecular exchange. This seemingly straightforward analogy has been found misleading—it leads to a quantity that vanishes in the limit of an NDO‐type integral approximation. The correct definition has been found by analyzing the exchange energy components connected with the delocalized bonding orbitals in a diatomics and generalizing the interatomic exchange energy contribution obtained in this simplest case by the analogy to the respective Coulomb energy component. This definition is adequate for all types of theories, has the correct asymptotic behavior, and exhibits the expected connections with the bond order indices. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Asymptotics of Quantum Mechanical Atom-Ion Systems

We have analyzed and reduced a general (quantum-mechanical) atom-ion diatomic exchange energy formulation into fundamental mathematical forms, namely a particular class of single and double definite integrals. These are of importance in the charge exchange of molecular processes in atmospheric physics and eventually of interest to matters related to climate. These integrals have been evaluated in terms of asymptotic expansions, with precise schemes for their numerical evaluation. Dividends for algebraic aspects concerning identities of hypergeometric functions as well as summation techniques for divergent series are also discussed in this context.

Atomic orbital participation on a chemical bond through a binding energy partitioning scheme

The participation of atomic orbitals in bond formation is presented here in terms of energy contributions. This approach is based on partition of inter-atomic energy in its components: resonance ( R), electron–electron repulsion ( J), attractive electron–nucleus ( V), exchange ( K), and nucleus–nucleus repulsion ( N) for pairs of interacting orbitals. In a similar way, changes of intra-atomic energy per atomic orbital were also considered. The proposed partition model allows a detailed analysis of the contribution of each atomic orbital in the formation of the bond. It is possible to distinguish the energetic changes or rearrangements that occur on each atom (monoatomic terms) and those that are associated to direct inter-atomic orbital–orbital interactions (diatomic terms). Thus, diatomic binding energy (DBE) is expressed as a sum of atomic orbital binding energies (AOBEs). A complementary picture is also introduced by analyzing inter-atomic electron–atom bonding interactions. To illustrate those models, an analysis of atomic orbital participation in Ni–Ni and Ni–O bonds of diatomic molecules and in Ni 5–O cluster were performed by using a parametric method.

Parametric calculations of Mo-allyl complexes anchored on silica

The SiO 2 anchored Mo(η 3-C 3H 5) 4 catalyst was modeled by means of the CNDO-UHF parametrical method. Two models (two separated centers (TSC) and two adjacent centers (TAC)) were proposed for the silica pre-treated at relatively low temperature. An analysis of total energies, bond indexes, diatomic energies, and parametric diatomic binding energies for selected bonds suggests the existence of both models on the surface. However, TSC is favored with respect to TAC. Furthermore, it is observed an allyl group interaction with the support through a CO bond that leads to a CC bond activation. Also, CH activation is found due to MoH interaction. These results support several features of the generally accepted mechanism for olefin metathesis in this type of catalyst. Finally, experimental results of NMR, obtained in previous work by some of the authors, are interpreted by inequivalency of different allyl ligands.

Performance of CCSDT for diatomic dissociation energies

Calculations of 11 diatomic dissociation energies with coupled cluster theory through iterative triple excitations highlight both the strength and limitations of this method. By combining very large basis sets (through septuple zeta in some cases) and complete basis set extrapolations with corrections for core/valence correlation, scalar relativistic and atomic/molecular spin–orbit effects, it was possible to achieve excellent agreement with experiment in most cases. However, for C2 and CN the extent of the multiconfigurational nature of the molecules caused problems for the single configuration-based couple cluster methods. In the worse case, the inclusion of iterative triples resulted in a change with respect to the perturbative triples result which was of the opposite sign to the full configuration interaction change. This work emphasizes the difficulties in achieving uniform chemical accuracy even for ground state, first and second row diatomics.

A comparison of techniques for predicting higher order correlation effects: Diatomic dissociation energies

The impact of higher-order correlation effects on dissociation energies was measured for three diatomic molecules (HF, N2, and CO) using standard coupled cluster theory, including a perturbative treatment of triple excitations, as the baseline for comparison. Among the higher-order methods examined were two variations of coupled cluster theory [CCSDT and CCSD(TQ)] and two approximations to full configuration interaction. Basis sets were chosen from the correlation-consistent family of basis sets, with the largest being the aug-cc-pVQZ set. Polarized valence double zeta quality basis sets were found to yield corrections that differed substantially from larger basis set results. At the double zeta level, higher order corrections increased the binding energies, whereas calculations with triple and quadruple zeta basis sets gave the opposite effect. Although the absolute magnitude of the higher-order corrections was small for these diatomics, they were nonetheless significant in light of a target accuracy of ±1 kcal/mol. Among molecules composed of first-through-third period elements, such as those in the G2 and G2/97 collections, the contribution to D0 from higher order correlation effects could easily exceed 1 kcal/mol. If further studies corroborate the present findings, CCSDT should provide an effective method of determining the magnitude of the higher-order correction, at least when basis sets of triple zeta or better quality can be used. CCSD(TQ) often overestimated the higher order correction, sometimes exceeding the estimated full configuration interaction result by a factor of three.