Set Of Diffuse Functions Research Articles

Ab initio studies of the ground and first excited states of the Sr-H2 and Yb-H2 complexes.

Accurate intermolecular potential-energy surfaces (IPESs) for the ground and first excited states of the Sr-H2 and Yb-H2 complexes were calculated. After an extensive methodological study, the coupled cluster with single, double, and non-iterative triple excitation method with the Douglas-Kroll-Hess Hamiltonian and correlation-consistent basis sets of triple-ζ quality extended with 2 sets of diffuse functions and a set of midbond functions were chosen. The obtained ground-state IPESs are similar in both complexes, being relatively isotropic with two minima and two transition states (equivalent by symmetry). The global minima correspond to the collinear geometries with R = 5.45 and 5.10 Å and energies of -27.7 and -31.7 cm-1 for the Sr-H2 and Yb-H2 systems, respectively. The calculated surfaces for the Sr(3P)-H2 and Yb(3P)-H2 states are deeper and more anisotropic, and they exhibit similar patterns within both complexes. The deepest surfaces, where the singly occupied p-orbital of the metal atom is perpendicular to the intermolecular axis, are characterised by the global minima of ca. -2053 and -2260 cm-1 in the T-shape geometries at R = 2.41 and 2.29 Å for Sr-H2 and Yb-H2, respectively. Additional calculations for the complexes of Sr and Yb with the He atom revealed a similar, strong dependence of the interaction energy on the orientation of the p-orbital in the Sr(3P)-He and Yb(3P)-He states.

Angular Dependence of Strong Field Ionization of CH3X (X = F, Cl, Br, or I) Using Time-Dependent Configuration Interaction with an Absorbing Potential.

Methyl halides have been used to test basis set effects on simulations of strong field ionization using time dependent configuration interaction with an absorbing potential. Standard atom centered basis sets need to be augmented by several sets of diffuse functions on each atom so that the wave function in the strong field can interact with the absorbing potential used to model ionization. An absorbing basis of 3 s functions, 2 p functions, 3 d functions, and 1 f function is sufficient for CH3F. Large absorbing basis sets with 4 s functions, 3 or 4 p functions, 4 or 5 d functions, and 2 f functions are recommended for the heavier halogens. The simulations used static fields in the 0.035-0.07 au range to explore the angular dependence of ionization of methyl halides. CH3F ionizes mainly from the methyl group; CH3Cl and CH3Br show ionization from both the methyl group and the halogen, and CH3I ionizes almost exclusively from the pπ orbitals of the iodine.

TD-CI Simulation of the Electronic Optical Response of Molecules in Intense Fields: Comparison of RPA, CIS, CIS(D), and EOM-CCSD

A number of different levels of theory have been tested in TD-CI simulations of the response of butadiene interacting with very short, intense laser pulses. Excitation energies and transition dipoles were calculated with linear-response time-dependent Hartree-Fock (also known as the random phase approximation, RPA), configuration interaction in the space of single excitations (CIS), perturbative corrections to CIS involving double excitations [CIS(D)], and the equation-of-motion coupled-cluster (EOM-CC) method using the 6-31G(d,p) basis set augmented with n = 0-3 sets of diffuse sp functions on all carbons and only on the end carbons [6-31 n+ G(d,p) and 6-31(n+)G(d,p), respectively]. Diffuse functions are particularly important for transitions between the pseudocontinuum states above the ionization threshold. Simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. Depending on the basis set, up to 500 excited states were needed for the simulations. Under the conditions selected, the response was too weak with the 6-31G(d,p) basis set, and the difference between levels of theory was more pronounced. When two or three set of diffuse functions were included on all of the carbons, the RPA, CIS, and EOM-CC results were comparable, but the CIS(D) response was too large compared to the more accurate EOM-CC calculations. Even though the frequency of the pulse is not resonant with any of the ground-to-excited transitions, excitations to valence and pseudocontinuum states occur readily above a threshold in the intensity.

Accurate dipole polarizabilities for water clusters n=2–12 at the coupled-cluster level of theory and benchmarking of various density functionals

The static dipole polarizabilities of water clusters (2<or=N<or=12) are determined at the coupled-cluster level of theory (CCSD). For the dipole polarizability of the water monomer it was determined that the role of the basis set is more important than that of electron correlation and that the basis set augmentation converges with two sets of diffuse functions. The CCSD results are used to benchmark a variety of density functionals while the performance of several families of basis sets (Dunning, Pople, and Sadlej) in producing accurate values for the polarizabilities was also examined. The Sadlej family of basis sets was found to produce accurate results when compared to the ones obtained with the much larger Dunning basis sets. It was furthermore determined that the PBE0 density functional with the aug-cc-pVDZ basis set produces overall remarkably accurate polarizabilities at a moderate computational cost.

A comparative effect of ring annelation on cation-benzene and anion-benzene

DFT/B3LYP calculations were carried out on several π-complexes formed by cations and anions with annelated benzene, respectively. The binding energies obtained with standard method were corrected by basis set superposition error (BSSE) and zero-point energy (ZPE) during the geometry optimization for all complexes at the same levels of theory, respectively. Some different aspects of the π–cation have been compared to those of π–anion, involving in binding energy changes in effect of ring annelation, the aromaticity of the ring upon complexation, Mulliken and NBO charge-transfer. The effect of BSSE correction during the optimization is very important in some π–anion complexes whether or not using diffuse functions in basis set, and results with at least one set of diffuse functions 6-31+G(d) basis set is a little better than results obtained by 6-31G(d, p) basis set for some π–anion especially for F − complexes.

Complete basis set extrapolations of dispersion, exchange, and coupled‐clusters contributions to the interaction energy: a helium dimer study

AbstractEffectiveness of various extrapolation schemes in predicting complete basis set (CBS) values of interaction energies has been investigated for the helium dimer as a function of interatomic separation R. The investigations were performed separately for the leading dispersion and exchange contributions to the interaction energy and for the interaction energy computed using the coupled cluster method with single and double excitations (CCSD). For all these contributions, practically exact reference values were obtained from Gaussian‐type geminal calculations. Sequences of orbital basis sets augmented with diffuse and bond functions or augmented with two sets of diffuse functions have been employed, with the cardinal numbers up to X = 7. The functional form EX = ECBS + A(X − k)−α was applied for the extrapolations, where EX is the contribution to the interaction energy computed with a basis set of cardinal number X. The main conclusion of this work is that CBS extrapolations of an appropriate functional form generally improve the accuracy of the interaction energies at a very small additional computational cost (of the order of 10%) and should be recommended in calculations of interatomic and intermolecular potentials. The effectiveness of the extrapolations significantly depends, however, on the interatomic separation R and on the composition of the basis set. Basis sets with midbond functions, well known to provide at a given size much more accurate nonextrapolated results than bases lacking such functions, have been found to perform best also in extrapolations. The X−1 extrapolations of dispersion energies computed with midbond function turned out to be very efficient (except at large R), reducing the errors by an order of magnitude for small X and a factor of two for large X (where the errors of nonextrapolated results are already very small). If midbond functions are not used, the X−3 formula is most appropriate for the dispersion energies. For the exchange component of the interaction energy, the best results are obtained—in both types of basis sets—with the X−4 extrapolation, which leads (in both cases) to almost an order of magnitude reduction of the error. The X−3 and (X − 1)−3 extrapolations work also well, but give smaller improvements. The correlation component of the CCSD interaction energy extrapolates best with α between 2 and 3 for bases with midbond functions and between 3 and 4 for bases without such functions. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Time-dependent density functional theory for nonlinear properties of open-shell systems

This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.

Density-functional generalized-gradient and hybrid calculations of electromagnetic properties using Slater basis sets.

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.

Three Lowest-Lying Electronic States of NH2

The three lowest-lying electronic states, X̃ 2B1, à 2A1, and B̃ 2B2, as well as the lowest linear 2Π stationary point of NH2 have been investigated systematically using ab initio electronic structure theory. The SCF, CASSCF, CISD, CASSCF-SOCI, CCSD, and CCSD(T) levels of theory have been employed to determine total energies, equilibrium structures, and physical properties including dipole moments, harmonic vibrational frequencies, and infrared intensities of NH2. According to the instability analysis of the reference SCF wave functions, physical properties of the three lowest-lying equilibrium states of NH2 may be obtained correctly in the variational sense with all wave functions employed in this study. The lowest linear stationary point (2Π) possesses two distinct imaginary vibrational frequencies along the bending coordinate, indicating a strong Renner−Teller interaction. The predicted geometries and physical properties of the two lowest states of NH2 are in good agreement with available experimental results. At the CCSD(T) level of theory with the largest basis set, the triple-ζ (TZ) plus triple polarization with two sets of higher angular momentum and two sets of diffuse functions [TZ3P(2f,2d)+2diff], the à 2A1 state of NH2, with a large bond angle of 144.9°, is predicted to lie 32.1 kcal/mol (1.39 eV, 11 200 cm-1) above the ground state. This is in excellent agreement with the experimental T0 value of 31.80 kcal/mol (1.379 eV, 11 122.6 cm-1). The second excited state (B̃ 2B2) possesses an acute bond angle of 49.3° and is determined to lie 100.1 kcal/mol (4.34 eV, 35 000 cm-1) above the ground state. The classical (and effective) barriers to linearity for the X̃ 2B1 and à 2A1 states were predicted to be 11 870 (12 310) cm-1 and 720 (790) cm-1, which are again in good accord with the experimentally estimated values of 12 024 cm-1 (X̃ 2B1) and 730 cm-1 (à 2A1).

Mg +NO and Mg +ON: potentially important ionospheric species

In order to determine the lowest energy isomer of the Mg + − NO complex, self-consistent field (SCF), configuration interaction including all single and double excitations (CISD), coupled cluster singles and doubles (CCSD), and CCSD with perturbatively evaluated triples [CCSD(T)] ab initio electronic structure methods were employed. Equilibrium geometries, relative energies, dipole moments, harmonic vibrational frequencies, and associated infrared (IR) intensities for the lowest triplet and closed-shell singlet structures were determined. At the CCSD(T) level with the largest basis set, triple-ζ plus double polarization augmented with one set of higher angular momentum and one set of diffuse functions (TZ2PF + diff), the global minimum was predicted to be closed shell, 1 A′ Mg +NO with equilibrium geometry r e (Mg − N) = 2.378 Å, r e (N − O) = 1.147 Å, and θ e = 122.6°. At this same level of theory, 1 A′ Mg +NO was predicted to lie approximately 14 kcal mol −1 below the Mg + + NO dissociation asymptote. At levels of theory below CCSD(T), the 3Π state of Mg +NO is erroneously predicted to be the ground state. The dipole moment with respect to the center of mass is predicted to be 4.9 debyes for the 1 A′ ground state of Mg +NO.

The X̃ 1A1, ã 3B1 and à 1B1 Electronic States of the Aluminum Dihydride Anion

The three lowest-lying electronic states of the aluminum dihydride anion (AlH2-) were systematically investigated using ab initio electronic structure theory. Self-consistent-field (SCF), two-configuration self-consistent-field (TCSCF), complete active space self-consistent-field (CASSCF), configuration interaction including single and double excitations (CISD), and CASSCF-based second-order configuration interaction (SOCI) levels of theory were employed with five basis sets of triple-ζ quality. All three electronic states were predicted to possess bent equilibrium geometries. Total electronic energies as well as physical properties including dipole moments, harmonic vibrational frequencies, and associated infrared (IR) intensities were determined for each state. At the CISD level with the largest basis set employed, triple-ζ plus triple polarization augmented with two sets of higher angular momentum functions and two sets of diffuse functions [TZ3P(2f,2d)+2diff)], the equilibrium geometries of the three states were predicted to be re = 1.681 Å and θe = 95.6° (X̃ 1A1), re = 1.617 Å and θe = 117.8° (ã 3B1), and re = 1.594 Å and θe = 118.7° (Ã 1B1). At the same level of theory, the dipole moments with respect to the center of mass were predicted to be 0.64 (X̃ 1A1), 0.03 (ã 3B1), and 0.24 D (Ã 1B1). The energy separations (T0) between the ground (X̃ 1A1) and first two excited states predicted at the CASSCF-SOCI level with the TZ3P(2f,2d)+2diff basis set were 14.1 (ã 3B1 ← X̃ 1A1) and 29.0 kcal mol-1 (Ã 1B1 ← X̃ 1A1).

Quantum Chemistry Study of the Interactions of Li+, Cl-, and I- Ions with Model Ethers

The geometries and energies of complexes of Li+, Cl-, and I- with methane and model ether molecules have been studied using ab initio electronic structure calculations. For Li+, a [5s3p2d] basis set which accurately describes core electrons was derived. For Cl-, basis sets as large as [8s7p4d1f] were considered, while for I- an 2sp1d ECP basis set augmented by a set of diffuse functions as large as [5sp4d1f] was employed. Calculations were performed at the SCF and MP2 levels of theory, and the effects of basis set superposition error on binding energies were considered. For the methane and ether molecules both D95** and cc-pVTZ basis sets with additional diffuse s and p functions were employed. The binding energies of Li+ to methane, dimethyl ether, and ttt 1,2-dimethoxyethane (DME) are found to be around 10, 40, and 40 kcal/mol, respectively. The binding energy of Li+ to tgt DME is approximately 60 kcal/mol due to the favorable interaction of Li+ with both DME oxygen atoms. The binding of Cl- and I- to dimethyl ether is much weaker, around 5−7 kcal/mol. A simple atomistic force field with two-body potential functions representing polarization effects is found to reproduce the ab initio complex energies quite well for the single ligand complexes. Polarization effects contribute significantly to the binding of Li+ to the neutral molecules, while the polarization effects in Cl- and I- complexes with dimethyl ether are relatively weak. The two-body force field accounts only partially for the decrease in binding per ligand in Li+−[O(CH3)2]n complexes with the number of ligands as observed in the quantum chemistry calculations.

The Rovibrational Energy Levels of Quasilinearc1A1Methylene

Usingab initiomethods we have calculated the potential energy surface of the third excited electronic state (c1A1) of the methylene radical CH2at a grid of 51 nuclear geometries which probe energies more than 20000 cm−1above the equilibrium energy of the state. The method employed the second eigenvalue of a secular equation incorporating all single and double excitations relative to a two-configuration self-consistent-field reference function. The basis set used [TZ3P(2f, 2d) + 2diff] was triple zeta plus triple polarization with two sets of higher angular momentum functions and two sets of diffuse functions. We find the state to be almost linear with an equilibrium angle of 171.6°, a barrier to linearity of only 12 cm−1, and an electronic term valueTe(c) of 21080 cm−1. After fitting an analytical function through the points we have used the variational MORBID procedure to calculate the rotation–vibration energies; we tabulate the calculated energies. This state is of interest both to theoreticians, because it presents the challenge of not being the lowest state of its symmetry, and to experimentalists, because its spectral signature has not yet been characterized. Its near linearity remains to be proven by experiment or perhaps by a higher level ofab initiotheory.

High-Level ab Initio Calculation of the Rotation−Vibration Energies in the c̃ 1A1 State of Methylene, CH2

For the third excited electronic state (c- {sup 1}A{sub 1}) of the methylene radical, CH{sub 2}, we calculate the electronic potential energy surface using a high-level ab initio method and the rotation-vibration energies using a variational technique with a large rotation-vibration basis set. The potential energy surface is calculated at a carefully selected grid of 48 nuclear geometries that cover all types of combination of stretching and bending deformations to energies more than 20000 cm{sup -1} above that the equilibrium configuration. We fit an analytical function, in which we vary 23 parameters, through the points and find that the state is almost linear with an equilibrium angle of 172.7{degree} and a barrier to linearity of only 6 cm{sup -1}. It is well-known that theoretical treatments of higher lying states in the same symmetry are substantially tedious and complicated. The basis set used [TZ3P(2f,2d)+2diff] was triple-{zeta} plus triple polarization with two sets of higher angular momentum functions and two sets of diffuse functions. We have used the variational MORBID procedure to calculate the rotation-vibration energies. Because of the peculiar shape of the bending part of the potential surface, some very large bending force constants f{sub 0}{sup (i)} are obtained, and this more » has necessitated the use of very large basis sets in the MORBID calculation in order to achieve acceptable convergence. 17 refs., 2 figs., 4 tabs. « less

Carbonyl–water hydrogen bonding: The H2CO–H2O prototype

The potential energy surface (PES) of the water–formaldehyde complex has been examined using ab initio methods. Three energetically low-lying stationary points were located on the potential surface corresponding to one minimum and two transition states. All stationary points were examined using a double-ζ plus polarization (DZP) basis set at the self-consistent field (SCF), single and double excitation configuration interaction (CISD), and single and double excitation coupled-cluster (CCSD) levels of theory. In addition, the minimum was more thoroughly investigated through the use of the triple-ζ plus double polarization (TZ2P) basis set, the TZ2P plus higher angular momentum functions [TZ2P(f,d)] basis, and the TZ2P basis set augmented by a set of diffuse functions (TZ2P+diff) with those same theoretical methods. For each of the stationary points, geometrical parameters, absolute energies, classical binding energies, and zero-point vibrational energy corrections are reported. Additional information concerning the minimum includes vibrational frequencies and corresponding infrared intensities, as well as predicted vibrational frequency shifts of the intramolecular frequencies for the complex and its deuterium substituted isotopomers.

Electronically excited states of ethylene

The transition energies for ethylene have been calculated via configuration interaction including all singly excited configurations (CIS) using a variety of basos sets. The minimum requirement for a satisfactory basis set is 6-311 (2+)G * having two sets of diffuse functions on the carbon atoms. The excited states were examined via charge density difference plots. The CIS and MP2-corrected CIS (CIS-MP2) methods provided good agreement with experiment for both vertical and adiabatic energies

Extensive theoretical studies of the hydrogen-bonded complexes (H2O)2, (H2O)2H+, (HF)2, (HF)2H+, F2H−, and (NH3)2

The structures and binding energies of the complexes (H2O)2, (H2O)2H+, (HF)2, (HF)2H+, F2H−, and (NH3)2 have been examined using much higher levels of theory than has been previously applied to these systems. These methods including large basis sets and full optimization of structures with the effects of electron correlation included, are known to give single bond energies to an accuracy of about 2 kcal mol−1 and are found in this study to give excellent agreement with the extensive experimental data available for the hydrogen fluoride and water dimers. The Cs open form of ammonia dimer remains a very shallow minimum energy structure at these levels, in agreement with previous theoretical results but seemingly in disagreement with experiment. The theoretical enthalpy of association of H5O+2 is found to be −35.0 kcal mol−1, in slight disagreement with the most recent experimental results, but in accord with earlier ones, which suggests that these experiments should be reexamined. The enthalpy of association of H2F+ is predicted to be −33.5 kcal mol−1, and that of F− with HF to be −46.4 kcal mol−1. A study of the effects of basis set expansion on the structure of the water dimer shows that the structure is much more sensitive to basis set at the Hartree–Fock level than when correlation is included. A valence triple-zeta basis plus two sets of first polarization functions and one set of diffuse functions appears to be necessary to approach the Hartree–Fock limiting structure. Counterpoise estimates of the effects of basis set deficiencies on the structure and binding energy of this complex are shown to be misleading. Examination of the complexes (HF)2, (H2O)2, (NH3)2, (H2O)2H+, (HF)2H+, and F2H− at the MP4/6-311++G(3df ,3pd)//MP2/6-311++G(2d,2p) level of theory indicates that previous studies using fourth order perturbation theory with some smaller basis sets and Hartree–Fock optimized structures are likely to be reliable, although part of the agreement reflects a cancellation of error. HF/6-31+G(d) estimates of zero-point vibrational energy contributions to association energies are found to be satisfactory for asymmetric complexes, but can both over and underestimate the contribution of this term for symmetrically bound complexes.

An ab initio study of isomerization in the nitrous acid (HONO) system

Ab initio calculations, Moller-Plesset perturbation theory carried to fourth order including triples, were used to study the cis-trans isomerization of HONO. The geometries were completely optimized, and the trans-cis energy difference was calculated to be 3.5 kJ/mol. The activation energy for the process was found to be 53.5 kJ/mol. It was found necessary to employ a very large basis set, a doubly split valence level with complete polarization, and a set of diffuse functions on both heavy and hydrogen atoms in order to obtain a reliable estimate of the energy difference between the isomers. The calculations also indicate that a re-examination of the structural assignments for both isomers might be in order. A harmonic analysis structure which occurs under rotation and can be ascribed to large contributions from the ionic structure H-O/sup -/N identical to O/sup +/. 19 references, 1 figure, 7 tables.

Excited states and photochemistry of saturated molecules. The 1B 1(1T 2) surface in silane

The potential energy surface for the lowest (1T 2) singlet state of silane is examined using a split valence basis set, augmented by a set of diffuse functions The (initially Rydberg) state is found to dissociate with no barrier to a valence state of silylene. The nature of the avoided crossings along the “dissociation path” are discussed.