Equilibrium Bond Length Research Articles

Calculation of Heats of Formation for Zn Complexes: Comparison of Density Functional Theory, Second Order Perturbation Theory, Coupled-Cluster and Complete Active Space Methods.

Heats of formation were predicted for nine ZnX complexes (X= Zn, H, O, F2, S, Cl, Cl2, CH3, (CH3)2) using fourteen density functionals, MP2 calculations and the CCSD and CCSD(T) coupled-cluster methods. Calculations utilized the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Heats of formation were most accurately predicted by the TPSSTPSS and TPSSKCIS density functionals, and the BLYP, B3LYP, MP2, CCSD and CCSD(T) levels were among the poorest performing methods based on accuracy. A wide range of Zn2 equilibrium bond distances were predicted, indicating that many of the studied levels of theory may be unable to adequately describe this transition metal dimer. To further benchmark the accuracy of the density functional methods, high-level CASSCF and CASPT2 calculations were performed to estimate bond dissociation energies, equilibrium bond lengths and heats of formation for the diatomic Zn complexes and the latter two quantities were compared with the results of DFT, MP2 and coupled-cluster calculations as well as experimental values.

The liquid structure of tetrachloroethene: Molecular dynamics simulations and reverse Monte Carlo modeling with interatomic potentials

The liquid structure of tetrachloroethene has been investigated on the basis of measured neutron and X-ray scattering structure factors, applying molecular dynamics simulations and reverse Monte Carlo (RMC) modeling with flexible molecules and interatomic potentials. As no complete all-atom force field parameter set could be found for this planar molecule, the closest matching all-atom Optimized Potentials for Liquid Simulations (OPLS-AA) intra-molecular parameter set was improved by equilibrium bond length and angle parameters coming from electron diffraction experiments [I. L. Karle and J. Karle, J. Chem. Phys. 20, 63 (1952)]. In addition, four different intra-molecular charge distribution sets were tried, so in total, eight different molecular dynamics simulations were performed. The best parameter set was selected by calculating the mean square difference between the calculated total structure factors and the corresponding experimental data. The best parameter set proved to be the one that uses the electron diffraction based intra-molecular parameters and the charges qC = 0.1 and qCl = -0.05. The structure was further successfully refined by applying RMC computer modeling with flexible molecules that were kept together by interatomic potentials. Correlation functions concerning the orientation of molecular axes and planes were also determined. They reveal that the molecules closest to each other exclusively prefer the parallel orientation of both the molecular axes and planes. Molecules forming the first maximum of the center-center distribution have a preference for <30° and >60° axis orientation and >60° molecular plane arrangement. A second coordination sphere at ∼11 Å and a very small third one at ∼16 Å can be found as well, without preference for any axis or plane orientation.

Coupled cluster calculations in the (0,2) and (2,0) sectors of the Fock space for the lowest electronic states of the O2 molecule

The Fock space (FS) multireference coupled cluster (CC) method in the (0,2) and (2,0) sectors has been applied to study the ground and excited states of the oxygen molecule O2. The considered FS sectors – when used for the neutral molecule – yield double ionisation potential (DIP) or double electron affinity (DEA) values. Once they are applied to the doubly negative/doubly positive ions the results provide description of the neutral molecule. In the current case the FS(0,2)-CC variant was used to generate potential energy curves (PEC) for the ground X3Σ−g and two lowest excited states, a1Δg and b1Σ+g, of the O2 molecule. Due to a closed shell nature of the reference function, the PECs could be easily extended to the ca. 6 Å which is not very common for the system as complex as the oxygen molecule. A similar attempt has been made to use the FS(2,0)-CC scheme by doing calculations for the ion (isoelectronic with the N2 molecule). The energy values obtained for the equilibrium bond length could be considered as acceptable; however, the PECs are limited to the short range of interatomic distances.

The chemical bond in external electric fields: Energies, geometries, and vibrational Stark shifts of diatomic molecules

It is shown that the response of molecular properties of diatomics such as the total energy, the bond length, and the vibrational Stark shift to an external homogenous electric field (EF) can be predicted from field-free observable properties such as the equilibrium bond length, the bond dissociation energy, the polarizability and dipole moment functions, and the vibrational frequency. Delley [J. Mol. Struct.: THEOCHEM 434, 229 (1998)] suggested to approximate the potential energy surface under an EF by a Morse function augmented with a EF term proportional to the internuclear separation. In this work, this term is replaced by the expression of the field-induced energy change which yields a field-perturbed Morse potential that tends to a constant asymptotic limit when the EF term itself become proportional to the sum of the polarizabilities of the separated atoms. The model is validated by comparison with direct calculations on nine diatomics, five homo-nuclear (H2, N2, O2, F2, and Cl2) and four hetero-nuclear (HF, HCl, CO, and NO), covering a range and combinations of dipole moments and polarizabilities. Calculations were conducted at the quadratic configuration interaction with single and double excitations (QCISD) and density functional theory (DFT)-B3LYP levels of theory using the 6-311++G(3df,2pd) basis set. All results agree closely at the two levels of theory except for the Stark effect of NO which is not correctly predicted by QCISD calculations as further calculations, including at the coupled cluster with single and double excitation (CCSD) level of theory, demonstrate.

A Neoteric Neodymium Model: Ground and Excited Electronic State Analysis of NdF2+

Neodymium monofluoride dication was studied as a model of the Nd-F bond in NdFx. Multiconfigurational self-consistent field (MCSCF) and second order multireference quasi-degenerate perturbation theory (MCQDPT2) methods were used with a variety of active spaces to elucidate the roles of the Nd 4f, 5d, and 6s orbitals. Spin-orbit coupling calculations were performed at the SO-MCQDPT2 level, and potential energy curves were obtained for the four lowest energy quartet states as well as for the four lowest doublet states and the lowest sextet state. Inclusion of spin-orbit coupling splits these states into 30 levels. Equilibrium bond lengths, dissociation energies, transition energies, and crossing points were determined.

Néel to spin-Peierls transition in a quasi-one-dimensional Heisenberg model coupled to bond phonons

The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-$\frac{1}{2}$ Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature ${T}_{c}$ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to ${T}_{c}$, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.

A possibility of oscillations of equilibrium bond lengths in cyclohexa-1,3,5-triene derivatives

In continuation of quantum-chemical investigation of the cyclohexa-1,3,5-triene derivatives [1], in the present work we calculated the equilibrium structural parameters of the hypothetical molecules I–IV by M06-2X/cc-pVTZ method using the program GAUSSIAN-09 [2]. Vibrational spectra of all four isomers contain only real frequencies. The calculated energy of compounds I–IV are close enough for their co-existence as tautomers. Unlike Kekule who has assumed the reciprocal reversible conversion of the C=C and C–C bonds in the benzene molecule, we are discussing the possibility of reversible conversion of double and ordinary cyclohexa-1,3,5-triene bonds into the sesquialteral bonds. DOI: 10.1134/S1070363213080276

The 3[formula omitted] state of Cs2 molecule

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved deformed four-parameter exponential-type potential energy model. It is found that the deformed four-parameter exponential-type potential function is identical to the well-known Tietz potential function for diatomic molecules. The present model can well model the interaction potential energy curve for the 33Σg+ state of Cs2 molecule. The vibrational levels computed by using the improved deformed four-parameter exponential-type potential model are in good agreement with the experimental RKR data and DPF values.

SplitGAS Method for Strong Correlation and the Challenging Case of Cr2.

A new multiconfigurational quantum chemical method, SplitGAS, is presented. The configuration interaction expansion, generated from a generalized active space, GAS, wave function is split in two parts, a principal part containing the most relevant configurations and an extended part containing less relevant, but not negligible, configurations. The partition is based on an orbital criterion. The SplitGAS method has been employed to study the HF, N2, and Cr2 molecules. The results on these systems, especially on the challenging, multiconfigurational Cr2 molecule, are satisfactory. While SplitGAS is comparable with the GASSCF method in terms of memory requirements, it performs better than the complete active space method followed by second-order perturbation theory, CASPT2, in terms of equilibrium bond length, dissociation energy, and vibrational properties.

Equivalence of the deformed Rosen–Morse potential energy model and Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed Rosen–Morse potential energy model. It is found that the deformed Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. With the help of the energy spectrum expression of the deformed Rosen–Morse potential model, we obtain exact closed-form expressions of diatomic anharmonicity constants $$\omega _e x_e $$ and $$\omega _e y_e $$ .

First-Principles Study of the Structural, Electronic, and Magnetic Properties of Cu-Fe, Cu-Co, and Cu-Ni Linear and Zigzag Nanowires

By using first-principles calculations, we have systematically investigated the equilibrium structure, electronic, and magnetic properties of free-standing Cu-Fe, Cu-Co, and Cu-Ni bimetallic linear and zigzag nanowires, and a comparison was carried out with the corresponding monatomic chains. It was found that all the bimetallic linear and zigzag chains have stable ferromagnetic (FM) states, and the total energies of all the considered zigzag chains are lower than those of the corresponding linear chains. The equilibrium bond lengths of the bimetallic Cu-Fe, Cu-Co, and Cu-Ni nanowires lie in between the values of the corresponding monatomic systems. The magnetic moments in linear nanowires are generally larger than the ones of the corresponding zigzag nanowires, and the Fe, Co, and Ni atoms in bimetallic nanowires have quite high local magnetic moments. The calculations suggest that there is hybridization between the Cu-3d and Fe (Co or Ni) 3d states, which leads to lower cohesive energies of the bimetallic nanowires than those of the corresponding monatomic nanowires. The bimetallic Cu-Fe and Cu-Co nanowires also have high spin polarizations and may be good potential materials for spintronic devices.

Nature of closed‐ and open‐shell interactions between noble metals and rare gas atoms

Interactions between noble metals and rare gases have become an interesting topic over the last few years. In this work, a computational study of the open‐shell (d10s1) and closed‐shell (d10s and d10s2) noble metals (M = Cu, Ag, and Au) with three heaviest rare gas atoms (Rg = Kr, Xe, and Rn) has been performed. Potential energy curves based on ab initio [MP2, MP4, QCISD, and CCSD(T)] and DFT functionals (M06‐2X and CAM‐B3LYP) were obtained for ionic and neutral AuXe complexes. Dissociation energies indicate that neutral metals have the lowest and cationic metals have the highest affinities for interaction with rare gas atoms. For the same metals, there is a continuous increase in dissociation energies (De) from Kr to Rn. The nature of bonding and the trend of De and equilibrium bond lengths (Re) have been interpreted by means of quantum theory of atoms in molecules, natural bond orbital, and energy decomposition analysis. © 2013 Wiley Periodicals, Inc.

High‐resolution stimulated Raman spectroscopy and analysis of the ν1, 2ν1–ν1, ν2, 2ν2, and 3ν2–ν2 bands of CF4

The spectra of the ν1, 2ν1–ν1, ν2, 2ν2, and 3ν2–ν2 bands of CF4 were obtained with a quasi‐continuous wave stimulated Raman spectrometer. These five bands were studied at a temperature of 135 and 300 K (for the hot bands). The spectrum of ν1 was obtained at a sample pressure of 2 mbar. For the spectra of the other regions, which are much weaker, higher pressures were used. The analysis has been performed thanks to the xtds and spview softwares developed in Dijon for such highly symmetric molecules. Combining the present results with a previous infrared study, we could determine a very accurate value for the C–F equilibrium bond length, i.e. re = 1.31588(6) Å. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Half-Metallic Ferromagnetism in MgS by Doping with &lt;i&gt;Sp&lt;/i&gt;-Element: A First-Principles Calculations

The first-principles calculations using full potential linearized augmented plane wave method (FP-LAPW) was performed to determine the influence of dopants (N, P, As and Sb) on the electronic structure of MgS in the rock salt structure. In the present work both local spin density approximation (LSDA) and generalized gradient approximation (GGA) were used for exchange correlation potential functional. Among the group V elements N-doping alone induce half-metallic ferromagnetism in MgS host with a magnetic moment of 1.00 μB/f.u. Total energy calculations show that ferromagnetic state is more stable than non-magnetic state in all the compounds. The ground state properties such as equilibrium lattice constant, bulk modulus and bond length were calculated. The spin polarized electronic band structure, total and partial density of states calculations were carried out to study the origin of half-metallic ferromagnetism in these compounds. The difference between two exchange-correlation functions is also analyzed.

Equivalence of the deformed modified Rosen–Morse potential energy model and the Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed modified Rosen–Morse potential energy model. It is found that the deformed modified Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. In terms of the energy spectrum expression of the deformed modified Rosen–Morse potential model, we obtain exact closed-form expressions for diatomic anharmonicity constants ωexe and ωeye . The anharmonicity constants for the X1Σ+g state of the N2 molecule have been computed and compared with the observed data.

Hybrid Coupled Cluster Methods Based on the Split Virtual Orbitals: Barrier Heights of Reactions and Spectroscopic Constants of Open-Shell Diatomic Molecules

We report an efficient implementation of the coupled cluster (CC) singles, doubles, and a hybrid treatment of triples based on the split virtual orbitals (SVO-CCSD(T)-h) method [J. Chem. Phys.2012, 136, 044101]. In this approach, virtual orbitals are split into two subsets, and correspondingly triple excitations are divided into active and inactive subsets. The active triple excitations are treated with the CCSDt (CC singles, doubles, and active triples) method, while the inactive triple excitations are treated with the CCSD(T) (CC singles, doubles, and perturbative triples) method. In the present work, the use of semicanonical molecular orbitals allows the CCSD(T)-like equations in SVO-CCSD(T)-h to be solved without iteration. As a result, the present SVO-CCSD(T)-h scheme does not need a large disk space to store the large number of triple excitation amplitudes, which is required by the original scheme. Test applications indicate that the present method can give results almost identical to those of the original scheme. The present method is then applied to investigate the reaction barriers for a number of simple reactions and spectroscopic constants including the equilibrium bond lengths and vibrational frequencies in several open-shell diatomic molecules. The SVO-CCSD(T)-h method is demonstrated to provide a significant improvement upon the CCSD(T) method in many cases.

Fock space multireference coupled cluster theory: Study of shape resonance

AbstractThe complex absorbing potential along with correlated independent particle potential (CIP) Fock space multireference coupled cluster method is used for the study of resonances. We have studied shape resonance of e−‐ F2, e−‐ N2O and e−‐CO molecules. In particular, we have studied e−‐ F2 scattering at different bond lengths to know whether $ {\rm F}_2^- $ is bound at the equilibrium bond length of F2. © 2013 Wiley Periodicals, Inc.

Spin–orbit coupling and electron correlation at various coupled-cluster levels for closed-shell diatomic molecules

In this work, equilibrium bond lengths and harmonic frequencies of some closed-shell diatomic heavy-element compounds are calculated at a series of coupled-cluster (CC) levels including CCS, CC2, CCSD and CCSD(T) with spin-orbit coupling (SOC) included in post-Hartree-Fock (HF) step. The purpose of this work is to demonstrate the performance of CC2 for heavy element compounds and to investigate the separability between SOC and electron correlation at different correlation levels. According to our calculations, CC2 results agree well with MP2 results for these molecules except for SnO, Sb2, PbO and Bi2 and the bond lengths of SnO and PbO with CC2 are overestimated by about 0.25 Å compared to when using other approaches. Furthermore, SOC effects on electron correlation are significant for Bi2 and At2 at CCSD(T) level, while this is the case only for Bi2 at CCSD level. For 5th-row element compounds, SOC effects on bond lengths and harmonic frequencies at different levels agree well with each other except for Sb2. On the other hand, SOC effects at CCSD level are in good agreement with those at CCSD(T) level for the investigated 6th-row element compounds except for At2, whereas SOC effects at low correlation levels will be different from those at CCSD(T) level to some extent.

Potential energy curves and vibrational levels of ground and excited states of LiAl

The potential energy curves (PECs) for ground electronic state (X1∑+) and seven excited electronic states (a3∏, A1∏, b3∑+, c3∑+, B1∏, C1∑+, d3∏) of LiAl are obtained using the multi-configuration reference single and double excited configuration interaction method. Equilibrium bond length Re, adiabatic excited energy Te and vertical excited energy Tv are obtained. It is shown that c3∑+ is an unstable repulsive state, A1∏ is a weak bound state and the others are all bound states. Predissociation can be found between b3∑+ and c3∑+ states. Eight electronic states are dissociated along two channels, Li(2S)+Al(2P0) and Li(2P0)+Al(2P0). And then PECs are fitted to analytical Murrell-Sorbie (MS) potential function to deduce the spectroscopic parameters:the Re is 0.2863 nm, ωe is 316 cm-1 and De is 1.03 eV for the ground state; the values of Tv of excited states are 0.27, 0.83, 1.18, 1.14, 1.62, 1.81 and 2.00 eV; the values of De are 1.03, 0.82 and 0.26, repulsive state, 1.54, 1.10, 0.93 eV, and the values of corresponding frequency ωe are 339, 237, 394, repulsive state, 429, 192, 178 cm-1. By solving the radial Schrödinger equation of nuclear motion, the vibration levels, inertial rotation constants (J=0) are reported for the first time.

Structural properties of ZnO molecules under an external electric field

Based on the equilibrium structure obtained, the ground states of ZnO molecule under external electric fields ranging from -0.05 to 0.05 a.u. were optimized using the density functional theory B3P86 at 6-311++g(d,p) level. Effects of electric fields on the bond length, total energy, charge distribution, energy levels, HOMO-LUMO gap and the infrared spectrum of the ground states of ZnO molecule have been investigated systematically. The results show that the molecular geometry and electronic properties were dependent on the magnitude and direction of the external electric field considerebly. With the increase of electric field along the molecular axis O-Zn, the equilibrium bond length first decreased and then increased, while the total energy, the harmonic frequency and infrared spectrum first increased and then decreased. But the HOMO, LUMO energy levels and the energy gap decreased monotonically, indicateing that the molecule could be excited easily by a specific electric field. We think that the present results are useful for better understanding the physical mechanism underlying the electroluminescence properties of ZnO molecule.