Valence Triple-zeta Basis Research Articles

The equilibrium geometries of heptatriynylidene, cyclohepta-1,2,3,4-tetraen-6-yne, and heptahexaenylidene

The equilibrium geometries of heptatriynylidene (1), cyclohepta-1,2,3,4-tetraen-6-yne (2), and heptahexaenylidene (3) have been theoretically investigated at various level of theories. The methods employed are Møller–Plesset perturbation level of theory until second-order, coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triple excitations [CCSD(T)]. Correlation consistent polarized valence double and triple zeta (cc-pVXZ; X=D and T) basis sets are used in all calculations, which are compatible with the frozen-core approximation entreated in this study. The relative energies of the ground triplet electronic state (X∼3Σg-) of 1 – the most stable isomer of C7H2 – to the ground singlet electronic states of 2 (X∼1A1) and 3 (X∼1A1) have also been estimated at different levels. With zero-point vibrational energy corrections, 2 and 3 are found to lie ∼12.27 and ∼20.62kcalmol−1, respectively, above 1 at the highest level of theory (CCSD(T)/cc-pVTZ). While 1 and 3 are observed in the laboratory, 2 is a hypothetical molecule hitherto. Since the optimal geometry of 2 suggests the presence of biradical character, the singlet–triplet (X∼1A1–3B1) energy gap for isomer 2 was also calculated at various levels. The ab initio data presented here may be useful for the laboratory detection of 2 and astronomical detection of2and3.

Ab initio adiabatic and quasidiabatic potential energy surfaces of H++ CN system

We present restricted geometry (collinear and perpendicular approaches of proton) ab initio three dimensional potential energy surfaces for H++ CN system. The calculations were performed at the internally contracted multi-reference configuration interaction level of theory using Dunning’s correlation consistent polarized valence triple zeta basis set. Adiabatic and quasidiabatic surfaces have been computed for the ground and the first excited electronic states. Nonadiabatic effects arising from radial coupling have been analyzed in terms of nonadiabatic coupling matrix elements and coupling potentials. We present ab initio three dimensional potential energy surfaces for H+ + CN system. The calculations were performed at the internally contracted multi-reference configuration interaction (icMRCI) level of theory using Dunning’s correlation consistent polarized valence triple zeta (cc-pVTZ) basis set. Adiabatic and quasidiabatic surfaces were computed for ground and first excited electronic states for the collinear and perpendicular approaches of H+. Nonadiabatic effects arising from radial coupling have been analyzed in terms of nonadiabatic coupling matrix elements (NACME) and coupling potentials.

Rotational excitation of NCO induced by collision with Helium at low temperatures

We report the cross sections and the transitional rates of the first 11 rotational levels of the NCO induced by collision with He at low temperatures. For this purpose, we have calculated the potential energy surface (PES), i.e transitional structure between the NCO(X1Σ) and He() by using the coupled cluster singles and doubles perturbed by triple excitations (CCSD(T)). The augmented correlation consistent polarized valence triple zeta (AVTZ) basis set to which we have associated the mid-bond functions, between the molecule and the projectile for a better description of the van der Waals interaction, was used. The PES was interpolated by the Legendre polynomials, analytically fitted, then used for the evaluation of the integral state-to-state rotational transitions cross sections in the close-coupling approach. The rate coefficients were subsequently computed for low kinetic temperature (T 150K).

Density functional theoretical study on the preferential selectivity of macrocyclic dicyclohexano-18-crown-6 for Sr+2 ion over Th+4 ion during extraction from an aqueous phase to organic phases with different dielectric constants

The preferential selectivity of dicyclohexano-18-crown-6 (DCH18C6) for bivalent Sr(+2) ion over tetravalent Th(+4) ion was investigated using generalized gradient approximated (GGA) BP86 and the hybrid B3LYP density functional, employing split valence plus polarization (SV(P)) and triple-zeta valence plus polarization (TZVP) basis sets in conjunction with the COSMO (conductor-like screening model) solvation approach. The calculated theoretical selectivity of DCH18C6 for Sr(+2) ion over Th(+4) ion was found to be in accord with the selectivity for Sr(+2) ion over Th(+4) ion observed when performing liquid-liquid extraction experiments in different organic solvents. While 1:1(M:L) stoichiometric complexation reactions can be used to predict the preferential selectivity of Sr(2+) ion over Th(4+) ion, the results obtained are not consistent with the experimental results observed upon increasing the dielectric constant of the solvent. The calculated theoretical gas-phase data for the free energy of complexation, ∆G, fail to explain the selectivity for Sr(+2) ion over Th(+4) ion. However, when 1:2 (M:L) stoichiometric complexation reactions (reported in previous X-ray crystallography studies) are considered, correct and consistent results for the selectivity for Sr(+2) ion over a wide range of dielectric constants are predicted. The distribution constant for Sr(2+) and Th(4+) ions was found to gradually increase with increasing dielectric constant of the organic solvent, and was found to be highest in nitrobenzene. The selectivity data calculated from ∆∆G ext are in excellent agreement with the results obtained from solvent extraction experiments.

Structure and energetics of small iron clusters

Electronic properties of Fe(2-10) clusters and their ions are described by an all-electron ab initio density functional theory computational analysis using the Handy's OPTX exchange and the gradient-corrected correlation functional of Perdew, Burke and Ernzerhof with a triple-zeta valence basis set plus polarization functions. Ground state structures, magnetic moments, dissociation energies, binding energies, IR vibrational spectra, vertical and adiabatic ionization energies, and electron affinities are reported. Two possible states for Fe(2) which are separated by 81.54 meV are described as possible Fe(2), while the septet (ground state) yields an accurate bond distance (error of 0.02Å); the nonet yields a precise vibrational frequency (error of 10.1cm(-1)). Fe(2) binding energy (0.05 eV/atom error) more closely resembles experimental data than any other previously reported computational methods. In addition, the Fe(6) is found to be the most stable cluster within our set being analyzed.

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.

New vibrational assignments for the ν 1 to ν 17 vibrational modes of aziridine and first analysis of the high-resolution infrared spectrum of aziridine between 720 and 1050 cm−1

Fourier transform spectra of aziridine (C2H4NH) were recorded at high resolution (0.002 or 0.003 cm−1) in the 600–1750 and 1750–4000 cm−1 regions, using a Bruker IFS125HR (an upgraded version of the IFS120HR) spectrometer, located at the LISA facility in Creteil. In parallel, the harmonic force field of aziridine was evaluated analytically at the optimized geometry with second-order Møller–Plesset perturbation theory (MP2) together with the correlation-consistent polarized valence triple zeta basis sets cc-pVTZ. These ab initio predictions were used to perform consistent vibrational assignments for the ν 1 to ν 17 fundamental bands of aziridine observed in the infrared spectra recorded during this study. Finally, a first detailed rotational assignment was performed for two B-type bands located at 772.3571 cm−1 (ν 10, CH2 rock) and 997.1592 cm−1 (ν 8, NH bend) and for an A-type band located at 904.0429 cm−1 (ν 17, ring deform). We noticed that the ν 10 band is weakly perturbed, presumably because the v 10 = 1 rotational levels are coupled with those of the v 18 = 1 dark band located around 817 cm−1 through B-type and C-type Coriolis resonances.

Study of vibrational spectra and their assignments for phenylphosphonic and phenylthiophosphonic acid and comparison to experiments

The structures and conformational stabilities of phenylphosphonic and phenylthiophosphonic acids are investigated using calculations mostly at the DFT/6-311G** level and ab initio ones at the MP2/6-311G** level (no frequency calculations in the latter case), because we know from our previous results that the addition of diffuse functions to a valence triple zeta basis with polarization functions might lead to an unbalanced basis set. Further, the experience tells that for large energy differences between conformers, DFT works very well. From the calculations the molecules are predicted to exist in a conformational equilibrium consisting of two non (near)-planar conformers that are identical by symmetry. Interestingly, in the internal rotation potential functions the planar conformer appears to be a stable minimum (also optimization converges to planar), however the vibrational frequencies were computed and the planar conformer exhibited an imaginary one, indicating that it is a maximum with respect to one of the internal coordinates. Only optimization without any restrictions and starting from a non (near)-planar structure converged to a real minimum with a non (near)-planar geometry. In the minimum structure, vibrational infrared and Raman spectra are calculated and those for phenylphosphonic acid are compared to experimental ones, showing satisfactory agreement. The rather low intensity of the OH bands in the experimental infrared spectrum (as compared to normal organic acids) indicates rather weak hydrogen bonding with at most dimers present. Normal coordinate calculations are carried out and potential energy distributions are calculated for the molecules in the non (near)-planar conformations providing a complete assignment of the vibrational modes to atomic motions in the molecules. From the rather low rotational barriers we conclude, in agreement with the results from the literature (for other P=O compounds) based on localized orbitals, that conjugation effects are absent — or at least negligible — as compared to electrostatic and steric ones.

Matrix-isolation FT-IR study of (CsBr) n and (CsI) n ( n = 1–3)

The species present in the vapours of CsBr and CsI have been isolated in krypton and xenon matrices and were investigated by FT-IR spectroscopy in the range of 180–30 cm −1. The recorded spectra revealed the presence of substantial amounts of dimer beside the alkali halide monomers. The assignment of the bands and characterization of the fundamentals was carried out on the basis of DFT quantum chemical calculations. The applied B3P86 exchange-correlation functional in conjunction with the Stuttgart–Cologne relativistic effective core potentials and polarized triple-zeta valence basis set reproduced the accurate experimental monomer Cs–Br and Cs–I bond distances within 0.001 Å, and the harmonic stretching frequency within 1.1 cm −1. Based on calculations at this level we report reliable geometrical parameters and fundamental frequencies for the dimer and trimer species (CsBr) n and (CsI) n . Utilizing the computed data we propose the identification of the E′ asymmetric stretching mode of the trimer (CsI) 3 trapped in a Xe matrix and that of (CsBr) 3 in Kr and Xe matrices.

Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon, and silicon

The isoelectronic series of Be, Ne, and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy, various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans' theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single-particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple, and quadruple zeta basis sets.

Quantum dynamics of vibrational excitations and vibrational charge transfer processes in H+ + O2 collisions at collision energy 23 eV

Quantum mechanical study of vibrational state-resolved differential cross sections and transition probabilities for both the elastic/inelastic and the charge transfer processes have been carried out in the H+ + O2 collisions at the experimental collision energy of 23 eV. The quantum dynamics has been performed within the vibrational close-coupling rotational infinite-order sudden approximation framework employing our newly obtained quasi-diabatic potential energy surfaces corresponding to the ground and the first excited electronic states which have been computed using ab initio procedures and Dunning’s correlation consistent-polarized valence triple zeta basis set at the multireference configuration interaction level of accuracy. The present theoretical results for elastic/inelastic processes provide an overall agreement with the available state-selected experimental data, whereas the results for the charge transfer channel show some variance in comparison with those of experiments and are similar to the earlier theoretical results obtained using model effective potential based on projected valence bond method and using semi-empirical diatomics-in-molecules potential. The possible reason for discrepancies and the likely ways to improve the results are discussed in terms of the inclusion of higher excited electronic states into the dynamics calculation.

Full-dimensional ab initio potential energy surface and vibrational configuration interaction calculations for vinyl

The potential energy landscape and two permutationally invariant, full-dimensional ab initio-based potential energy surfaces (PESs) for the doublet vinyl radical, C(2)H(3), are described. The first of the two surfaces, denoted as PES/S, describes the equivalent CH(2)CH global minimum and the saddle point separating them, planar and nonplanar H-atom migration saddle points, a methylcarbyne local minimum that is due to a Jahn-Teller conical intersection, and the saddle point connecting it with the global minimum. The second PES, denoted PES/D, contains all stationary points of PES/S and in addition describes dissociation to C(2)H(2)+H fragments, including the saddle point to dissociation along a least-energy path. The surfaces are least-squares fits to electronic energies obtained with use of the spin-restricted coupled cluster singles and doubles with perturbative treatment of triples method and augmented correlation consistent polarized valence triple zeta basis sets, using permutationally invariant polynomials in "Morse variables" and a many-body expansion. PES/S is a fit to roughly 34,000 and PES/D to roughly 50,000 electronic structure energies. PES/S is used in full-dimensional, vibrational configuration interaction calculations of the vinyl zero-point energy and fundamental vibrational energies, which are compared to recent experiments.

Factorial design analysis of the effects of wave function modifications on calculated HC and CC stretching frequencies in H 2C [dbnd]CHX and HC [tbnd]CX

Two-level factorial designs (FD) have been used to determine the effects of wave function modifications on calculated CH and CC harmonic stretching frequencies of the H 2C CHX and HC CX molecules with X = H, CH 3, F, Cl and CN. These modifications were treated at two levels, which consists in: (I) using either a double- or a triple-zeta valence basis set; (II) including or not diffuse functions in basis set, (III) including or not polarization functions in basis set, and (IV) performing a calculation with or without electron correlation beyond the Hartree–Fock level, i.e., MP2 or B3LYP. Our results have shown that valence (Val), diffuse (Dif), polarization (Pol) and electron correlation (Corr) main effects as well as the Pol/Corr second-order interaction effect are significant to build factorial models for these vibrational modes. When valence and diffuse functions are introduced in the basis set, the calculated HC and CC stretching frequencies are decreased in both the HC CX and H 2C CHX molecules. As expected, by far the correlation principal effect is the most important on the frequency values. This effect provokes a decrease of −281.4 cm −1 and −153.3 cm −1 in the C C and C C vibrational frequencies, respectively, using the MP2 calculations, whereas this decrease for the H C oscillator is −156.1 cm −1 and −116.1 cm −1 in HC CX and H 2C CHX, respectively. This same effect produces an important Pol/Corr interaction effect on HC and CC stretching frequencies, increasing their values by +45.3 cm −1 and +18.4 cm −1 in HC CX, respectively, whereas their corresponding values in H 2C CHX are +43.9 cm −1 and +11.0 cm −1, respectively. Finally, algebraic models were then established to explain how calculated HC and CC stretching frequencies in HC CX and H 2C CHX depend on the characteristics of the molecular orbital wave functions.

Calculation of the O−H Stretching Vibrational Overtone Spectrum of the Water Dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.

Ab initio potential energy surfaces and nonadiabatic collision dynamics in H++O2 system

The adiabatic potential energy surfaces for the lowest five electronic states of (3)A" symmetry for the H(+)+O(2) collision system have been obtained at the multireference configuration interaction level of accuracy using Dunning's correlation consistent polarized valence triple zeta basis set. The radial nonadiabatic coupling terms and the mixing angle between the lowest two electronic states (1 (3)A" and 2 (3)A"), which adiabatically correlate in the asymptotic limit to H((2)S)+O(2) (+)(X (2)Pi(g)) and H(+)+O(2)(X (3)Sigma(g)(-)), respectively, have been computed using ab initio procedures at the same level of accuracy to yield the corresponding quasidiabatic potential energy matrix. The computed strengths of the vibrational coupling matrix elements reflect the trend observed for inelastic vibrational excitations of O(2) in the experiments at collision energy of 9.5 eV. The quantum dynamics has been preformed on the newly obtained coupled quasidiabatic potential energy surfaces under the vibrational close-coupling rotational infinite-order sudden framework at the experimental collision energy of 9.5 eV. The present theoretical results for vibrational elastic/inelastic excitations of O(2) are in overall good agreement with the available experimental data obtained from the proton energy-loss spectra in molecular beam experiments [F. A. Gianturco et al., J. Phys. B 14, 667 (1981)]. The results for the complementary charge transfer processes are also presented at this collision energy.

Quantum dynamics of inelastic excitations and charge transfer processes in the H++NO collisions

State-resolved differential cross section, integral cross section, average vibrational energy transfer, and the relative transition probability are computed for the H(+)+NO system using our newly obtained ab initio potential energy surfaces (PES) at the multireference configuration interaction level of accuracy employing the correlation consistent polarized valence triple zeta basis set. The quantum dynamics is treated within the vibrational close-coupling rotational infinite-order sudden approximation using the coupled ground state and first excited state ab initio quasidiabatic PES. The computed collision attributes for the inelastic vibrational excitation are compared with the state-to-state scattering data available at E(c.m.)=9.5 eV and E(c.m.)=29.03 eV and are found to be in overall good agreement with those of the experiments. The results for the vibrational charge transfer processes at these collision energies are also presented.

Ab initio potential energy surfaces and nonadiabatic interactions in the H++NO collision system

Ab initio calculations on the H(+)+NO system have been carried out in Jacobi coordinates at the multireference configuration interaction level employing Dunning's correlation-consistent polarized valence triple zeta basis set to analyze the role of low-lying electronic excited states in influencing the collision dynamics relevant to the experimental collision energy range of 9.5-30 eV. The lowest two adiabatic potential energy surfaces, asymptotically correlating to H(+)+NO(X (2)Pi) and H((2)S)+NO(+)(X (1)Sigma(+)), have been obtained. Using ab initio procedures, the (radial) nonadiabatic couplings and the mixing angle between the lowest two electronic states (1 (2)A' and 2 (2)A') have been obtained to yield the corresponding quasidiabatic potential energy matrix. The strengths of the computed vibrational coupling matrix elements reflect a similar trend, as has been observed experimentally in the magnitudes of the state-to-state transition probability for the inelastic vibrational excitations [J. Krutein and F. Linder, J. Chem. Phys. 71, 559 (1979); F. A. Gianturco et al., J. Phys. B 14, 667 (1981)].

Ab initio characterization of XH3 (X = N,P). Part II. Electric, magnetic and spectroscopic properties of ammonia and phosphine

The coupled cluster theory in conjunction with core valence triple and quadruple zeta basis sets has been employed for investigating electric, magnetic and spectroscopic properties of ammonia and phosphine. Namely molecular dipole and quadrupole moments, NMR shielding and spin-rotation constants, as well as spectroscopic properties such as rotational and centrifugal distortion constants as well as harmonic and anharmonic frequencies of NH3 and PH3 have been determined at a high level of accuracy. To obtain parameters directly comparable to experiment, vibrational effects have also been taken into account. In addition, the basis set convergence has been investigated for the molecular dipole moment.

Absence of Conjugation in Vibrational Spectra and Assignments of Dichloro(vinyl)phosphine and Dichloro(phenyl)phosphine Oxides and Sulfides

The structure and conformational stability of dichloro(vinyl)phosphine and dichloro(phenyl)- phosphine oxides and sulfides were investigated using calculations at the DFT/6-311G** and ab initio ones at the MP2/6-311G** level. We know from our previous results that the addition of diffuse functions to a valence triple zeta basis with polarization functions might lead to an unbalanced basis, which performs even worse than the smaller basis without diffuse functions, as it is the case for the 6-311++G** basis set in the Gaussian program. For large energy differences between conformers, DFT works very well, in some cases even better than MP3 or MP4. The vinyl derivatives were predicted to exist in a cis/gauche conformational equilibrium with cis (the PX bond, X being oxygen or sulfur eclipses the vinyl groups) being the predominant conformer at ambient temperature. In the phenyl case case the two planar forms are equivalent minima. The asymmetric potential function for the internal rotation was determined for each of the molecules. The vibrational frequencies were computed and the spectra, where possible, were compared with the experimental ones. Normal coordinate calculations were carried out and potential energy distributions were calculated for the molecules in the cis and gauche conformations (in the vinyl case, planar one for phenyl), providing a complete assignment of the vibrational lines to symmetry coordinates in the molecules. From our results and their analysis we conclude, in agreement with literature results based on localized orbitals, that conjugation effects are absent - or at least negligible - as compared with electrostatic ones in determining the structures of the stable conformers in both the vinyl and the phenyl derivatives. The P-O bond should be a highly polarized triple bond, as confirmed by analysis of Mulliken populations. The polarization turned out to be much less in the sufides due to the much smaller electronegativity of sulfur as compared with oxygen.

Calculations of Polarizabilities and Their Gradients for Electron Energy-Loss Spectroscopy

We illustrate for a set of small hydrocarbons, CH4, C2H4, C3H6 and C3H8, the important role of the electric dipole polarizability tensor and its geometric derivatives in theoretical models of electron energy-loss spectra (EELS). The coupled cluster linear response method together with Sadlej's polarized valence triple zeta basis set of atomic orbitals were used to calculate the polarizabilities and polarizability gradients. Incorporation of these ab initio data into the discrete momentum representation method (DMR) leads to perfect agreement between theory and collision experiments.