Basis Set Calculations Research Articles

Quantum chemical calculations and X-ray crystallographic studies of cis-dioxomolybdenum(VI) Schiff base complex

Treatment of the Schiff base 2-((E)-(2-hydroxy propylimino)methyl)phenol with MoO2(acac)2 in dry methanol gave the mononuclear complex (methanol{6-[(2-oxidopropyl)iminometh-yl]phenolato}dioxidomolybdenum(VI), which was characterized by X-ray crystal analysis, and it has monoclinic space group p21/c, and a=10.330(17)Å, b=9.397(15)Å, c=13.695(2)Å, V=1252.1(3)Å3, and Z=4. B3LYP theoretical method with DZP basis sets calculations nicely reproduces the X-ray experimental geometry, molecular orbital levels and the other structural properties for this complex.

Interactions of Boranes and Carboranes with Aromatic Systems: CCSD(T) Complete Basis Set Calculations and DFT-SAPT Analysis of Energy Components

The noncovalent interactions of heteroboranes with aromatic systems have only recently been acknowledged as a source of stabilization in supramolecular complexes. The physical basis of these interactions has been studied in several model complexes using advanced computational methods. The highly accurate CCSD(T)/complete basis set (CBS) value of the interaction energy for the model diborane···benzene complex in a stacking geometry exhibiting a B(2)H···π hydrogen bond was calculated to be -4.0 kcal·mol(-1). The DFT-SAPT/CBS approach, which is shown to reproduce the CCSD(T)/CBS data reliably asserted that the major stabilizing component was dispersion, followed by electrostatics. Furthermore, the effect of the benzene heteroatom- and exosubstitutions was studied and found to be small. Next, when aromatic molecules were changed to cyclic aliphatic ones, van der Waals complexes stabilized by the dispersion term only were formed. As the last step, interactions of two larger icosahedral borane cages with benzene were explored. The complex of the monoanionic CB(11)H(12)(-) exhibited two minima: the first stacked above the plane of the benzene ring with a C-H···π hydrogen bond and the second planar, in which the carborane cage bound to benzene via five B-H···H-C dihydrogen bonds. The DFT-SAPT/CBS calculations revealed that both of these binding motifs were stabilized by dispersion followed by electrostatic terms, with the planar complex being 1.4 kcal·mol(-1) more stable than the stacked one. The dianionic B(12)H(12)(2-) interacted with benzene only in the planar geometry, similarly as smaller anions do. The large stabilization energy of 11.0 kcal·mol(-1) was composed of dominant attractive dispersion and slightly smaller electrostatic and induction terms. In summary, the borane/carborane···aromatic interaction is varied both in the complex geometries and in the stabilizing energy components. The detailed insight derived from high-level quantum chemical computations can help us understand such important processes as host-guest complexation or carborane···biomolecule interactions.

The molecular structure of difluoroisocyanato silane: A combined microwave spectral and theoretical study

The microwave (MW) spectrum of HF 2SiNCO (1) has been obtained and analyzed in the I r representation for C S symmetry. The rotational constants (RC) are: A 7111.28104(179), B 1565.77581(49) and C 1347.52275(77) MHz; the centrifugal distortion constants are: Δ J 2.661(11), Δ JK 455.44(25), δ J 0.4237(51), ϕ K −54.96(29) kHz; the 14N nuclear quadrupole coupling constants are: χ aa +1.8833(27) and ( χ bb − χ cc ) −0.0214(58) MHz. The low value for ( χ bb − χ cc ) implies a nearly linear SiNC structure, while the experimental A value is only consistent with cis-HSiNC and trans-SiNCO orientations. The MW analysis was assisted by calculations of the equilibrium structure. Whilst small bases give a linear SiNCO skeleton, a 6-311G ++ (3df,3pd) basis set calculation shows that the molecule is quasi-linear for all four methodologies: DFT, MP2, MP4 or CCSD(T). However, all these methods find the lowest energy conformer has trans-HSiNC and trans-SiNCO dihedral angles, although the energy difference is very small. The internal rotation barrier for the HF 2Si group is less than 1 cm −1, with the lower energy conformer having a trans-HSiNC moiety. The calculated SiNC angles for the cis-HSiNC conformer are: 171.2 (B3LYP), 167.7 (MP2), 154.9 (MP4) and 154.6° (CCSD(T)), with differences up to 9° (MP2) in the trans-series. The potential energy (PE) surface for SiNC bending ( x) is unsymmetrical, but the differences from a symmetric form are very small. A B3LYP study leads to a polynomial fit of the SiNC angle ( x, radians) with the energy ( E, cm −1), where E = 1993(536) x 2 − 422(134) x 4 + 27(10) x 6 − 0.5(2) x 8; the alternating signs indicate a double minimum potential. We have re-determined the PE surfaces for silyl group rotation for several other isocyanates using similar methods.

Approaching chemical accuracy using full configuration-interaction quantum Monte Carlo: A study of ionization potentials

A new quantum Monte Carlo (QMC) method is used to calculate exact, full configuration-interaction (FCI) energies of the neutral and cationic elements from Li to Mg, in a family of commonly used basis sets. Annihilation processes between positive and negative walkers enable the exact N-electron wave function to emerge as a linear superposition of the (factorially large) space of Slater determinants, with individual determinants being stochastically sampled. As a result, extremely large spaces (exceeding 10(15) determinants) become accessible for FCI calculations. No fixed-node approximation is necessary, and the only remaining source of error is the one-electron basis set, which can be systematically reduced by enlargement of the basis set. We have investigated the family of aug-cc-pVXZ Dunning basis sets up to X=5. The resulting ionization potentials are--with one exception (Na)--consistently accurate to within chemical accuracy. The anomalous case of Na suggests that its basis set may be improvable. Extrapolation schemes are examined as a way of further improving the values obtained, and although an improvement is seen in the mean-absolute error, the results of extrapolation are not uniformly better than the largest basis set calculations reported. More generally, these results demonstrate the utility of the QMC method to provide FCI energies for realistic systems and basis sets.

FT‐Raman, FT‐IR spectra and DFT calculations on monomeric and dimeric structures of 5‐fluoro‐ and 5‐chloro‐salicylic acid

AbstractThe experimental and theoretical study on the structures and vibrations of 5‐fluoro‐salicylic acid and 5‐chloro‐salicylic acid (5‐FSA and 5‐ClSA, C7H5FO3 and C7H5ClO3) is presented. The Fourier transform infrared spectra (4000–400 cm−1) and the Fourier transform Raman spectra (4000–50 cm−1) of the title molecules in the solid phase were recorded. The molecular structures, vibrational wavenumbers, infrared intensities, Raman intensities and Raman scattering activities were calculated for a pair of molecules linked by the intermolecular OH···O hydrogen bond. The geometrical parameters and energies of 5‐FSA and 5ClSA were obtained for all eight conformers/isomers from density functional theory (DFT) (B3LYP) with 6‐311++G(d,p) basis set calculations. The computational results identified the most stable conformer of 5‐FSA and 5‐ClSA as the C1 form. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. The spectroscopic and theoretical results were compared with the corresponding properties for 5‐FSA and 5‐ClSA monomers and dimer of C1 conformer. The optimized bond lengths, bond angles and calculated wavenumbers showed the best agreement with the experimental results. Copyright © 2010 John Wiley & Sons, Ltd.

Molecular structure, vibrational spectroscopic studies and NBO analysis of the 3,5‐dichlorophenylboronic acid molecule by the density functional method

AbstractIn this study, the Fourier‐transform infrared (FT‐IR) and FT‐Raman spectra of 3,5‐dichlorophenylboronicacid (3,5‐dcpba) were recorded in the solid phase. The structural and spectroscopic analysis of the 3,5‐dichlorophenylboronic was made by using density functional harmonic calculations. There are three conformers for this molecule. The computational results diagnose the most stable conformer of 3,5‐dcpba as the ct form. The geometrical parameters and energies have been obtained for all three conformers from DFT (B3LYP) with 6‐311+ + G(d,p) basis set calculations. The vibrations of stable and unstable conformers of 3,5‐dcpba are researched by using quantum chemical calculations. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes calculated with the scaled quantum mechanics (SQM) method. The stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analyzed using the natural bond orbital (NBO) analysis. The results show that the charge in electron density (ED) in the π* and σ* antibonding orbitals and E2 energies confirms the occurrence of ıntermolecular charge transfer (ICT) within the molecule. Finally, the calculation results were applied to simulated infrared and Raman spectra of the title compound, which show agreement with the observed spectra. Copyright © 2010 John Wiley & Sons, Ltd.

Improved interaction energy benchmarks for dimers of biological relevance

The set of interaction energies for 22 systems of biological importance, developed by Jurecka et al. [Phys. Chem. Chem. Phys., 2006, 8, 1985] and called S22, became an often used benchmark for evaluating the performance of various computational methods. As the quality of such methods improves, the uncertainties of the S22 energies are becoming too large to enable meaningful comparisons. We therefore improved the benchmarks by performing calculations in larger basis sets than used by Jurecka et al. The basis extensions included additions of higher angular momentum, diffuse, and midbond functions. The percentage deviations of the original S22 interaction energies from our values are up to 15.4%. We have estimated that the average (unsigned) uncertainty of our results should be about 1.0%. This estimate includes contributions from basis set truncation, frozen-core approximation, and neglected electron excitations.

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two-dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono- and bi-electronic integrals that enter into the Fock (Kohn-Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M x 2M matrix. The efficiency and accuracy of the computational scheme is documented.

Symmetry dilemmas in oxocarbons

SCF minimal basis set calculations on oxocarbons demonstrate the occurrence of Hartree-Fock instabilities in these compounds.

An extension of koopmans' theorem III. ionization energies of the open-shell atoms Li and B

Extended Koopmans' theorem orbital energies are calculated using unsymmetrized hole states for the Li 2S and B 2P states. These orbital energies are compared with ionization energies obtained from Δci calculations in the same basis sets as well as with experimental ionization energies. The extended Koopmans' orbital energies over unsymmetrized hole states for the outer shell orbital 2sα of Li and for the two outer shell orbitals 2pα and 2sβ of B agree well with Δci ionization energies and with experimental ionization energies. The overlap of the 2sα hole state of Li with a ci wave function of Li+ is 0.999983. The corresponding overlaps of the 2pα and 2sβ hole states of B with ci wave functions are 0.996588 and 0.999258, respectively. The unsymmetrized hole states for inner shell orbitals are strong mixtures of different symmetry types and yield increasingly poorer ionization energies.

Reduced hamiltonian orbitals. I. a new approach to the many-electron problem

The partitioning of energy into 0-energy, 1-energy, and 2-energy is developed. A new definition of correlation energy as the 2-energy is proposed. The natural orbitals of the 1-energy operator are discussed. These reduced Hamiltonian orbitals are uniquely determined by a one-step diagonalization procedure and correspond to an independent-particle model suitable simultaneously for ground as well as excited states. Minimum basis set calculations are presented for LiH and H2O and compared with similar SCF and basis orbital studies.

Elimination of spurious solutions of the Dirac equation using the Lanczos algorithm

Spurious solutions of the Dirac equation which arise and also occur in finite basis-set calculations can easily be identified and eliminated using the Lanczos algorithm. Numerically convergent eigensolutions of the Dirac Hamiltonian for a relativistic electron in an external central Coulomb-like potential are obtained to demonstrate the method.

Approximate time-dependent density functional theory

In this contribution, we summarize recent advances in the development of the time-dependent density functional based tight-bind method (TD-DFTB). The scheme is characterized by (i) the use of a limited, usually minimal basis, (ii) a two-center approximation for the Kohn–Sham Hamiltonian, (iii) a second-order functional expansion of the total energy and (iv) the simplification of two-electron integrals in the Mulliken approximation. The range of validity of these approximations is assessed by comparison to first principles time-dependent density functional theory (TDDFT) calculations in converged basis sets. Within the TD-DFTB framework, several strategies to solve the time-dependent Kohn–Sham equations are discussed. These include a linear response treatment in the frequency domain, direct propagation in the time domain leading to a non-adiabatic molecular dynamics scheme, and an O ( N ) implementation. The numerical efficiency is investigated and several illustrative applications of the method are reviewed. Results are reported for the absorption and luminescence spectra of passivated and functionalized Silicon nanocrystals with hundreds of atoms, the potential energy surfaces of azulene and Retinal chromophores, and the vibrational response of C 60 due to electronic excitation with femtosecond laser pulses. Within its well characterized range of validity we find that TD-DFTB provides an excellent ratio of accuracy over computational cost.

An ab Initio Calculation of the Valence Excitation Spectrum of H2O···Cl2: Comparison to Condensed Phase Spectra

Valence electronic excitation spectra are calculated for the H(2)O...Cl(2) dimer using state-of-the art ab initio potentials for both the ground and the valence excited states, a basis set calculation of the ground state nuclear wave function, and a wave packet analysis to simulate the dynamics on the excited state surface. The peak of the H(2)O...Cl(2) dimer spectrum is blue-shifted by 1250 cm(-1) from that of the free Cl(2) molecule. This is less than the value previously estimated from vertical excitation energies but still significantly more than the blue shift in aqueous solution and clathrate-hydrate solid. Seventy percent of the blue shift is attributed to ground state stabilization, the rest to excited state repulsion. Spin-orbit effects are found to be small for this dimer. Homogeneous broadening is found to be slightly smaller for the dimer than for the free Cl(2). The reflection principle and spectator model approximations were tested and found to be quite satisfactory. This is promising for an eventual simulation of the condensed phase spectra.

The effect of approximating some molecular integrals in coupled-cluster calculations: fundamental frequencies and rovibrational spectroscopic constants for isotopologues of cyclopropenylidene

The effect of approximating the three- and four-virtual molecular orbital integrals in single and double coupled-cluster theory including a perturbational correction for connected triple excitations [CCSD(T)] is investigated for the calculation of higher-order properties, specifically the calculation of a molecular quartic force field and spectroscopic constants. The approach was proposed previously, but investigated for only second- and lower-order properties. It is shown that the conclusions reached previously are essentially unchanged on moving to higher-order properties. That is, approximating the selected integrals has essentially no effect on the accuracy of CCSD(T) calculations, and the error due to approximating integrals is much smaller than the residual error due to one-particle basis set deficiencies. The advantage of this approach is that it significantly reduces the amount of data needed to perform CCSD(T) calculations, thereby reducing computational requirements associated with input/output operations and message passing in massively parallel, distributed memory algorithms. These savings are particularly important for large basis set calculations where the reduction in data can be as high as three orders of magnitude for ∼1000 unoccupied molecular orbitals. The approach was tested by computing the quartic force field, vibrational frequencies, and spectroscopic constants of cyclopropenylidene and isotopologues. Comparison of our best results with available experimental data shows excellent agreement between theory and experiment. It is hoped that the theoretical spectroscopic data presented herein for cyclopropenylidene and isotopologues is useful in the interpretation of future laboratory experiments and astronomical observations.

Alignment dependence in above-threshold ionization of H+2: role of intermediate resonances

We report a 3D ab initio investigation of the dependence of above-threshold ionization of the H+2 molecule on the orientation of a linearly polarized intense femtosecond laser pulse with respect to the molecular axis. The calculations were performed in the frozen nuclei approximation for the 2Σ+g(1sσg) ground and the 2Σ+u(2pσu) first excited electronic states, in laser pulses of seven optical cycles (19 fs) with a wavelength of 800 nm and for different intensities. The numerical procedure combines two different techniques, a grid-based split-step method to propagate the wave packet during the pulse, and a bound and scattering states B-spline basis set calculation to extract the information from the former. We show that the orientation dependence of the above-threshold ionization spectra is very sensitive to the intensity of the field and to the final electron energy. For some intensities and final electron energies the orientation dependence of the above-threshold ionization spectrum reflects directly the charge distribution of the initial state, but in general intermediate resonances of symmetry different from that of the initial state are populated during the pulse leading to a distorted bound-state charge density, and hence a more rich orientation dependence of the above-threshold ionization spectrum.

Microwave spectra, r0 structural parameters, and conformational stability from xenon solutions of silylcyclohexane

The FT-microwave spectrum of silylcyclohexane, c-C 6H 11SiH 3 has been investigated from 11,000 to 21,000 MHz and 43 transitions for the 28Si isotopomer have been observed and assigned for the chair-equatorial conformer and likewise for 23 and 18 transitions for the 29Si and 30Si isotopomers, respectively. The SiH a and SiH s distances have been determined from their stretching frequencies with values of 1.486 and 1.487 Å, respectively. With these parameters and by utilizing ab initio MP2(full)/6-311+G(d,p) predicted structural values, adjusted r 0 have been obtained. The determined heavy atom structural parameters for the most stable chair-equatorial conformer are: the distances (Å) r 0(C 1–C 10, 11) = 1.534(3); r 0(C 10, 11–C 16, 17) = 1.530(3); r 0(C 4–C 16, 17) = 1.544(3); r 0(C 4–Si 6) = 1.880(5) and the angles in degrees: C 1C 10, 11C 16, 17 = 111.1(5)°; Si 6C 4C 16, 17 = 111.6(5)° with the dihedral angle C 1C 10,11C 16,17C 4 = 56.0(10)°. Variable temperature (−55 to −100 °C) studies of the infrared spectra (4000 to 400 cm −1) of silylcyclohexane dissolved in liquefied xenon have been carried out as well as the infrared spectra of the gas and solid. By measuring the temperature dependency of three conformer pairs from the spectra of xenon solutions, a standard enthalpy difference of 414 ± 19 cm −1 (1.18 ± 0.05 kcal/mol) was obtained with the chair-equatorial conformer the more stable form. At ambient temperature, the abundance of the axial conformer is 12.7 ± 1%. From MP2 ab initio calculations utilizing various basis sets, the equatorial conformer is predicted to be more stable by 525 ± 10 cm −1 from the four largest basis set calculations, which is consistent with experimental results. However, the average from the corresponding B3LYP density functional theory calculations is 671 ± 5 cm −1 which is certainly too large. A few of the previously reported vibrational assignments have been corrected. The results of these spectroscopic and theoretical studies are discussed and compared to the corresponding results for some similar molecules.

Lattice dynamics of chalcopyrite semiconductors LiAlTe2, LiGaTe2 and LiInTe2

AbstractWithin density functional perturbation theory using norm‐conserving pseudopotentials and a plane‐wave basis set calculations of phonon dispersion relations and densities of states of LiAlTe2, LiGaTe2 and LiInTe2 compounds being crystallized into the tetragonal chalcopyrite structure have been performed. Theoretical values of phonon mode frequencies in LiGaTe2 and LiInTe2 are in good agreement with the experimental data available for these crystals obtained by the methods of Raman and infrared spectroscopies. The similarity of the physical and chemical properties of the crystals concerned manifests itself in the similarity of their phonon spectra that are especially close to each other in low‐ and high‐frequency ranges. Phonon modes of the upper phonon band are predominantly caused by the lithium sublattice vibrations and have an upper bound of 350–370 cm–1. In a mid‐frequency range a significant downshift of the vibrational frequencies is observed on going from LiAlTe2 to LiGaTe2 and LiInTe2 that is a consequence of the third group cation mass reduction. From calculated electron density maps it follows that Li‐containing chalcopyrites are characterized by a less pronounced bond between the first group cation and anion as compared with the Cu‐ and Ag‐based analogs due to the absence of pd‐hybridization. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Infrared and Raman spectrum, molecular structure and theoretical calculation of 3,4-dichlorophenylboronic acid

In this work, the experimental and theoretical study on the structures and vibrations of 3,4-dichlorophenylboronic acid (3,4-dcpba, C 6H 3B(OH) 2Cl 2) are presented. The Fourier Transform Infrared spectra (4000–400 cm −1) and the Fourier Transform Raman spectra (3500–5 cm −1) of the title molecule in the solid phase have been recorded. There are four conformers for this molecule. The computational results diagnose the most stable conformer of 3,4-dcpba as the ct form. The geometrical parameters and energies have been obtained for all four conformers from DFT (B3LYP) with 6-311++G(d,p) basis set calculations. The vibrations of stable and unstable conformers of 3,4-dcpba are researched with the aid of quantum chemical calculations. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. The molecular structures, vibrational frequencies, Infrared intensities and Raman scattering activities were calculated. The spectroscopic and theoretical results are compared. The optimized bond lengths, bond angles and calculated frequencies showed the excellent agreement with the experimental results. The theoretical spectrogram for the Infrared and Raman spectrum of the title molecule has been constructed.