Augmented Basis Sets Research Articles

Geometry-dependent atomic multipole models for the water molecule.

Models of atomic electric multipoles for the water molecule have been optimized in order to reproduce the electric potential around the molecule computed by ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set. Different models of increasing complexity, from atomic charges up to models containing atomic charges, dipoles, and quadrupoles, have been obtained. The geometry dependence of these atomic multipole models has been investigated by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For several models, the atomic multipole components have been fitted as a function of the geometry by a Taylor series of fourth order in monomer coordinate displacements.

On the hydrogen activation by frustrated Lewis pairs in the solid state: benchmark studies and theoretical insights.

Recently, the concept of small molecule activation by frustrated Lewis pairs (FLPs) has been expanded to the solid state showing a variety of interesting reactivities. Therefore, there is a need to establish a computational protocol to investigate such systems theoretically. In the present study, we selected several FLPs and applied multiple levels of theory, ranging from a semi-empirical tight-binding Hamiltonian to dispersion corrected hybrid density functionals. Their performance is benchmarked for the computation of crystal geometries, thermostatistical contributions, and reaction energies. We show that the computationally efficient HF-3c method gives accurate crystal structures and is numerically stable and sufficiently fast for routine applications. This method also gives reliable values for the thermostatistical contributions to Gibbs free energies. The meta-generalized gradient approximated TPSS-D3 evaluated in a projector augmented plane wave basis set is able to produce sufficiently accurate reaction electronic energies. The established protocol is intended to support experimental studies and to predict new reactions in the emerging field of solid-state FLPs.This article is part of the themed issue 'Frustrated Lewis pair chemistry'.

Effects of All-Electron Basis Sets and the Scalar Relativistic Corrections in the Structure and Electronic Properties of Niobium Clusters.

In this paper, an augmented all-electron double-ζ basis set is used in calculations of the structure and electronic properties of small niobium clusters. The B3PW91 and M06 DFT functionals with and without second order Douglas-Kroll-Hess (DKH) scalar relativistic corrections are also utilized. Furthermore, an additional d Gaussian type function is introduced in the standard basis sets in order to improve the description of the clusters orbitals in the valence band. Our findings show that the extra d function is important to yield accurate results of electronic properties and, in addition, the DKH corrections can be relevant when the all-electron basis sets are used in the calculations. Our best results are obtained with the M06 functional together with the DKH second order corrections and with the extra d function added to the all-electron basis set.

Accurate Theoretical Study of LiS Radical and Its Singly Charged Cation and Anion in their Ground Electronic State

Potential energies of LiS(2Π), LiS−(1Σ+) and LiS+(3Σ−) are calculated by using the multireference configuration interaction method including Davidson correction and the augmented correlation-consistent basis sets aug-cc-PV(X+d)Z (X=T, Q). Such obtained potential energies are subsequently extrapolated to the complete basis set limit. Both the core-valence correction and the relativistic effect are also considered. The analytical potential energy functions are then obtained by fitting such accurate energies utilizing a least-squares fitting procedure. By using such analytical potential energy functions, we obtain the accurate spectroscopic parameters, complete set of vibrational levels and classical turning points. The present results are compared well with the experimental and other theoretical work.

A combined high-temperature experimental and theoretical kinetic study of the reaction of dimethyl carbonate with OH radicals.

The reaction kinetics of dimethyl carbonate (DMC) and OH radicals were investigated behind reflected shock waves over the temperature range of 872-1295 K and at pressures near 1.5 atm. Reaction progress was monitored by detecting OH radicals at 306.69 nm using a UV laser absorption technique. The rate coefficients for the reaction of DMC with OH radicals were extracted using a detailed kinetic model developed by Glaude et al. (Proc. Combust. Inst. 2005, 30(1), 1111-1118). The experimental rate coefficients can be expressed in Arrhenius form as: kexpt'l = 5.15 × 1013 exp(-2710.2/T) cm3 mol-1 s-1. To explore the detailed chemistry of the DMC + OH reaction system, theoretical kinetic analyses were performed using high-level ab initio and master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) calculations. Geometry optimization and frequency calculations were carried out at the second-order Møller-Plesset (MP2) perturbation level of theory using Dunning's augmented correlation consistent-polarized valence double-ζ basis set (aug-cc-pVDZ). The energy was extrapolated to the complete basis set using single point calculations performed at the CCSD(T)/cc-pVXZ (where X = D, T) level of theory. For comparison purposes, additional ab initio calculations were also carried out using composite methods such as CBS-QB3, CBS-APNO, G3 and G4. Our calculations revealed that the H-abstraction reaction of DMC by OH radicals proceeds via an addition elimination mechanism in an overall exothermic process, eventually forming dimethyl carbonate radicals and H2O. Theoretical rate coefficients were found to be in excellent agreement with those determined experimentally. Rate coefficients for the DMC + OH reaction were combined with literature rate coefficients of four straight chain methyl ester + OH reactions to extract site-specific rates of H-abstraction from methyl esters by OH radicals.

All-electron Gaussian basis sets of double zeta quality for the actinides.

For the actinides, two segmented all-electron basis sets of valence double zeta quality plus polarization functions (DZP) are developed. One of them must be used along with the non-relativistic Hamiltonian, whereas the other with the Douglas-Kroll-Hess (DKH) one. Adding diffuse functions of s, p, d, f, and g symmetries to the non-relativistic and relativistic sets, augmented basis sets are developed. These functions are essential to describe correctly electrons far away from the nuclei. For some compounds, geometric parameters, atomic charges and valence orbital populations of the actinides, and bond dissociation energies are calculated using the Becke 3-parameter (exchange) and the Lee, Yang, and Parr (correlation) functional in conjunction with the DZP-DKH basis set. For Am and No, the static electric mean dipole polarizabilities are also reported. Comparison with benchmark theoretical and experimental values found in the literature is carried out. It is verified that the performances of the relativistic compact size basis sets generated in this work are regular, efficient, and reliable. They will be extremely helpful in molecular property calculations that need explicitly to consider the core electrons.

Convergence of coupled cluster perturbation theory.

The convergence of a recently proposed coupled cluster (CC) family of perturbation series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between two CC models-a low-level parent and a high-level target model-is expanded in orders of the Møller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet CH2, distorted HF, and F-) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii have been determined by probing for possible front- and back-door intruder states, the existence of which would make the series divergent. In summary, we conclude how it is primarily the choice of the target state, and not the choice of the parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series which target the full configuration interaction limit, such as the standard MP series. Furthermore, we find that whereas a CC perturbation series might converge within standard correlation consistent basis sets, it may start to diverge whenever these become augmented by diffuse functions, similar to the MP case. However, unlike for the MP case, such potential divergences are not found to invalidate the practical use of the low-order corrections of the CC perturbation series.

Investigating tunnel and above-barrier ionization using complex-scaled coupled-cluster theory.

The theory and implementation of the complex-scaled coupled-cluster method with singles and doubles excitations (cs-CCSD) for studying resonances induced by static electric fields are presented. Within this framework, Stark shifts and ionization rates are obtained directly from the real and imaginary parts of the complex energy. The method is applied to the ground states of hydrogen, helium, lithium, beryllium, neon, argon, and carbon at varying field strengths. Complex-scaled Hartree-Fock, second-order many-body perturbation theory, and CCSD results are reported and analyzed with a focus on the impact of electron correlation on the ionization process. cs-CCSD calculations with suitably augmented standard Gaussian basis sets are found to deliver accurate strong-field ionization rates over a range of six orders of magnitude. The field-induced resonances are characterized beyond energy and ionization rate through their dipole moments, second moments, as well as Dyson orbitals and comparisons are drawn to autoionizing and autodetaching resonances. Marked differences are found between the tunneling and above-barrier regimes allowing for a clear distinction of the two mechanisms.

Investigations of the Rg-BrCl (Rg = He, Ne, Ar, Kr, Xe) binary van der Waals complexes: ab initio intermolecular potential energy surfaces, vibrational states and predicted pure rotational transition frequencies

The intermolecular potential energy surfaces (PESs) of the ground electronic state for the Rg-BrCl (Rg=He, Ne, Ar, Kr, Xe) van der Waals complexes have been constructed by using the coupled-cluster method in combination with the augmented quadruple-zeta correlation-consistent basis sets supplemented with an additional set of bond functions. The features of the anisotropic PESs for these complexes are remarkably similar, which are characterized by three minima and two saddle points between them. The global minimum corresponds to a collinear Rg-Br-Cl configuration. Two local minima, correlate with an anti-linear Rg-Cl-Br geometry and a nearly T-shaped structure, can also be located on each PES. The quantum bound state calculations enable us to investigate intermolecular vibrational states and rotational energy levels of the complexes. The transition frequencies are predicted and are fitted to obtain their corresponding spectroscopic constants. In general, the periodic trends are observed for this complex family. Comparisons with available experimental data for the collinear isomer of Ar-BrCl demonstrate reliability of our theoretical predictions, and our results for the other two isomers of Ar-BrCl as well as for other members of the complex family are also anticipated to be trustable. Except for the collinear isomer of Ar-BrCl, the data presented in this paper would be beneficial to improve our knowledge for these experimentally unknown species.

Density functional theory basis set convergence of sulfuric acid-containing molecular clusters

We investigate the basis set convergence of three density functionals (M06-2X, PW91, and ωB97X-D) with respect to the binding energy, thermal contribution to the Gibbs free energy, and optimized geometry. We apply correlation consistent, Pople-type, and polarization consistent basis sets with different amount of diffuse and polarization functions. Our test set contains six molecular cluster formation reactions which represent key noncovalent interactions in the atmosphere. In most cases partially augmented basis sets yield as accurate results as the fully augmented basis sets, with significant gain in computational efficiency. Relatively small basis sets are found to be sufficient to optimize geometries and to calculate thermal contributions to the Gibbs free energy. For binding energies, slightly bigger basis sets are needed to reach the complete basis set limit. The PW91 functional with the 6-311++G(3df,3pd) basis set gives a mean absolute error of 0.9kcal/mol in the binding energy, indicating that it has not reached the complete basis set limit. We estimate the effect of anharmonicity and derive scale factors to correct for it. When the lowest vibrational frequencies are treated separately, the errors arising from the anharmonicity of the remaining frequencies are small regardless of system size. We treated the low frequencies as free rotors and calculate thermal contributions to the Gibbs free energy using the quasi-harmonic approximation. We identify an error of a few percent of the total harmonic thermal contributions, which is larger than the error arising from vibrational anharmonicity.

Potential energy surfaces of the electronic states of Li2F and Li2F(.).

The potential energy surfaces of the ground and low-lying excited states for the insertion reaction of atomic fluorine (F) and fluoride (F(-)) into the dilithium (Li2) molecule have been investigated. We have carried out explicitly correlated multi-reference configuration interaction (MRCI-F12) calculations using Dunning's augmented correlation-consistent basis sets. For the neutral system, the insertion of F into Li2 proceeds via a harpoon-type mechanism on the ground state surface, involving a covalent state and an ionic state which avoid each other at long distance. A detailed analysis of the changes in the dipole moment along the reaction coordinate reveals multiple avoided crossings among the excited states and shows that the charge-transfer processes play a pivotal role for the stabilization of the low-lying electronic states of Li2F. For the anionic system, which is studied for the first time, the insertion of F(-) is barrierless for many states and there is a gradual charge transfer from F(-) to Li2 along the reaction path. We also report the optimized parameters and the spectroscopic properties of the five lowest states of the neutral and seven lowest states of the anionic systems, which are strongly stabilized with respect to their respective Li2 + F/F(-) asymptotes. The observed barrierless insertion mechanisms for both systems make them good candidates for investigation under the ultracold regime.

Conformational Transformations in Aromatic Nitroso Oxides.

A systematic theoretical study on conformational transformations of monosubstituted (ortho- and para-) aromatic nitroso oxides R-C6H4NOO was performed. The existence of two rotation axes enables two types of conformational transitions in substituted arylnitroso oxides: trans/cis (rotation around the N-O bond) and syn/anti (rotation around the C-N bond, which is important in ortho isomers). The complete set of conformers was localized for R-C6H4NOO using four selected density functional (M06-L, mPWPW91, OLYP, and HCTH) and augmented polarization basis set of triple splitting. It was found that the activation enthalpy of the trans-cis conformational transition is nearly insensitive to the nature of R and ranges within 58-60 kJ/mol for para isomers. The ortho substituent has an insignificant effect on ΔH(≠)trans→cis: it increases this value by ∼5 kJ/mol in syn isomers and decreases it by ∼3 kJ/mol in anti isomers. On the contrary, the syn-anti conformational barrier is considerably affected by the substituent R; an increase in the electron-withdrawing properties of R decreases ΔH(≠)syn→anti. The activation enthalpies grow with increasing polarity of the solvent, as it was found using IEFPCM calculation. The values of relaxation time for all conformational equilibria were calculated and compared with known lifetimes of aromatic nitroso oxides. Our results suggest that syn/anti transitions occur fast enough in the scale of the experimental lifetime. However, trans/cis transformations proceed more slowly. And under certain conditions discussed in the paper, the rate of this conformational transition limits that of irreversible decay of nitroso oxide.

Geometry-dependent distributed polarizability models for the water molecule.

Geometry-dependent distributed polarizability models have been constructed by fits to ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set for the water molecule in the field of a point charge. The investigated models include (i) charge-flow polarizabilities between chemically bonded atoms, (ii) isotropic or anisotropic dipolar polarizabilities on oxygen atom or on all atoms, and (iii) combinations of models (i) and (ii). For each model, the polarizability parameters have been optimized to reproduce the induction energy of a water molecule polarized by a point charge successively occupying a grid of points surrounding the molecule. The quality of the models is ascertained by examining their ability to reproduce these induction energies as well as the molecular dipolar and quadrupolar polarizabilities. The geometry dependence of the distributed polarizability models has been explored by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For each considered model, the distributed polarizability components have been fitted as a function of the geometry by a Taylor expansion in monomer coordinate displacements up to the sum of powers equal to 4.

Electronic and Optical Properties of TiS2 Determined from Generalized Gradient Approximation Study

The electronic and optical properties of TiS2 are studied by using an ab-initio calculation within the frame of density functional theory. A linearized and augmented plane wave basis set with the generalized gradient approximation as proposed by Perdew et al. is used for the energy exchange-correlation determination. The results show a metallic character of TiS2, and the plots of total and partial densities of states of TiS2 show the metallic character of the bonds and a strong hybridization between the states d of Ti and p of S below the Fermi energy. The optical properties of the material such as real and imaginary parts of dielectric constant (ϵ(ω) = ϵ1(ω) + iϵ2(ω)), refractive index n(ω), optical reflectivity R(ω), for E//x and E//z are performed for the energy range of 0–14 eV.

NR2 and P3+: Accurate, Efficient Electron-Propagator Methods for Calculating Valence, Vertical Ionization Energies of Closed-Shell Molecules.

Two accurate and computationally efficient electron-propagator (EP) methods for calculating the valence, vertical ionization energies (VIEs) of closed-shell molecules have been identified through comparisons with related approximations. VIEs of a representative set of closed-shell molecules were calculated with EP methods using 10 basis sets. The most easily executed method, the diagonal, second-order (D2) EP approximation, produces results that steadily rise as basis sets are improved toward values based on extrapolated coupled-cluster singles and doubles plus perturbative triples calculations, but its mean errors remain unacceptably large. The outer valence Green function, partial third-order and renormalized partial third-order methods (P3+), which employ the diagonal self-energy approximation, produce markedly better results but have a greater tendency to overestimate VIEs with larger basis sets. The best combination of accuracy and efficiency with a diagonal self-energy matrix is the P3+ approximation, which exhibits the best trends with respect to basis-set saturation. Several renormalized methods with more flexible nondiagonal self-energies also have been examined: the two-particle, one-hole Tamm-Dancoff approximation (2ph-TDA), the third-order algebraic diagrammatic construction or ADC(3), the renormalized third-order (3+) method, and the nondiagonal second-order renormalized (NR2) approximation. Like D2, 2ph-TDA produces steady improvements with basis set augmentation, but its average errors are too large. Errors obtained with 3+ and ADC(3) are smaller on average than those of 2ph-TDA. These methods also have a greater tendency to overestimate VIEs with larger basis sets. The smallest average errors occur for the NR2 approximation; these errors decrease steadily with basis augmentations. As basis sets approach saturation, NR2 becomes the most accurate and efficient method with a nondiagonal self-energy.

An ab initio investigation on the ground electronic state of chlorine monoxide and its singly charged cation and anion

The MRCI method has been utilized to calculate the equilibrium structure of the ground electronic state for the ClO radical and its singly charged cation and anion, ClO+ and ClO−. The augmented correlation-consistent basis sets up through sextuple-zeta quality are used to derive equilibrium structural parameters, potential energy curves and spectroscopic constants of the systems. Two extrapolating schemes enable us to remove the basis set truncation error and to estimate the complete basis set limit. Corrections of core-valence correlation and relativistic effect are included in our calculations. By solving the radial Schrödinger equation of nuclear motion, the vibrational energy levels as well as rotational and centrifugal distortion constants of the ground electronic states for the three species are obtained. Ionization potentials and the electron affinities are also obtained on the RCCSD(T)/AV6Z level. The knowledge extracted from this work are anticipated to extend our understanding on molecular characteristics of the ClOn (n=−1, 0, +1) systems and can serve as guidelines for further experimental or theoretical researches.

All-electron segmented contraction basis sets of triple zeta valence quality for the fifth-row elements

All-electron contracted Gaussian basis set of triple zeta valence quality plus polarisation functions (TZP) for the elements Cs, Ba, La, and from Hf to Rn is presented. Douglas–Kroll–Hess (DKH) basis set for fifth-row elements is also reported. We have recontracted the original TZP basis set, i.e., the values of the contraction coefficients are re-optimised using the second-order DKH Hamiltonian. By addition of diffuse functions (s, p, d, f, and g symmetries), which are optimised for the anion ground states, an augmented TZP basis set is constructed. Using the B3LYP hybrid functional, the performance of the TZP–DKH basis set is assessed for predicting atomic ionisation energy as well as spectroscopy constants of some compounds. Despite its compact size, this set demonstrates consistent, efficient, and reliable performance and will be especially useful in calculations of molecular properties that require explicit treatment of the core electrons.

Rotational study of the NH3-CO complex: millimeter-wave measurements and ab initio calculations.

The rotational spectrum of the van der Waals complex NH3-CO has been measured with the intracavity OROTRON jet spectrometer in the frequency range of 112-139 GHz. Newly observed and assigned transitions belong to the K = 0-0, K = 1-1, K = 1-0, and K = 2-1 subbands correlating with the rotationless (jk)NH3 = 00 ground state of free ortho-NH3 and the K = 0-1 and K = 2-1 subbands correlating with the (jk)NH3 = 11 ground state of free para-NH3. The (approximate) quantum number K is the projection of the total angular momentum J on the intermolecular axis. Some of these transitions are continuations to higher J values of transition series observed previously [C. Xia et al., Mol. Phys. 99, 643 (2001)], the other transitions constitute newly detected subbands. The new data were analyzed together with the known millimeter-wave and microwave transitions in order to determine the molecular parameters of the ortho-NH3-CO and para-NH3-CO complexes. Accompanying ab initio calculations of the intermolecular potential energy surface (PES) of NH3-CO has been carried out at the explicitly correlated coupled cluster level of theory with single, double, and perturbative triple excitations and an augmented correlation-consistent triple zeta basis set. The global minimum of the five-dimensional PES corresponds to an approximately T-shaped structure with the N atom closest to the CO subunit and binding energy De = 359.21 cm(-1). The bound rovibrational levels of the NH3-CO complex were calculated for total angular momentum J = 0-6 on this intermolecular potential surface and compared with the experimental results. The calculated dissociation energies D0 are 210.43 and 218.66 cm(-1) for ortho-NH3-CO and para-NH3-CO, respectively.

Scaled Quantum Mechanical scale factors for vibrational calculations using alternate polarized and augmented basis sets with the B3LYP density functional calculation model

The Scaled Quantum Mechanical (SQM) method of scaling calculated force constants to predict theoretically calculated vibrational frequencies is expanded to include a broad array of polarized and augmented basis sets based on the split valence 6-31G and 6-311G basis sets with the B3LYP density functional. Pulay’s original choice of a single polarized 6-31G(d) basis coupled with a B3LYP functional remains the most computationally economical choice for scaled frequency calculations. But it can be improved upon with additional polarization functions and added diffuse functions for complex molecular systems. The new scale factors for the B3LYP density functional and the 6-31G, 6-31G(d), 6-31G(d,p), 6-31G+(d,p), 6-31G++(d,p), 6-311G, 6-311G(d), 6-311G(d,p), 6-311G+(d,p), 6-311G++(d,p), 6-311G(2d,p), 6-311G++(2d,p), 6-311G++(df,p) basis sets are shown. The double d polarized models did not perform as well and the source of the decreased accuracy was investigated. An alternate system of generating internal coordinates that uses the out-of plane wagging coordinate whenever it is possible; makes vibrational assignments via potential energy distributions more meaningful. Automated software to produce SQM scaled vibrational calculations from different molecular orbital packages is presented.

Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements.

We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange–correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange–correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.