Equilibrium Bond Length Research Articles

Modified Rosen-Morse potential-energy model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the generalized Woods-Saxon potential. It is exactly shown that the generalized Woods-Saxon potential and the well-known Rosen-Morse potential are the same empirical potential-energy function for diatomic molecules. Based on the measure of inner-shell radii of two atoms, we propose a modified Rosen-Morse potential-energy model. Evaluation of the average deviations from the experimental data is carried out on six molecules. The modified Rosen-Morse potential is found to be more accurate than the Morse and Rosen-Morse potentials in fitting experimental data for the six molecules examined.

An analytical potential function for stable diatomic molecules

We propose an analytical five-parameter potential function for stable diatomic molecules V(x) = K/x(3) - e(-tx)(a + bx + cx(2)). Here x=r/r(e), where r is the internuclear distance and re the equilibrium bond length. K, t, a, b, c are five parameters of the function, which are obtained from molecular spectroscopic data in terms of known molecular constants

Characterization of the Double Perovskite Ba2BixSc0.2Co1.8–xO6−δ (x = 0.1, 0.2)

The Ba2BixSc0.2Co1.8–xO6−δ (x = 0.1 or 0.2) cubic perovskites are confirmed to be mixed-valent Co3+/Co2+ oxides that, as mixed oxide-ion and electronic conductors, are superior cathode materials for an intermediate-temperature solid oxide fuel cell catalyzing the oxygen-reduction reaction. Neutron powder diffraction for x = 0.2 was used to confirm also that these compounds have the double-perovskite structure Ba2BB′O6−δ at room temperature with B = Co, B′ = Bi0.2Sc0.2Co0.6, δ ≈ 1.3, and a B–O bond length a little longer than the mean B′–O bond length. These data indicate that the room-temperature x = 0.2 phase is Ba2Co2+B′O4.7 with B′ = (Bi5+)0.2(Sc3+)0.2(Co3+)0.6. The presence of Bi5+ was confirmed by comparing the Bi4f core-level X-ray photoelectron spectrum of the x = 0.2 sample with that of BaBiO3. BaCoO3 crystallizes in the 2H hexagonal polytype as a result of t ≡ (A–O)/[√2(B–O)] > 1, where A–O and B–O are the equilibrium bond lengths of an ABO3 perovskite. Substitution of Bi and Sc for Co as well as the incorporation of oxygen vacancies increases the mean B–O bond length to reduce t > 1 to where cubic stacking of close-packed BaO3 planes is energetically favored over hexagonal stacking that introduces large B-cation Coulombic repulsions across a shared octahedral-site face. Cooperative oxygen displacements that create larger B–O than B′–O mean bond length are characteristic of oxide ions in a cubic perovskite with geometric tolerance factor t > 1 as illustrated by ferroelectric BaTiO3. Disordering of the double-perovskite oxide-ion displacements occurs over the range 350–400 °C; long-range, frustrated magnetic order occurs below a Tc ≈ 35 K. X-ray absorption spectroscopy measurements show the absence of low-spin Co3+ at room temperature, and the rate-limiting step of the oxygen-reduction reaction on these oxides acting as cathodes of a solid oxide fuel cell is shown to be electron transfer from the oxide to an adsorbed O2, which we conjecture occurs at surface intermediate-spin Co3+ ions.

Fourier transform emission spectra of the A2Π → X2Σ+ and B2Σ+ → X2Σ+ transitions of CaD

Emission spectra of the A2Π→X2Σ+ and B2Σ+→X2Σ+ transitions of CaD were produced in a discharge-furnace emission source and recorded with a high resolution Fourier transform spectrometer. The Δv=0 and Δv=−1 sequences up to v′=3 of the A2Π state and v′=2 of the B2Σ+ state have been observed and rotationally analyzed. Empirical band constants and Dunham-type constants were determined for all electronic states using N2 Hamiltonians. The equilibrium constants Te, ωe and ωexe were determined to be 14407.604(2), 957.330(4) and 10.415(2)cm−1 for the A2Π state, and 15751.570(2), 925.840(4) and 12.417(2)cm−1 for the B2Σ+ state, respectively. The equilibrium bond lengths (re) of the A2Π and B2Σ+ states are 1.977495(3) and 1.963467(6)Å, respectively.

LIF spectroscopy of ScP

The electronic transition 1Σ+–X1Σ+ of scandium monophosphide (ScP) has been observed around 11900cm−1 using laser induced fluorescence spectroscopy. This is the first observation of the ScP spectrum. The spectrum covering ten vibronic bands with v up to 4 was assigned and analyzed. Molecular constants for the vibronic levels involved were obtained by least-squares fitting of the measured line positions. The equilibrium bond length in the upper 1Σ+ state was found to be 2.1590Å, which was slightly shorter than that of 2.1995Å in the X1Σ+ state, in agreement with results from recent calculations.

High-Resolution Spectroscopy and Structure of Osmium Tetroxide. A Benchmark Study on 192OsO4

Osmium tetroxide (OsO(4)) is a heavy tetrahedral molecule that constitutes a benchmark for quantum chemistry calculations. Its favorable spin statistics (due to the zero nuclear spin of oxygen atoms) is such that only A(1) and A(2) (T(d) symmetry) rovibrational levels are allowed, leading to a dense but quite easily resolvable spectrum. We reinvestigate here the ν(1)/ν(3) stretching fundamental (940-980 cm(-1)) dyad region and perform new assignments and effective Hamiltonian parameter fits for the main isotopologue ((192)OsO(4)). We also investigate the ν(2)/ν(4) bending fundamental dyad (300-360 cm(-1)) for the first time and perform a preliminary analysis. New experimental data have been obtained at 0.001 cm(-1) resolution using an isotopically pure (192)OsO(4) sample and the Synchrotron SOLEIL light source. Assignments and analyses were performed using SPVIEW and XTDS software, respectively. We provide precise effective Hamiltonian parameters, including the band centers for all of the fundamental levels and rotational constants for the ground state and for all four fundamental levels. We discuss isotopic shifts, estimate the equilibrium rotational constant B(e), and derive a precise value for the equilibrium bond length r(e)(Os-O) = 1.70919(16) Å. We also performed experiments to measure for the first time the IR integrated intensities for the ν(2)/ν(4) bending fundamental dyad. These new data are compared to current ab initio predictions.

First principles study of half-metallic ferromagnetism in (N, P, As and Sb) doped alkaline-earth sulfides

Structural, electronic and magnetic properties of AeS0.875X0.125 (Ae=Mg, Ca and Sr; X=N, P, As and Sb) are investigated using density functional theory within the local spin density approximation and also generalized gradient approximation for the electronic exchange and correlation. The total energy calculation reveals that group V elements as dopants can induce stable ferromagnetic state in alkaline-earth sulfides. The variation of ground state properties such as equilibrium lattice constant, bulk modulus and bond length against atomic size of the dopants were investigated. The possibility of half-metallic ferromagnetism in AeS0.875X0.125 (Ae=Mg, Ca and Sr; X=N, P, As and Sb) were analyzed by electronic band structure and density of states calculations. The half-metallic gap, exchange energy, total and partial magnetic moments were calculated.

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves (PECs) for the ground state (X2Σ+) and the four excited electronic states (A2Π, B2Π, C2Σ+, 4Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction (MRCI) approach in combination with the aug-cc-pVTZ basis sets. The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm, and the equilibrium bond length Re and the vertical excited energy Te are determined directly. It is evident that the X2Σ+, A2Π, B2Π, C2Σ+ states are bound and 4Π is a repulsive excited state. With the potentials, all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero (J = 0) by numerically solving the radial Schrödinger equation of nuclear motion. Then the spectroscopic data are obtained including the rotation coupling constant ωe, the anharmonic constant ωexe, the equilibrium rotation constant Be, and the vibration-rotation coupling constant αe. These values are compared with the theoretical and experimental results currently available, showing that they are in agreement with each other.

Electronic states and rovibrational spectroscopy of the HAlF+ and HAlCl+ cations

Ab initio calculations have been performed to investigate the nature of the low-lying electronic states and the rovibrational energy levels of the electronic ground state of HAlF+ and HAlCl+. The one-dimensional cuts of the low-lying states of both cations have been investigated at the complete active space self-consistent field level, revealing the single-configuration nature of the electronic ground states. Using explicitly correlated coupled-cluster methodology and core-valence basis sets, the three-dimensional potential energy surfaces of both species have then been generated, and the rovibrational energy levels were computed variationally. The analysis of the results reveals the similar nature of the Al–H bond in both species, according to their equilibrium bond lengths and to the Al–H stretching mode frequencies. The rovibrational energy levels of the deuterated isotopologues are also presented.

Resilience of gas-phase anharmonicity in the vibrational response of adsorbed carbon monoxide and breakdown under electrical conditions

In surface catalysis, the adsorption of carbon monoxide on transition-metal electrodes represents the prototype of strong chemisorption. Notwithstanding significant changes in the molecular orbitals of adsorbed CO, spectroscopic experiments highlight a close correlation between the adsorbate stretching frequency and equilibrium bond length for a wide range of adsorption geometries and substrate compositions. In this work, we study the origins of this correlation, commonly known as Badger's rule, by deconvoluting and examining contributions from the adsorption environment to the intramolecular potential using first-principles calculations. Noting that intramolecular anharmonicity is preserved upon CO chemisorption, we show that Badger's rule for adsorbed CO can be expressed solely in terms of the tabulated Herzberg spectroscopic constants of isolated CO. Moreover, although it had been previously established using finite-cluster models that Badger's rule is not affected by electrical conditions, we find here that Badger's rule breaks down when the electrified surface is represented as a periodic slab. Examining this breakdown in terms of anharmonic contributions from the effective surface charge reveals limitations of conventional finite-cluster models in describing electrical conditions at metal electrodes.

Improved expressions for the Schiöberg potential energy models for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for both versions of the Schiöberg potential energy function. Both versions of the Schiöberg potential function are the Rosen–Morse potential function and Manning–Rosen potential functions. By choosing the experimental values of the dissociation energy, equilibrium bond length and equilibrium harmonic vibrational frequency as inputs, we calculate the average deviations of the energies calculated with the potential model from the experimental data for five diatomic molecules, and find that no one of six three-parameter empirical potential energy functions is superior to the other potentials in fitting experimental data for all molecules examined.

Density functional theory study of yttrium monohalides

The molecular properties of the ground state and some low-lying excited states of the yttrium monohalides, YX (X = F, Cl, Br, and I), have been calculated using the B3P86 method of density functional theory (DFT). For each state, the equilibrium bond lengths of re , the harmonic vibrational frequencies of ωe , the dissociation energies of D0 , the term values of Te , the dipole moments of μ, for all the yttrium monohalides were obtained analytically and compared with the experimental and other theoretical values. Compared with the experimental results, the hybrid density functional B3P86 is superior to or comparable with the other theoretical results and predicts well all the spectroscopic parameters such as equilibrium bond lengths and the harmonic vibrational frequencies, but underestimates the term values. By comparing the computed results for B3P86 and CCSD(T), a reasonable explanation has been given for the discrepancy between the computed and experimental term values of YX. In addition, the effect of the halogens on the spectroscopic parameters for the group of YX has been discussed with the help of the molecular orbital diagram.

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.

Helium aggregates doped with alkali dimer impurities: A finite temperature study of [formula omitted] complexes

A path integral Monte Carlo method has been used to study small (4He)N–Rb2(3Σu+) complexes at low temperatures. We focus our investigation on the range 1K⩽T⩽2K for aggregates of different sizes containing between 10 and 40 helium atoms. The extremely weak He–Rb2 interaction, with a shallower potential depth and a longer equilibrium bond length than in the case of the He–He interaction, favors the preference of the alkali molecular dopant to reside on the helium droplet surface. In spite of the slight perturbation introduced by the rubidium dimer, it serves like a glue for the helium host that, at a given temperature, would not exist as a pure aggregate without the presence of the dopant molecule. It is found that the stability of the clusters increases with the number of He atoms surrounding the Rb2 dimer.

State-specific complete active space multireference Møller–Plesset perturbation approach for multireference situations: illustrating the bond breaking in hydrogen halides

Assessment of the complete active space-based state-specific multireference Moller–Plesset perturbation theory, SS-MRMPPT, has been performed on the ground states of HX (X = F, Cl, and Br) systems through the computation of potential energy surface (PES) and spectroscopic constants (such as equilibrium bond lengths, rotational constants, centrifugal distortion constants, vibrational frequencies, anharmonicity constants, and dissociation energies that are closely related to the shape and accuracy of the energy surfaces) extracted from the computed PES. The SS-MRMPPT (involves multiple amplitude sets to parametrize the exact wavefunction) approach isolates one of the several states provided by an effective Hamiltonian in an attempt to avert intruder states in size-extensive manner and hence it forms the basis of a robust approach to the electron correlation problem in cases where a multireference formalism is required. The absence of intruder problem makes SS-MRMPPT an interesting choice for the calculation of the dissociation energy surface(s). The performance of the method has been judged by comparing the results with calculations provided by current generation ab initio methods (multireference or single-reference methods) and we found, in general, a very good accordance between them which clearly demonstrates the usefulness of the SS-MRMPPT method.

Equivalence of the three empirical potential energy models for diatomic molecules

It is found that the Manning–Rosen potential, Schiöberg potential and Deng–Fan potential are the same solvable empirical potential energy function for diatomic molecules. We calculate the anharmonicity ωexe and vibrational rotational coupling parameter αe for 16 molecules by choosing the experimental values of the dissociation energy De, equilibrium bond length re and vibrational frequency ωe as inputs. The results show that the Manning–Rosen potential, Deng–Fan potential and Schiöberg potential are not better than the traditional Morse potential.

Relativistic coupled cluster calculations of the electronic structure of KrH+, XeH+ and RnH+

Potential energy curves of NgH+ cations (Ng = Kr, Xe, Rn) were obtained by using four-component relativistic CCSD(T) coupled cluster calculations. Dissociation energies, equilibrium bond lengths, electronic properties, such as dipole moments and electric field gradients at the nuclei, and the related spectroscopic parameters of the electronic ground state have been determined. The results obtained for KrH+ and XeH+ are in good agreement with available experimental data, while those for RnH+ have been determined for the first time at this level of theory.

Can orbital-free density functional theory simulate molecules?

Orbital-free density functional theory (OFDFT), with its attractive linearly scaling computation cost and low prefactor, is one of the most powerful first principles methods for simulating large systems (~10(4)-10(6) atoms). However, approximating the electron kinetic energy with density functionals limits the accuracy and generality of OFDFT compared to Kohn-Sham density functional theory (KSDFT). In this work, we test whether the Huang-Carter (HC) kinetic energy density functional (KEDF), which contains the physics to properly describe covalently bonded semiconductor materials, can also be used to describe covalent bonds in molecules. In particular, we calculate a variety of homonuclear diatomic molecules with the HC functional within OFDFT. The OFDFT bond dissociation energy, equilibrium bond length, and vibrational frequency of these dimers are in remarkably good agreement with benchmark KSDFT results, given the lack of orbitals in the calculation. We vary the two parameters λ (controlling the reduced density gradient contribution to the nonlocal kernel) and β (the exponent of the density in the nonlocal term) present in the HC KEDF and find that the optimal λ correlates with the magnitude of the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap. Although the HC KEDF represents a significant improvement over previous KEDFs in describing covalent systems, deficiencies still exist. Despite the similar overall shape of the KSDFT and OFDFT ground state electron densities, the electron density within the bonding region is still quite different. Furthermore, OFDFT is not yet able to give reasonable description of magnetic states. The energy orderings of the triplet and singlet states of Si(2) and Al family dimers are not consistent with KSDFT or experimental results and the spin polarization distributions also differ widely between the two theories.

Theoretical investigation for spectroscopic constants of ground-state alkaline-earth dimers with high accuracy

In this work, we provide highly accurate theoretical estimates for spectroscopic constants of the ground-state alkaline-earth dimers (Ca2, Sr2, and Ba2). Electron correlation energies are calculated with coupled-cluster method at the single, double, and noniterative triple excitations [CCSD(T)] level, and the effects of full triples as well as quadruple excitations are also taken into account at the CCSDT and the CCSDT(Q) level. Our results demonstrate that high-order electron correlation is important to achieve results with high accuracy. We also find that results for Ca2 with counterpoise corrections, which are designed to eliminate the basis set superposition error, deviate further away from those at the complete basis set limit than the uncorrected ones. The calculated binding energies and equilibrium bond lengths for Ca2 and Sr2 are in excellent agreement with recent experimental data. On the other hand, our results for Ba2 are quite different from previous theoretical data, and there is no available experimental equilibrium bond length and binding energy for calibration. Based on the performance of the adopted approach for Ca2 and Sr2, our results should be more reliable and could be helpful for future investigations.

Equilibrium CO bond lengths

Based on a sample of 38 molecules, 47 accurate equilibrium CO bond lengths have been collected and analyzed. These ultimate experimental (reEX), semiexperimental (reSE), and Born–Oppenheimer (reBO) equilibrium structures are compared to reBO estimates from two lower-level techniques of electronic structure theory, MP2(FC)/cc-pVQZ and B3LYP/6-311+G(3df,2pd). A linear relationship is found between the best equilibrium bond lengths and their MP2 or B3LYP estimates. These (and similar) linear relationships permit to estimate the CO bond length with an accuracy of 0.002Å within the full range of 1.10–1.43Å, corresponding to single, double, and triple CO bonds, for a large number of molecules. The variation of the CO bond length is qualitatively explained using the Atoms in Molecules method. In particular, a nice correlation is found between the CO bond length and the bond critical point density and it appears that the CO bond is at the same time covalent and ionic. Conditions which permit the computation of an accurate ab initio Born–Oppenheimer equilibrium structure are discussed. In particular, the core–core and core–valence correlation is investigated and it is shown to roughly increase with the bond length.