Diatomic Energy Research Articles

Diatomic molecule energies of the modified Rosen−Morse potential energy model

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

Physical Nature of Interactions in ZnIIComplexes with 2,2′-Bipyridyl: Quantum Theory of Atoms in Molecules (QTAIM), Interacting Quantum Atoms (IQA), Noncovalent Interactions (NCI), and Extended Transition State Coupled with Natural Orbitals for Chemical Valence (ETS-NOCV) Comparative Studies

In the present account factors determining the stability of ZnL, ZnL2, and ZnL3 complexes (L = bpy, 2,2′-bipyridyl) were characterized on the basis of various techniques: the quantum theory of atoms in molecules (QTAIM), energy decomposition schemes based on interacting quantum atoms (IQA), and extended transition state coupled with natural orbitals for chemical valence (ETS-NOCV). Finally, the noncovalent interactions (NCI) index was also applied. All methods consistently indicated that the strength of the coordination bonds, Zn–O and Zn–N, decreases from ZnL to ZnL3. Importantly, it has been identified that the strength of secondary intramolecular heteropolar hydrogen bonding interactions, CH···O and CH···N, increases when going from ZnL to ZnL3. A similar trend appeared to be valid for the π-bonding as well as electrostatic stabilization. In addition to the above leading bonding contributions, all techniques suggested the existence of very subtle, but non-negligible additional stabilization from the CH···HC electronic exchange channel; these interactions are the weakest among all considered here. From IQA it was found that the local diatomic interaction energy, Eint(H,H), amounts at HF to −2.5, −2.7, and −2.9 kcal mol(–1) for ZnL, ZnL2, and ZnL3, respectively (−2.1 kcal mol(–1) for ZnL at MP2). NOCV-based deformation density channels showed that formation of CH--HC contacts in Zn complexes causes significant polarization of σ(C–H) bonds, which accordingly leads to charge accumulation in the CH···HC bay region. Charge depletion from σ(C–H) bonds was also reflected in the calculated spin–spin (1)J(C–H) coupling constants, which decrease from 177.06 Hz (ZnL) to 173.87 Hz (ZnL3). This last result supports our findings of an increase in the local electronic CH···HC stabilization from ZnL to ZnL3 found from QTAIM, IQA, and ETS-NOCV. Finally, this work unites for the first time the results from four methods that are widely used for description of chemical bonding.

An optimized interatomic potential for Cu–Ni alloys with the embedded-atom method

We have developed a semi-empirical and many-body type model potential using a modified charge density profile for Cu–Ni alloys based on the embedded-atom method (EAM) formalism with an improved optimization technique. The potential is determined by fitting to experimental and first-principles data for Cu, Ni and Cu–Ni binary compounds, such as lattice constants, cohesive energies, bulk modulus, elastic constants, diatomic bond lengths and bond energies. The generated potentials were tested by computing a variety of properties of pure elements and the alloy of Cu, Ni: the melting points, alloy mixing enthalpy, lattice specific heat, equilibrium lattice structures, vacancy formation and interstitial formation energies, and various diffusion barriers on the (100) and (111) surfaces of Cu and Ni.

Approaching chemical accuracy with density functional calculations: Diatomic energy corrections

Density functional theory (DFT) is widely used to predict materials properties, but the local density approximation (LDA) and generalized gradient approximation (GGA) exchange-correlation functionals are known to poorly predict the energetics of reactions involving molecular species. In this paper, we obtain corrections for the O${}_{2}$, H${}_{2}$, N${}_{2}$, F${}_{2}$, and Cl${}_{2}$ molecules within the Perdew-Burke-Enzerhof GGA, Perdew-Wang GGA, and Perdew-Zunger LDA exchange-correlation functionals by comparing DFT-calculated formation energies of oxides, hydrides, nitrides, fluorides, and chlorides to experimental values. We also show that the choice of compounds used to obtain the correction is significant, and we use a leave-one-out cross-validation approach to rigorously determine the proper fit set. We report confidence intervals with our correction values, which quantifies the variation caused by the choice of fit set after outlier removal. The remaining variation in the correction values is of the order of 1 kcal/mol, which indicates that chemical accuracy is a realistic goal for these systems.

Critical Reynolds number of the couette flow of a vibrationally excited diatomic gas energy approach

An energy balance equation for plane-parallel flows of a vibrationally excited diatomic gas described by a two-temperature relaxation model is derived within the framework of the nonlinear energy theory of hydrodynamic stability. A variational problem of calculating critical Reynolds numbers Recr determining the lower boundary of the possible beginning of the laminar-turbulent transition is considered for this equation. Asymptotic estimates of Recr are obtained, which show the characteristic dependences of the critical Reynolds number on the Mach number, bulk viscosity, and relaxation time. A problem for arbitrary wave numbers is solved by the collocation method. In the realistic range of flow parameters for a diatomic gas, the minimum critical Reynolds numbers are reached on modes of streamwise disturbances and increase approximately by a factor of 2.5 as the flow parameters increase.

Fully relativistic rovibrational energies and spectroscopic constants of the lowest $$ {\text{X}}:(1)0_g^{ + } $$ , A′:(1)2 u , A:(1)1 u , $$ {\text{B}}\prime :(1)0_u^{ - } $$ and $$ {\text{B}}:(1)0_u^{ + } $$ states of molecular chlorine

The main goal of this paper is to present the rovibrational energies and spectroscopic constants of the Cl(2) molecular system in the relativistic states [Formula: see text], A':(1)2( u ), A:(1)1( u ), [Formula: see text] and [Formula: see text]. More precisely, we have evaluated the Cl(2) ω ( e ), ω ( e ) x ( e ), ω ( e ) y ( e ), α ( e ), γ ( e ) and B ( e ) rovibrational spectroscopic constants using two different procedures. The first was obtained by combining the rovibrational energies, calculated through solving Schrödinger's nuclear equation and the diatomic rovibrational energy equation. The second was obtained by using the Dunham method. The calculated properties are in good agreement with available experimental data.

Intermolecular diatomic energies of a hydrogen dimer with non-Born–Oppenheimer nuclear and electron wave packets

We have developed an efficient theoretical framework of a non-Born–Oppenheimer (non-BO) nuclear and electron wave packet (NWP and EWP) method and applied it to intra- and intermolecular energies of a hydrogen dimer. The energy surface functions were derived at low computational cost. In contrast with the ordinary BO nuclear quantization on a given energy surface that reduces the effective barrier, non-trivial non-BO interactions between the EWPs and NWPs resulted in increases of intermolecular rotational and translational barriers. A direct comparison demonstrated that the non-BO effect on the intermolecular energy is significant.

Relativistic ground state of diatomic molecules from the numerical solution of the Dirac equation on parallel computers

The parallel implementation of a variational method for the numerical solution of the time-independent Dirac equation is presented. This is utilized in the calculation of diatomic molecule relativistic wave functions and ground state energy, in the Born-Oppenheimer approximation. Following [1], a functional equation predicting the same spectrum as the Dirac equation is discretized over a set of basis functions. We find that the combination of B-spline basis functions and prolate spheroidal coordinate systems facilitate the vectorization of the technique using domain decomposition. This procedure results in a non-linear eigenvalue problem which is solved by iteration using Brent's method. We validate our methodology by comparing with existing results and show that it yields very accurate ones. We also analyze the parallelization and demonstrate that our implementation has a good scaling performance. Finally, the utilization of this method for laser-matter interaction and other physical applications will be discussed.

Energy decomposition analysis of cis and trans isomers of 1,2-dihaloethylenes and 2-butene

Mayer’s energy decomposition method was applied inthe study of the relative stability of cis and trans isomers of 1,2-disubstituted ethylenes, XHC CHX (X = F, Cl, Br) and 2-butene. The trans to cis isomerization energy for each system was determined at the Hartree–Fock level, with several basis sets, and then divided into monoatomic and diatomic energy contributions. The results point to a different energy distribution for the dihaloethylenes, known for exhibiting a cis isomer that is more stable than the trans one, a behavior that is known as the cis effect, when compared to 2-butene. The main stabilizing effects of the cis isomer in the dihaloethylenes, at this level of theory, are energy terms associated with the interaction of the X substituents with the C atoms.

Methodologies to analyze surface bonding properties using parametric and density functional methods

AbstractThis work presents two general methodologies to calculate bond adsorption energy (BAE) between surface and adsorbate using parametric quantum (PQM) and density functional (DFM) methods. The first one corresponds to the bond partition energy technique that is directly applied to PQMs by using energy partition approach and considering diatomic and monoatomic energy changes. The second methodology to evaluate BAE, as well as for PQMs and DFMs, is by means of the following equation: where Eads is the adsorption energy and ΔEs and ΔEa correspond to energy changes in the surface and substrate due to adsorption, respectively. Applications to radical adsorption: H°, CH2°, and CH3° is performed on a grafitic grain model, using a polyaromatic hydrocarbon (PAH), such as coronene. The methods employed are a PQM (CATIVIC program) and DFMs (GAUSSIAN and DMol software packages). Results show that Eads is completely different of BAE, because of distortion of surface and adsorbate. There is a strong destabilization in the region adjacent to the adsorption site and stabilization in the rest of the surface. Two terms for BAE are reported: one that corresponds to direct bonding interaction (BAEb) and other to long range ones, due to electrostatic interaction (BAEe). Owing to the important effects of bond strength adsorbate–surface interaction, results suggest that BAE is fundamental for understanding bond activation in adsorbate and surface, cooperative effects, diffusion, reaction, and desorption process. In general, similar results were found for both CATIVIC and DFMs, by using the second methodology. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

A detailed comparison of centrifugal sudden and J-shift estimates of the reactive properties of the N + N2 reaction

An extended comparison of the reactive properties of the N + N(2) exchange reaction calculated on a non-collinear dominant potential energy surface using both a centrifugal sudden and a J-shift quantum method is reported. The choice of carrying out such an investigation for N + N(2) is motivated by the fact that the best available (and currently used for spacecraft re-entry simulations) computed set of kinetic data has been worked out using the low level J-shift approximation though based on exact quantum zero total angular momentum probabilities. The fact that our investigation is carried out for a heavy system and a potential energy surface free of wells in the strong interaction region minimizes the occurrence of tunnel, resonance and interference effects which would make the rationalization of the result difficult and the centrifugal sudden treatment less accurate. The study has provided evidence of two important limits of the J-shift approximation: the wrong determination of the maximum value of the total angular momentum quantum number J contributing to reactivity and the lack of deformation of the partial reactive probability dependence on energy at fixed J value. Accordingly, it has been found that the J-shift state-specific cross sections underestimate the corresponding CS values when the initial diatomic rotational energy is low while the situation reverses when the initial diatomic rotational energy is high.

Energy decomposition based on the extended virial theorem: Hartree–Fock and second‐order Møller–Plesset results

AbstractThe article shows how the extended virial theorem within the Born–Oppenheimer framework can be used to decompose the total energy of a molecule into atomic and diatomic energy contributions under various conditions. For the stationary points of a series of potential energy surfaces corresponding to wave functions built up by using one‐electron basis functions centered rigidly on atomic nuclei, computational results are presented at the Hartree–Fock and second‐order Møller–Plesset levels of theory. After a partial redistribution of the original diatomic energy contributions into atomic ones, the transformed diatomic energy contributions are “on the chemical scale.” It turns out that the transformed diatomic energies at the second‐order Møller–Plesset perturbation level are characteristic of the strength of the chemical bonds present in the system. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Two complementary molecular energy decomposition schemes: The Mayer and Ziegler–Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density rho(A) has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities.

Theoretical study of olefin oxidation process on a dioxo‐μ‐oxo Mo catalyst

AbstractThe dimeric complex dioxo (μ‐oxo) thiocyanato of molybdenum(VI) bearing a 4,4′‐di‐ter‐butyl‐2,2′‐bipyridine ligand in trans conformation (complex 1) has been used in catalytic reactions of olefins (ethylene) oxidation, giving as intermediate a dimeric complex oxo bis (μ‐oxo) thiocyanato of molybdenum(V) in cis conformation (complex 2). Binding and electronic properties were calculated using the parametric quantum chemistry method for catalytic reactions, CATIVIC. The interaction of an ethylene molecule with complex 3 (cis version of complex 1) leads to the formation of the intermediate named complex 4. This complex is dissociated to form complex 5 plus ethylene oxide. Changes of electronic and bonding properties are analyzed in terms of atomic charge, orbital population, total binding energies, diatomic bond energies, diatomic energies, and Wiberg indexes, and equilibrium bond distances. The energy balance for the complete catalytic process is presented in a schematic way. Results confirm the extraordinary oxo‐transfer abilities of this complex, considering that the whole process is exothermic (−44 kcal/mol). Regeneration of the catalyst is also calculated by the interaction of H2O2 with complex 5. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Rovibrational energies and spectroscopic constants of the H system in the electronic states 1Sσ, 7iσ, 5fπ, 5gπ, 6iπ, and 6iϕ

AbstractIn this work, we present the rovibrational energies and spectroscopic constants of the molecular ion H in the electronic states 1sσ, 7iσ, 5fπ, 5gπ, 6iπ, and 6iϕ. The H electronic energies were obtained from the solution of Hamilton–Jacobi equations in association with the series established by Wind–Jaffe. The calculated energies were fitted using the extended Rydberg functions and polynomials in bond order coordinates. From these analytical forms, we evaluated the H rovibrational spectroscopic constants for each state using two different procedures. The first was obtained combining the rovibrational energies, determined through the nuclear Schrödinger equation solution, and a diatomic rovibrational energy equation. The second was determined using the Dunham method. The results obtained are in a good agreement with both experimental and theoretical data available in the literature. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Partitioning of atomization energy

AbstractThe present work provides a technique for partitioning the atomization energy of a molecule into diatomic contributions. The method is largely based on the redistribution of the kinetic energy term in Mayer's energy partitioning and uses free‐atom energies as a reference. The comparison of Mayer's original method, the alternative Ichikawa–Yoshida approach, and the new atomization energy partitioning (AEP) shows that the new approach has advantages in describing trends in diatomic energies in molecules with triple bonds, as well as for hydrogen bonds. The proposed AEP is a viable alternative to Mayer's energy partitioning method. © 2007 Wiley Periodicals, Inc. Int. J. Quantum Chem, 2008

One- and two-center physical space partitioning of the energy in the density functional theory

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one- and two-atomic energy components, and is realized in the "fuzzy atoms" framework. (Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.) The new scheme uses the new concept of "bond order density" to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact (Hartree-Fock) exchange for the same Kohn-Sham orbitals.

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 De 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.

Collisional relaxation of Feshbach molecules and three-body recombination inRb87Bose-Einstein condensates

We predict the resonance enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a $^{87}$Rb Bose-Einstein condensate (BEC) close to 1007 G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.

Energy partitioning schemes: a dilemma

Two closely related energy partitioning schemes, in which the total energy is presented as a sum of atomic and diatomic contributions by using the "atomic decomposition of identity", are compared on the example of N,N-dimethylformamide, a simple but chemically rich molecule. Both schemes account for different intramolecular interactions, for instance they identify the weak C-H...O intramolecular interactions, but give completely different numbers. (The energy decomposition scheme based on the virial theorem is also considered.) The comparison of the two schemes resulted in a dilemma which is especially striking when these schemes are applied for molecules distorted from their equilibrium structures: one either gets numbers which are "on the chemical scale" and have quite appealing values at the equilibrium molecular geometries, but exhibiting a counter-intuitive distance dependence (the two-center energy components increase in absolute value with the increase of the interatomic distances)--or numbers with too large absolute values but "correct" distance behaviour. The problem is connected with the quick decay of the diatomic kinetic energy components.