Equilibrium Bond Length Research Articles

Vibrationally resolved photoelectron imaging of gold hydride cluster anions: AuH− and Au2H−

Photoelectron spectra and angular distributions in photodetachment of gold hydride anions AuH(-) and Au(2)H(-) have been obtained using photoelectron velocity-map imaging. Both the images exhibit vibrationally resolved ground state transitions. The adiabatic electron affinities of AuH and Au(2)H are measured to be 0.758(20) and 3.437(3) eV, respectively. Franck-Condon analyses of the AuH spectra determined that the equilibrium bond length of the ground state of AuH(-) is 1.597(6) A. The photoelectron images of Au(2)H(-) show a vibrational progression of 148(4) cm(-1) assigned to the Au-Au stretching mode at the ground state. Ab initio calculation results are in excellent agreement with the experimental results. For the ground state of Au(2)H, a new bent Au-Au-H structure with the angle of 131 degrees is suggested. Moreover, energy-dependent photoelectron anisotropy parameters are also reported and discussed.

LiH potential energy curves for ground and excited states with the free complement local Schrödinger equation method

The two lowest singlet and triplet Σ + potential energy curves of LiH were calculated using the free complement (FC) local Schrödinger equation (LSE) method. The overall potential curves and the properties calculated therefrom, like equilibrium bond length, dissociation energy, adiabatic and vertical excitation energies, zero point energy, vibrational spacings, etc., demonstrated the high accuracy of the FC LSE method for both the ground and excited states in comparison to the reference calculations and experiments.

Van der Waals Interactions for Isolated Systems Calculated Using Density Functional Theory within Plasmon-Pole Approximation

We have developed a new method of calculating the van der Waals interaction in isolated systems on the bases of the van der Waals density functional theory. This method is designed to be absolutely nonempirical, applicable to any three-dimensional isolated system and implementable into various first-principles electronic state calculation codes utilizing local density approximation (LDA). The validity of this method is tested by comparing the adiabatic potentials of an Ar dimer and a Kr dimer obtained by this method to those obtained in experiments and other theoretical studies. We find that the LDA error is largely mitigated in both equilibrium bond length and cohesive energy.

Modeling of Amorphous Polyaniline Emeraldine Base

Amorphous polyaniline emeraldine base has been investigated using atomistic classical molecular dynamics simulations. Initially, different sets of force-field parameters, which differ in the atomic charges and/or the van der Waals parameters, were tested. The experimental density of polyaniline was satisfactorily reproduced using the following combination: (i) equilibrium bond lengths, equilibrium bond angles, and electrostatic charges derived from quantum mechanical calculations and (ii) van der Waals parameters extrapolated from GROMOS for all atoms with the exception of the CH pseudoparticles of the phenyl ring, which were taken from an anisotropic united atom potential. Next, this force field was used to investigate the structure of the polymer in the amorphous state, the trajectories performed for this purpose allowing accumulation of 750 ns. Analyses of the energies evidence that the interactions between one repeating unit containing an amine nitrogen atom and another unit with an imine nitrogen are favored with respect to those between two identical repeating units. This conclusion is also supported by quantum mechanical and quantum mechanical/molecular mechanics calculations. On the other hand, the partial radial distribution functions indicate that this material only exhibits short-range intramolecular correlation, which is in excellent agreement with experimental evidence.

Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

The magnetic properties of small ${\text{Cr}}_{N}$ clusters $(N\ensuremath{\le}6)$ are investigated in the framework of density-functional theory. The interplay between electron correlations, cluster structure, and magnetic order is quantified by performing fully spin-unrestricted calculations allowing for noncollinear spin arrangements within both the local-spin-density approximation (LSDA) and the generalized-gradient approximation (GGA). The possible transition or saddle-point states are identified by determining the vibrational frequencies from diagonalizing the dynamical matrix. In agreement with previous studies, a dimer-based growth pattern is found in all considered low-lying isomers with very short equilibrium bond lengths (typically ${d}_{eq}^{\text{GGA}}=1.55--1.65\text{ }\text{\AA{}}$) alternating with relative long ones (typically ${d}_{eq}^{\text{GGA}}=2.75--2.85\text{ }\text{\AA{}}$) in the relaxed geometries. Strong local magnetic moments ${\stackrel{P\vec}{\ensuremath{\mu}}}_{i}$ are, in general, obtained for the relaxed geometries (e.g., $|{\ensuremath{\mu}}_{i}^{\text{GGA}}|\ensuremath{\simeq}2\text{ }{\ensuremath{\mu}}_{\text{B}}$ in ${\text{Cr}}_{4}$), which show a collinear magnetic order with antiparallel (parallel) alignment of the ${\stackrel{P\vec}{\ensuremath{\mu}}}_{i}$ along the short (long) bonds. In contrast to the GGA, the LSDA yields vanishing magnetization density in some cases ($|{\ensuremath{\mu}}_{i}^{\text{LSDA}}|=0\text{ }\ensuremath{\forall}\text{ }i$ for $N=2$ and 4). Despite quantitative differences, both LSDA and GGA functionals always yield collinear ground-state solutions for the fully relaxed structures. In fact, noncollinear spin arrangements are found only for particular symmetric (nondimerized) geometries. However, the structures are not local minima and involve considerably large excitation energies. The results clearly indicate that the magnetic frustration, which one would physically expect in compact antiferromagnetic spin systems, is solved by dimerization rather than by noncollinearity of the local moments.

Atomic Radii for Depicting Atoms in a Molecule: Cu in Inert Gas Matrix

Abstract The effective atomic radius imaging the atoms in an equilibrium molecular structure is discussed for He, Ne, Ar, Kr, and Xe, based on the electrostatic field calculated with the Hartree–Fock and configuration interaction singles and doubles methods, both with and without the Douglas–Kroll–Hess relativistic transformation. The effective atomic radius r is defined as a distance from the nucleus at which the magnitude of the electric field is that in He at one half of the equilibrium bond length of He2. The resulting radii are ca. 20% larger than Bondi’s radii, which are conventionally recognized as the van der Waals radii. Valence radii and inner core radii are also defined and discussed.

Computation of the internuclear distances of some heteronuclear diatomic molecules in terms of the revised electronegativity scale of Gordy

We have calculated the electronegativity of the atoms of 103 elements relying upon the basic approach of Gordy but carefully allaying the dimensional mismatch seemingly prevalent in all previous calculations. In absence of any theoretical or experimental benchmark to perform the validity test of any scale of electronegativity, we have resorted to the method of linking the electronegativity scale with the physical descriptors that occur in the real world and can be conceived in terms of electronegativity. The equilibrium internuclear bond distances of heteronuclear diatomic molecules are experimentally determined physical constants. Such descriptor like the equilibrium bond distance can easily be linked with electronegativity and the physical process of electronegativity equalization. The mathematical formula is derived to calculate theoretically such bond distances using the scale of electronegativity. In this report we have calculated the equilibrium bond lengths of as many as eleven sets of heteronuclear diatomic molecules of widely diverse nature using our scale of electronegativity and absolute radii evaluated by us. When the theoretically evaluated bond lengths are compared with their experimental counterparts, an excellent correlation between the two sets of data is evident. It therefore transpires that our scale of electronegativity is a good descriptor of charge rearrangement on molecule formation.

Structure of gallium(III) monofluoride phthalocyaninate: A quantum chemical study

The B3LYP/6-31G quantum chemical method is used to calculate the structural parameters of [F(PcGaF)7]-, [(PcGaF)6PcGa]+ heptamers and the (PcGaF)∞, polymer of gallium(III) monofluoride phthalocyaninate. The eclipsed (ecl.) configuration (D4h point symmetry group) corresponds to the energy minimum of the [FGa(Pc)FGa(Pc)F]- dimer. The calculated equilibrium bond lengths in the central unit of all-ecl. heptamer (GaN 1.988 A; GaF 1.933 A) are similar to the bond lengths in the all-ecl. polymer (GaN 1.988 A and GaF 1.940 A) and to the respective single crystal X-ray diffraction parameters.

Infrared Spectra of12CF2═12CH2and12CF2═13CH2, Quantum-Chemical Calculations of Anharmonicity, and Analyses of Resonances

Infrared spectra obtained in gas and liquid argon phases are reported for (12)CF(2) horizontal line(12)CH(2) and (12)CF(2) horizontal line(13)CH(2). These spectra firmly establish the positions of nu(3)(A(1)) and nu(6)(A(2)) for both isotopomers. Using anharmonicity constants from MP2 calculations, Fermi resonances affecting nu(1)(A(1)), nu(2)(A(1)), nu(3), and nu(8)(B(1)) are analyzed. Deperturbed fundamental frequencies from these analyses are used in conjunction with unaffected fundamentals and ab initio anharmonicity data to predict all 12 "observed" harmonic frequencies. A Darling-Dennison type resonance between 2nu(6) and nu(11) + nu(12) is diagnosed, the calculation of which from ab initio data requires modification of the existing second-order treatment of such constants, where Fermi resonance type terms are also present. Predictions are made of many overtone and combination band frequencies, aiding assignment of observed spectra. From the isolated CH stretching frequency obtained here of 3125.4 cm(-1), the C-H equilibrium bond length is predicted to be 1.0762(11) A.

Stability and dynamics of two-soliton molecules

The problem of soliton-soliton force is revisited. From the exact two-soliton solution of a nonautonomous Gross-Pitaevskii equation, we derive a generalized formula for the mutual force between two solitons. The force is given for arbitrary soliton amplitude difference, relative speed, phase, and separation. The latter allows for the investigation of soliton molecule formation, dynamics, and stability. We reveal the role of the time-dependent relative phase between the solitons in binding them in a soliton molecule. We derive its equilibrium bond length, spring constant, frequency, effective mass, and binding energy of the molecule. We investigate the molecule's stability against perturbations such as reflection from surfaces, scattering by barriers, and collisions with other solitons.

Spectroscopic parameters and rest frequencies of isotopic methylidynium, CH+

Astronomical observations toward Sagittarius B2(M) as well as other sources with APEX have recently suggested that the rest frequency of the J = 1 - 0 transitions of 13CH+ is too low by about 80 MHz. Improved rest frequencies of isotopologs of methylidynium should be derived to support analyses of spectral recording obtained with the ongoing Herschel mission or the upcoming SOFIA. Laboratory electronic spectra of four isotopologs of CH+ have been subjected to one global least-squares fit. Laboratory data for the J = 1 - 0 ground state rotational transitions of CH+, 13CH+, and CD+, which became available during the refereeing process, have been included in the fit as well. An accurate set of spectroscopic parameters has been obtained together with equilibrium bond lengths and accurate rest frequencies for six CH+ isotopologs: CH+, 13CH+, 13CD+, CD+, 14CH+, and CT+. The present data will be useful for the analyses of $Herschel$ or SOFIA observations of methylidynium isotopic species.

Multi-scale simulation of L-selectin–PSGL-1-dependent homotypic leukocyte binding and rupture

L-selectin-PSGL-1-mediated polymorphonuclear (PMN) leukocyte homotypic interactions potentiate the extent of PMN recruitment to endothelial sites of inflammation. Cell-cell adhesion is a complex phenomenon involving the interplay of bond kinetics and hydrodynamics. As a first step, a 3-D computational model based on the Immersed Boundary Method is developed to simulate adhesion-detachment of two PMN cells in quiescent conditions. Our simulations predict that the total number of bonds formed is dictated by the number of available receptors (PSGL-1) when ligands (L-selectin) are in excess, while the excess amount of ligands influences the rate of bond formation. Increasing equilibrium bond length results in a higher number of receptor-ligand bonds due to an increased intercellular contact area. On-rate constants determine the rate of bond formation, while off-rates control the average number of bonds by modulating bond lifetimes. Application of an external pulling force leads to time-dependent on- and off-rates and causes bond rupture. Moreover, the time required for bond rupture in response to an external force is inversely proportional to the applied load and decreases with increasing off-rate.

Study of the Ground State Dissociation of Diatomic Molecular Systems Using State-Specific Multireference Perturbation Theory: A Brillouin-Wigner Scheme.

The size-extensive second-order state-specific (or single root) multireference (MR) perturbation theory (SS-MRPT) in the Brillouin-Wigner (BW) form using Mϕller-Plesset perturbative evaluations of orders up to 2 [termed as SS-MRMPPT(BW)] presents a viable, as well as promising, approach to include both nondynamic and dynamic correlations in the study of the bond-stretching (in multireference/quasidegenerate situations) of molecular species with a manageable cost/accuracy ratio. It combines numerical stability in the presence of an intruder state problem with strict size consistency (when localized orbitals are used). In this paper, the SS-MRMPPT(BW) method has been shown to properly break the bonds (in the ground state) of several diatomic molecules (such as F2, Cl2 and Br2, and BH) that have posed a severe challenge to any many-body theoretical approach due to the presence of quasidegeneracy of varying degrees in the ground state. A comparison of the resulting potentials with the various theoretical results reveals that the method represents a valuable tool that is capable of properly accounting even for very strong quasidegeneracies, while also performing well in nondegenerate situations. In this work, we have also calculated spectroscopic constants (such as equilibrium bond lengths, vibrational frequencies, and dissociation energies) of the ground state of these molecular systems. The SS-MRMPPT spectroscopic constants are compared with the most accurate available ab initio calculations and other theoretical estimates of previous works to calibrate the efficacy of the method. For the sake of completeness, we also compare the computed spectroscopic constants with the experimental observations. The accuracy of computed spectroscopic parameters appears to be rather consistent over a multitude of systems for various basis sets. The SS-MRMPPT enables quantitatively accurate and computationally affordable analysis of potential energy surfaces and spectroscopic constants of various multireference systems in the ground state. It is particularly visible for spectroscopic parameters and nonparallelism error (NPE) calculations. The calculations further reveal that the SS-MRMPPT(BW) method compared to its Rayleigh-Schrödinger counterpart [SS-MRMPPT(RS)] provides a more accurate and consistent solution for the whole dissociation path and spectroscopic constants.

Applications of Screened Hybrid Density Functionals with Empirical Dispersion Corrections to Rare Gas Dimers and Solids.

An empirical dispersion correction is added to the range-separated hybrid density functionals HSE and HISS via parametrization versus a standard test bed of weakly bound complexes. The performance of the resulting HSE-D and HISS-D functionals is evaluated by calculating the equilibrium bond length, harmonic frequency, and dissociation energy for a number of rare gas dimers, and the lattice constants, band gaps, and sublimation energies of the rare gas solids. Both HSE-D and HISS-D are shown to provide accurate results for both molecules and extended systems, suggesting that the combination of a screened hybrid functional with an empirical dispersion correction provides an accurate, widely applicable method for use in solid-state and gas-phase electronic structure theory.

Improved version of a local contracted configuration interaction of singles and doubles with partial inclusion of triples and quadruples

A local contracted single and double configuration interaction (LC-CISD) method, which introduces contracted singly and doubly excited vectors within the framework of bond functions, has been recently proposed [P. Reinhardt et al., J. Chem. Phys. 129, 164106 (2008)]. The present work improves this method by introducing a coupled-electron pair approximation (CEPA-3) dressing and by incorporating the leading part of linked effects of triples (T) and quadruples (Q) through a series of local four-electron full CI calculations. Two different ways have been adopted to incorporate this linked TQ effect. One consists of dressing the first column/line of the whole LC-CISD matrix. The other one introduces an additional contracted wave function responsible for the linked effect for each bond pair. The present LC-CEPA-3+TQ treatments have been applied to the evaluation of equilibrium bond lengths and harmonic frequencies of diatomic molecules (HF, BF, CuH, N(2), F(2), and Cl(2)) and single bond breaking in HF, CH(4), ClCH(3), ClSiH(3), n-butane, and F(2) molecules, symmetrical stretching of the two OH bonds in a water molecule, and symmetrical expansion of a triangular Be(3) cluster. The results show that the performance of the LC-CEPA-3+TQs compares favorably with coupled-cluster singles and doubles (CCSD) and CCSD(T) methods, presenting similar behaviors around equilibrium and better ones for stretched geometries. The LC-CEPA-3 method is strictly separable, and the size consistency error of our treatment of triples and quadruples is extremely small. The strict separability can be further achieved by dressing the doubly excited bond functions with the linked TQ effect. The efficiency of truncations on the bielectronic integrals has also been tested.

Molecular electric dipole moments using the GVVPT2 variant of multireference perturbation theory

A Lagrangian approach for electric dipoles within second order Generalized Van Vleck Perturbation Theory (GVVPT2) is presented. The Lagrangian approach for this response property requires that only one, perturbation-independent, set of simultaneous equations needs to be solved. The presented formulation is demonstrated numerically on several well studied molecules at their equilibrium bond lengths and on the complete potential energy curves of the ground and first excited states of LiH. Numerical corroboration of the expected continuity for molecular properties for the GVVPT2 method is observed. It is seen that the GVVPT2 electric dipoles are in good agreement with experiment and with other high accuracy theoretical methods.

Gas-Phase Structures of Iron Trihalides: A Computational Study of all Iron Trihalides and an Electron Diffraction Study of Iron Trichloride

The molecular structures of the monomers and dimers of all iron trihalides, FeF(3), FeCl(3), FeBr(3), and FeI(3), were determined by computations, and the structure of iron trichloride monomers and dimers was determined also by gas-phase electron diffraction. The thermal-average bond length, r(g), of FeCl(3) is 2.136(5) A, and the estimated equilibrium bond length from experiment, 2.122(6) A, is in excellent agreement with the computed value. Vibrational and thermodynamic properties have also been calculated for all species. The stability of iron trihalides decreases toward the iodide; neither the bromide nor the iodide can be evaporated without decomposition. The structures of isomers of trimers and tetramers for iron trichloride have also been calculated. The connection between the gas-phase and crystal-phase structures and the exceptional stability of the dimer is discussed.

Investigations on molecular structure and analytic potential energy function of the AsH(X3Σ-) and AsH2(C2v，X2B1) radicals

The CCSD(T) theory in combination with the cc-pV5Z basis set is used to determine the equilibrium geometry，dissociation energy and vibrational frequencies of AsH2(C2v，X2B1) radical. By comparison，excellent agreement can be found between the present results and the experiments. The values obtained at present are of 01508 nm for the equilibrium bond length RAs-H，912231° for the bond angle ∠HAsH，28795 eV for the dissociation energy De(HAs-H) and 10133361 cm-1，22251347 cm-1 and 22337565 cm-1 for the vibrational frequencies ν1(a1)，ν2(a1) and ν3(a1)，respectively. The equilibrium geometry，harmonic frequency and potential energy curve of the AsH(X3Σ-) radical are calculated at the CCSD(T)/cc-pV5Z level of theory. The ab initio results are fitted to the Murrell-Sorbie function with the least-square method. The spectroscopic parameters are in excellent agreement with the experiments. The analytic potential energy function of the AsH2(C2v，X2B1) radical is derived by using the many-body expansion theory. This function correctly describes the configuration and dissociation energy of the AsH2(C2v，X2B1) radical. Two symmetrical saddle points have been found at (0160 nm，0296 nm) and (0296 nm，0160 nm)，respectively. And the barrier height is equal to 01512×4184 kJ/mol.

Curious matrix effects: a computational, electron diffraction, and vibrational spectroscopic study of dysprosium triiodide

The molecular and electronic structure of dysprosium triiodide, DyI(3), and its dimer, Dy(2)I(6), was determined by high level computations, gas-phase electron diffraction, and gas-phase infrared and matrix-isolation infrared and Raman spectroscopy. The free monomeric molecule is planar from all methods with an equilibrium bond length of 2.808(9) A; the thermal average bond length from electron diffraction is 2.828(6) A. The molecule forms complexes in the matrix-isolation experiments causing pyramidalisation of planar monomeric molecules. The likelihood of having both pyramidal and planar DyI(3) molecules in the matrix is discussed in order to explain certain features of the spectra. Our computations suggest that the dimer geometry depends on the occupation of the partially filled 4f orbitals. As this is the third molecule in the dysprosium trihalide series studied, trends in their electronic and molecular structures are presented and discussed.

Multi-reference configuration interaction of the ground and low-lying excited states of LiC

The potential energy curves (PECs) for the ground electronic state X4Σ-and five low-lying excited electronic states (a2Π, b2Δ, c2Σ-, d2Σ+, A4Π) of LiC have been calculated using the multiconfiguration reference configuration interaction method including Davidson correction (MRCI+Q). And PECs were fitted to analytical Murrell-Sorbie potential function to deduce the spectroscopic parameters of equilibrium bond length Re, rotation coupling constant ωe, anharmonic constant ωeχe, equilibrium rotation constant Be and vibration-rotation coupling constant αe. Those values were also compared with the other results currently available. By solving the radial Schrdinger equation of nuclear motion, the vibration levels, inertial rotation constant and six centrifugal distortion constants (Dν, Hν, Lν, Mν,Nν,and Oν) are reported for the first time.