Equilibrium Bond Length Research Articles

Laser spectroscopy of the C1Σ+–X1Σ+ transition of ScBr

The laser induced fluorescence spectrum of scandium monobromide (ScBr) between 795 and 845nm has been recorded and analyzed. ScBr was produced by reacting laser vaporized Sc atoms with ethyl bromide (C2H5Br). Spectra of six vibrational bands of both Sc79Br and Sc81Br isotopomers of the C1Σ+–X1Σ+ transition were observed. A least-squares fit of the measured line positions yielded accurate molecular constants for the v=0–3 levels of the C1Σ+ state and the v=0–2 levels of the X1Σ+ state. The equilibrium bond length of the C1Σ+ state has been determined to be 2.4776Å.

Electron collisions with the BeH+ molecular ion in the R-matrix approach

The R-matrix method is used to study electron collisions with the BeH+ molecular ion. The diatomic version of the UK Molecular R-matrix codes is used and a configuration-interaction calculation is first performed for the BeH+ target to obtain its potential energy curves for 19 lowest singlet and triplet states. Scattering calculations are then done to yield excitation and rotational excitation cross sections in the energy range 0 − 14 eV. Additionally we also obtain bound states of BeH and their quantum defects at the BeH equilibrium bond length 2.5369a0. Resonance positions and widths for Feshbach resonances in the e-BeH+ system are also obtained and presented at the equilibrium bond length 2.5369a0.

Neutral and cationic free-space oxygen–silicon clusters [formula omitted] ([formula omitted]), and possible relevance to crystals of SiO2 under pressure

Motivated by the theoretical study of Saito and Ono (2011) on three crystalline forms of SiO2 under pressure, quantum-chemical calculations on various free-space clusters of SiOn and GeOn for 1<n⩽6 are reported here. Both neutral and cationic clusters have been examined, for both geometry and equilibrium bond lengths. Coupled clusters and correlation-corrected MP2 calculations are presented. For the cations, we emphasize especially the structural distortions occurring in removing degeneracies.

Theoretical study of spectroscopy, interaction, and dissociation of linear and T-shaped isomers of RgClF (Rg = He, Ne, and Ar) van der Waals complexes

Spectroscopy, interaction energy, and dissociation of linear and T-shaped isomers of HeClF, NeClF, and ArClF van der Waals complexes in their ground state have been studied in detail using MP2 and CCSD(T) methods in conjunction with correlation consistent valence triple and quadruple zeta basis sets. A method, called potential method, has been developed to remove the discrepancy between theoretical and experimental values for the depth of the potential well and dissociation energies for these complexes. This is also supported by the supermolecular approach. Most of the structural and spectroscopic properties of these complexes are first reported and the rest agree very well with the experimental and theoretical values wherever available. Two local minima corresponding to linear and asymmetric T-shaped are found for RgClF complexes. For NeClF complex, the predicted values for the equilibrium bond length and well depth are R NeCl = 3.096 A and $$ D_{\text{e}}^{\text{p}} $$ = 161.50 cm−1 for the linear isomer and R NeCl = 3.503 A and $$ D_{\text{e}}^{\text{p}} $$ = 126.10 cm−1 for the T-shaped isomer. Various dissociation channels are also investigated in detail.

Structural, Elastic Constant, and Vibrational Properties of Wurtzite Gallium Nitride: A First-Principles Approach

Perdew-Wang proposed generalized gradient approximation (GGA) is used in conjunction with ultrasoft pseudopotential to investigate the structural, elastic constant, and vibrational properties of wurtzite GaN. The equilibrium lattice parameters, axial ratio, internal parameter, bulk modulus, and its pressure derivative are calculated. The effect of pressure on equilibrium lattice parameters, axial ratio, internal parameter (u), relative volume, and bond lengths parallel and perpendicular to the c-axis are discussed. At 52 GPa, the relative volume change is observed to be 17.8%, with an abrupt change in bond length. The calculated elastic constants are used to calculate the shear wave speeds in the [100] and [001] planes. The finite displacement method is employed to calculate phonon frequencies and the phonon density of states. The first- and second-order pressure derivative and volume dependent Gruneisen parameter (γ(j)) of zone-center phonon frequencies are discussed. These phonon calculations calculated at theoretical lattice constants agree well with existing literature.

Accurate potential energy surfaces with a DFT+$U(\mathbf {R})$U(R) approach

We introduce an improvement to the Hubbard U augmented density functional approach known as DFT+U that incorporates variations in the value of self-consistently calculated, linear-response U with changes in geometry. This approach overcomes the one major shortcoming of previous DFT+U studies, i.e., the use of an averaged Hubbard U when comparing energies for different points along a potential energy surface is no longer required. While DFT+U is quite successful at providing accurate descriptions of localized electrons (e.g., d or f) by correcting self-interaction errors of standard exchange correlation functionals, we show several diatomic molecule examples where this position-dependent DFT+U(R) provides a significant two- to four-fold improvement over DFT+U predictions, when compared to accurate correlated quantum chemistry and experimental references. DFT+U(R) reduces errors in binding energies, frequencies, and equilibrium bond lengths by applying the linear-response, position-dependent U(R) at each configuration considered. This extension is most relevant where variations in U are large across the points being compared, as is the case with covalent diatomic molecules such as transition-metal oxides. We thus provide a tool for deciding whether a standard DFT+U approach is sufficient by determining the strength of the dependence of U on changes in coordinates. We also apply this approach to larger systems with greater degrees of freedom and demonstrate how DFT+U(R) may be applied automatically in relaxations, transition-state finding methods, and dynamics.

CI potential energy curves for three states of RuO2+

Three low-lying states of RuO2+ are analyzed using large-scale configuration interaction (CI) calculations based on multireference wavefunctions. Relativistic effects are included using relativistic effective core potentials and a spin–orbit (SO) CI approach. The ground state is predicted to be a triply bonded system of 0+ (1Σ+) symmetry having a dissociation energy of 83.8kcal/mol, an equilibrium bond length of 1.55Å and a vibrational frequency of 1227cm−1. Two close-lying states (3Φ) and (3Δ) states have dissociation energies, bond lengths and frequencies of 82.2 and 68.5kcal/mol, 1.83 and 1.90Å, and 974 and 974cm−1, respectively. The states differ in energy at their respective minima by 551 and 4777cm−1.

Magnetism of Mg atomic chains on the NaCl(100) surface

Based on the first-principles calculations within the density-functional theory, we have investigated the magnetism of 1D Mg nanowires, both unsupported and supported by the NaCl(100) surface. It is shown that Mg can exhibit magnetism in both the geometry of linear and zigzag chains. The freestanding Mg linear chain shows magnetization when the bonds are compressed. For an Mg zigzag chain, however, ferromagnetism is predicted at the equilibrium bond length. It is found that the magnetism of Mg chains can be maintained when deposited on the NaCl(100) surface. We have also analyzed the results by using the Stoner theory and the calculated electronic band structures.

Fine and hyperfine structure of the transition of ND() in vibrational excited states

The deuterated radical ND was produced in a DC discharge cell cooled at liquid nitrogen temperature. The discharge proved to be vibrationally hot, therefore the transient species could be detected in its vibrational excited states up to v = 6. By scanning in the 431–531 GHz frequency region, several fine-structure components of the transition in vibrational excited states were observed, each of them showing a complex hyperfine structure. A global analysis, including the measured frequencies and previous submillimetre-wave and infrared data, allowed an accurate determination of the equilibrium spectroscopic parameters of the ND radical including fine and hyperfine constants. A very precise determination of the equilibrium bond length r e was obtained. This value is not consistent with the value reported in the literature from NH data. This incongruity was discussed in terms of the breakdown of the Born–Oppenheimer approximation. In view of the recent detection of ND in a solar-mass protostar [A. Bacmann et al., Astron. Astrophys. 521, L42 (2010)], an extended spectroscopic characterization of this deuterated isotopologue of the NH species may prove useful, considering the large deuterium enhancement observed in molecular clouds.

Scaling of some chemical properties of tetrahedral and octahedral molecules plus almost spherical C and B cages

It is shown that for tetrahedral and octahedral molecules the quantity aRe/N1/3 is quadratic in the ratio z/N, where Re is the equilibrium bond length, ze is the central charge and N is the total number of electrons. Some scaling properties for the ‘breathing’ force constant k are proposed for a series of 5 tetrachlorides.

Origin of the Enhancement of the Second Hyperpolarizabilities in Open-Shell Singlet Transition-Metal Systems with Metal–Metal Multiple Bonds

Using the spin-unrestricted coupled-cluster method, we explore the origin of the second hyperpolarizabilities (γ) of singlet dichromium(II) and dimolybdenum(II) model systems with various bond lengths as a function of the diradical characters of the dσ, dπ, and dδ orbitals. Both systems exhibit enhanced γ values in the intermediate diradical character region, but by using a partitioning scheme, the dσ electrons are shown to play the essential role in contrast with the π-electrons of conventional organic π-conjugated systems. Then, in the equilibrium bond length region, the γ values are still governed by dσ electrons in the dichromium(II) system, although by dδ/dπ electrons in the dimolybdenum(II) system.

High-resolution infrared spectrum of cyanogen

The high-resolution spectrum of cyanogen ( 14N 12C 12C 14N) has been measured from 500 to 4900 cm −1. For this isotopomer many combination levels with both degenerate fundamentals, ν 4 and ν 5, have been measured for the first time and the effects of vibrational l-type resonance are observed as well as rotational l-type resonance. The effects of the vibrational resonance coupling ν 2 and 2 ν 4 have also been studied. The data have been combined with earlier measurements below 500 cm −1 to give a comprehensive catalog of the vibrational energy levels and the rovibrational constants for the normal isotopomer of cyanogen. A comparison of the term value constants for the three major symmetric isotopomers is given and they are compared with a recent ab initio calculation. The present data were combined with earlier work on the two symmetric isotopomers, 13C 2 14N 2 and 12C 2 15N 2, to obtain the equilibrium bond lengths, r CC = 138.109(60) pm and r CN = 115.976(40) pm.

Molecular dynamics simulation of the dielectric constant of water: The effect of bond flexibility

The role of bond flexibility on the dielectric constant of water is investigated via molecular dynamics simulations using a flexible intermolecular potential SPC/Fw [Y. Wu, H. L. Tepper, and G. A. Voth, J. Chem. Phys. 128, 024503 (2006)]. Dielectric constants and densities are reported for the liquid phase at temperatures of 298.15 K and 473.15 K and the supercritical phase at 673.15 K for pressures between 0.1 MPa and 200 MPa. Comparison with both experimental data and other rigid bond intermolecular potentials indicates that introducing bond flexibility significantly improves the prediction of both dielectric constants and pressure-temperature-density behavior. In some cases, the predicted densities and dielectric constants almost exactly coincide with experimental data. The results are analyzed in terms of dipole moments, quadrupole moments, and equilibrium bond angles and lengths. It appears that bond flexibility allows the molecular dipole and quadrupole moment to change with the thermodynamic state point, and thereby mimic the change of the intermolecular interactions in response to the local environment.

A benchmark quantum Monte Carlo study of the ground state chromium dimer

AbstractWe report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

A theoretical study of the structure and electron density of the peptide bond

We present a systematic study of the geometries and bond critical point electron densities of each of the 400 possible dipeptide structures. Equilibrium conformations for each of the dipeptides were located using the MMFF94 force field and the resultant geometries were further optimized using the B3LYP/6-311+G (d,p) method in the gas phase. We find that intramolecular hydrogen bonding is generally responsible for the observed conformations and that the peptide plane is significantly distorted in 15% of the compounds. The steric bulk of the amino acid side chains does not appear to be a significant contributor to the geometry about the peptide bond but rather the potential for hydrogen bonding determines the conformational preference. We also find that the electron density at the bond critical point ( ρ c ) of the peptide bond strongly correlates to the equilibrium bond length ( r e ) and that this relationship compares well with others reported for similar bond types. Using a power law relationship between ρ c and r e (i.e. ρ c = α r e - β ), we show that the regression coefficients ( α, β) for heteronuclear bonds may be estimated from those of homonuclear bonds.

Photoelectron Imaging and Theoretical Studies of Silver Monohalides AgX– (X = Cl, Br, I) and AuCl–

Photodetachment of AgX(-) (X = Cl, Br, I) and AuCl(-) is studied by a photoelectron velocity map imaging technique and theoretical calculations. Photoelectron spectra (PES) and photoelectron angular distributions (PADs) were obtained. The vibrationally resolved spectra provided approximately equal electron affinities (EAs) for AgX: 1.593(22) eV for AgCl, 1.623(21) eV for AgBr, and 1.603(22) eV for AgI, respectively. Franck-Condon simulations of these spectra gave the equilibrium bond lengths and vibrational frequencies of the title anions. Relativistic density functional theory (DFT) calculations using BLYP, PW91, PBE, and BP86 functionals have been performed to predict the EAs of the AgX (X = Cl, Br, I) molecules. The computed EAs at the BP86 level of theory are in good agreement with the experimental values. Energy partitioning analyses (EPA) at the BP86(ZORA)/QZ4P level of theory of both anions and their neutrals were reported.

Spin–orbit coupling and electron correlation in relativistic configuration interaction and coupled-cluster methods

We studied convergence characteristics of relativistic effective core potential (RECP) based configuration interaction (CI) and coupled-cluster (CC) schemes in terms of spin–orbit coupling and electron correlation. The relativistic correlated methods can be divided into Kramers restricted (KR) and spin–orbit (SO) methods which differ by the stage of spin–orbit treatment: the KR method employs two-component Kramers restricted Hartree–Fock (HF) spinors as the one-electron basis in which spin–orbit coupling is included, whereas the SO method is based on one-component molecular orbitals generated from scalar relativistic HF and the spin–orbit interaction is then entered in post-HF step. The KR method is usually superior to the SO method for molecules containing heavy elements since spin–orbit coupling is included from the HF step. A performance calibration of the SO method against the KR method is performed by computations of the ground state energies and equilibrium bond lengths of MH (M=Tl, Pb, Bi, Po, and At). Spin–orbit coupling of each molecule was systematically increased by adjusting the spin–orbit operator of RECP to investigate its impact on the SO method. Although KRCI and SOCI converged to the same full-CI limit, for the strong spin–orbit coupling SOCI required higher levels of correlation compared to KRCI to account for the orbital relaxation effect. SOCC, in contrast, was able to recover both spin–orbit interaction and electron correlation in CC steps regardless of the spin–orbit strength, implying that SOCC could be the reliable and efficient relativistic ab initio method for moderate sized molecules containing heavy elements.

Accurate Determination of the Structure of Cyclohexane by Femtosecond Rotational Coherence Spectroscopy and Ab Initio Calculations

We combine femtosecond time-resolved rotational coherence spectroscopy with high-level ab initio theory to obtain accurate structural information for the nonpolar molecules cyclohexane (C(6)H(12)) and cyclohexane-d(12) (C(6)D(12)). We measured the rotational B(0) and centrifugal distortion constants D(J), D(JK) of the v = 0 states of C(6)H(12) and C(6)D(12) to high accuracy, for example, B(0)(C(6)H(12)) = 4306.08(5) MHz, as well as B(v) for the vibrationally excited states ν(32), ν(6), ν(16) and ν(24) of C(6)H(12) and additionally ν(15) for C(6)D(12). To successfully reproduce the experimental RCS transient, the overtone and combination levels 2ν(32), 3ν(32), ν(32) + ν(6), and ν(32) + ν(16) had to be included in the RCS model calculations. The experimental rotational constants are compared to those obtained at the second-order Møller-Plesset (MP2) level. Combining the experimental and calculated rotational constants with the calculated equilibrium bond lengths and angles allows determination of accurate semiexperimental equilibrium structure parameters, for example, r(e)(C-C) = 1.526 ± 0.001 Å, r(e)(C-H(axial)) = 1.098 ± 0.001 Å, and r(e)(C-H(equatorial)) = 1.093 ± 0.001 Å. The equilibrium C-C bond length of C(6)H(12) is only 0.004 Å longer than that of ethane. The effect of ring strain due to the unfavorable gauche interactions is mainly manifested as small deviations from the C-C-C, C-C-H(axial), and C-C-H(equatorial) angles from the tetrahedral value.

Non linear adjustments with external conditions

A new non linear adjustment algorithm is proposed that includes the possibility to satisfy conditions involving non linear analytical functions of the adjustment parameters. It is based on the Levenberg-Marquardt algorithm and makes use of Lagrange multipliers to fulfill external conditions. As an application, the method is used to derive a modified Morse potential to represent the potential energy function of the 2Π1/2 ground state of nitric oxide (NO), while having both an acceptable description of the equilibrium bond length, the vibrational overtone spectrum to up to the 6th overtone, the energy and the dispersion coefficient at dissociation NO → N + O.

Complete vs Restricted Active Space Perturbation Theory Calculation of the Cr2 Potential Energy Surface

In this paper, we calculate the potential energy surface (PES) and the spectroscopic constants of the chromium dimer using the recently developed restricted active space second-order perturbation (RASPT2) method. This approach is benchmarked against available experimental measurements and the complete active space second-order perturbation theory (CASPT2), which is nowadays established as one of the most accurate theoretical models available. Dissociation energies, vibrational frequencies, and bond distances are computed at the RASPT2 level using several reference spaces. The major advantage of the RASPT2 method is that with a limited number of configuration state functions, it can reproduce well the equilibrium bond length and the vibrational frequency of the Cr dimer. On the other hand, the PES is well described only at short distances, while at large distances, it compares very poorly with the CASPT2. The dissociation energy is also ill-behaved, but its value can be largely improved using a simple workaround that we explain in the text. In the paper, we also address the effect of the Ionization Potential Electron Affinity (IPEA) shift (a parameter introduced in the zeroth-order Hamiltonian in the CASPT2 method to include the effect of two-electron terms) and show how its default value of 0.25 is not suitable for a proper description of the PES and of the spectroscopic parameters and must be changed to a more sound value of 0.45.