Atomic Natural Orbital Basis Sets Research Articles

Energies and structures of isomers of Cl 2O 2 calculated by density functional methods

The geometries and the relative energies of three low-lying (ClO) 2 isomers in the ground state have been calculated using density functional theory (DFT) methods. The DFT relative energies using extended basis sets vary by as much as 4.5 cal/mol, depending upon the functionals employed, but differ by less than 2.5 cal/mol from the available CCSD(T) results with large atomic natural orbital basis sets. DFT calculated geometries of the isomers are also in reasonable agreement with experiment. The present study shows that the DFT methods could be used to investigate relative energetics of (ClO) 2 isomers, for which large basis sets are essential even for modest accuracy.

Valence and excited states ofLiH−

Valence and excited dipole-bound states of the ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ anion are calculated with the recently developed electron-attachment equation-of-motion coupled-cluster technique. It is found that the first dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ corresponds to the second dissociation channel ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}{\ensuremath{\rightarrow}\mathrm{Li}}^{\mathrm{\ensuremath{-}}}{(}^{1}S)+\mathrm{H}{(}^{2}S).$ The second (excited) dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ is below the neutral ground-state potential energy curve only for some range of the Li-H internuclear distance. This state appears at bond lengths larger than $\ensuremath{\approx}2.0\AA{}$ and decays at Li-H distances longer than \ensuremath{\approx}4.2 \AA{}, where the dipole moment of LiH becomes smaller than the critical value of 2.5 D. The adiabatic electron affinity of LiH calculated at the coupled-cluster level with the iterative inclusion of all single, double, and triple excitations and a large atomic natural orbital basis set is 0.327 eV, almost matching the recently obtained experimental value of $0.342\ifmmode\pm\else\textpm\fi{}0.012\mathrm{eV}.$

Theoretical studies on mechanisms of the insertion of boron into methane and its consequent reactions

The potential energy surfaces for the insertion of a boron atom into CH4 and its consequent processes have been characterized employing MP2 and QCISD methods with the 6-311G(d,p) and 6-311 + + G(d,p) basis sets in order to locate the stationary points, followed by QCISD(T) calculations using a correlation-consistent atomic natural orbital basis set cc-pVTZ to determine the energetics. The detailed mechanisms leading to different products are obtained, and the initial insertion reaction is exothermic by 52.6 kcal mol−1 with a potential barrier of 20.8 kcal mol−1. The calculations predict that the B + CH4 system maintains Cs symmetry in the course of insertion. The stable conformations of the CH3BH molecule are finally formed by an intramolecular rotation. The CH2BH2 molecule found can isomerize to the planar CH2BH2 molecule with C2v symmetry through a barrier of 18.8 kcal mol−1. Production of the CH2BH molecule is found to involve a complex mechanism: the most likely pathway is direct dissociation of the CH3BH molecule into CH2BH and H atom. The HBCH molecule is formed only by 1,1-H2 elimination from the CH2BH molecule, while CH and BH are produced by the direct abstraction reaction.

Singlet-Triplet Splitting in Methylene: An Accurate Description of Dynamic and Nondynamic Correlation by Reduced Multireference Coupled Cluster Method

A classical multireference problem - the singlet-triplet separation in methylene - is examined by the recently introduced reduced multireference (RMR) singles and doubles coupled cluster (CCSD) method, using both double zeta plus polarization (DZP) and large atomic natural orbital (ANO) basis sets. In the former case, the performance of the RMR CCSD as well as of other approaches is assessed by a comparison with the full configuration interaction (FCI) result that represents the exact solution for this basis, while in the latter case a comparison is made with the experiment. It is shown that using a minimal two-configuration reference space, the RMR CCSD result compares well with either FCI or experiment; and is of the same quality as that provided by the two-reference state universal MR CCSD theory. Both MR CCSD approaches give a balanced description for the singlet and triplet states involved and correct the shortcomings of the single reference CCSD approach that is lacking in the presence of nondynamical correlation effects.

The tellurium dimer and its anion

A new atomic natural orbital type basis set, which includes high angular momentum functions up to l= 6, has been constructed for tellurium. Using this set in combination with relativistically corrected multi-reference configuration interaction and coupled cluster wavefunctions the potential curves of the ground and spectroscopically most important excited states of the neutral and anionic tellurium dimer have been determined. Predictions for spectroscopic constants and energetic details such as electron affinity, excitation energies and dissociation energies, for which in some cases only very limited experimental information exists, are reported.

The harmonic frequencies of benzene. A case for atomic natural orbital basis sets

The geometry and harmonic force field of benzene have been computed at the CCSD(T) level with basis sets of spdf quality. Two out-of-plane modes, ω 4 and ω 5 (and to a lesser extent ω 17), exhibit a pathological basis set dep to basis set superposition error. Using an atomic natural orbital (ANO) basis set of [4 s3 p2 d1 η/4 s2 p] quality, the best available experimentally derived harmonic frequencies can be reproduced with an RMS error of 6 cm −1 without any empirical corrections. We strongly recommend the use of ANO basis sets for accurate frequency calculations on unsaturated and aromatic systems. Our best estimate for the equilibrium geometry is r e ( CC) = 1.392(2), r e ( CH) = 1.081 A ̊ .

Electronic Structure of the Lowest Excited States of Cr(CO)(4)(2,2'-bipyridine): A CASSCF/CASPT2 Analysis.

The visible and UV absorption spectra of Cr(CO)(4)(bpy) are interpreted according to CASPT2 calculations based on CASSCF reference wave functions using atomic natural orbital (ANO) basis sets. The excitation energies of the lowest singlet MLCT (metal-to-ligand-charge-transfer) states range between 12 630 and 17 580 cm(-)(1). They originate in the excitation of chromium d electrons to the lowest pi(bpy) orbital of b(2) local symmetry. Dipole transition moments calculated for individual MLCT transitions show that the only transition expected to contribute significantly to the intense absorption band in the visible spectral region is the a(1)A(1) --> b(1)A(1) transition calculated at 17 580 cm(-)(1). This result agrees very well with the experimental spectra recorded in weakly solvating C(2)Cl(4), characterized by a band at 17 700 cm(-)(1). The low-energy emission band at 12 850 cm(-)(1) has been attributed to the lowest a(3)B(2) state calculated at 12 560 cm(-)(1). The next set of excited states corresponding to 3d --> pi(bpy,a)()2 excitations range between 25 370 and 26 200 cm(-)(1) for the singlets and between 24 630 and 25 750 cm(-)(1) for the triplets. The singlet excited states corresponding to d --> d excitations are calculated between 29 650 and 37 360 cm(-)(1). These results show that the intense absorption in the near-UV spectral region originates in strongly overlapping absorption bands due to closely spaced transitions into MLCT (a(2)) and dd excited states, respectively. The c(1)B(2) excited state corresponding to the 3d(xz)() --> 3d(z)()()2 excitation, proposed as photoactive in the mechanism of the efficient CO loss under irradiation at 27 630 cm(-)(1), is calculated at 36 320 cm(-)(1) and is far too high to be directly populated in these photochemical studies. Its mixing with one or several low-lying (singlet) MLCT states at the early stage of the reaction path could be responsible for the observed primary reaction. A comparison between the excitation energies of the lowest singlet states of Cr(CO)(4)(bpy) and Cr(CO)(4)(dab) is reported. The most significant feature is the lowering of the MLCT excited states on going from the bpy-containing molecule to its dab (1,4-diaza-1,3-butadiene) analog.

An ab initio MO study on structures and energetics of C3H−, C3H, and C3H+

The geometrical structures of cyclic and linear conformers in C3H−, C3H, and C3H+ are optimized using the full-valence CASSCF and CCSD(T) levels of theory. The atomic natural orbital ([5s3p2d1f/3s2p1d]) and correlation consistent basis (aug-cc-pVTZ) sets are used. The relative stability between the cyclic and linear conformers is investigated using the CCSD(T) and multireference CI levels of theory with the aug-cc-pVTZ basis set. The basis set dependency is checked with the 6-311+G(3d2 f,2pd) basis set. The most stable conformer in C3H− and C3H is C2v cyclic with a C3-ring, and that in C3H+ C∞v linear. The energy difference between the cyclic and linear in C3H radical is really small, being around 1.0 kcal/mol. The π-electron population on the C3-ring in cyclic C3H− is 2.00, which is a typical value predicted on the basis of the 4n+2 (n=0) aromatic-rule. The π-electron population on the C3-ring decreases in the order of C3H−, C3H, and C3H+, consistent with the order of the stability of the cyclic conformers. The adiabatic electron affinity and ionization potential in C3H are calculated to be 2.01 and 9.06 eV, respectively. The excitation energies from the most stable isomer are also calculated at the multireference CI level of theory with the aug-cc-pVTZ basis set.

Ab initio potential-energy curves for excited electronic states of the molecular ion AsCl +

This paper presents a comprehensive theoretical treatment of the low-lying electronic states of the molecular ion AsCl + correlating with the lowest dissociation asymptote As + ( 3P) + Cl ( 2P). All-electron CASSCF + CI calculations have been made with averaged atomic natural orbital basis sets. There are four bound states, namely X 2Π, A 2Π, 1 4Σ − and 1 4Π . Spectroscopic constants are calculated for the bound states and are in good agreement with experimental data for the doublet states.

A theoretical study of the excited electronic states of the molecular ion BBr+

A comprehensive theoretical treatment is presented of the low-lying electronic states of the molecular ion BBr+ correlating with the two lowest dissociation asymptotes B+(1S) Br(2P) and B(2P)+Br+(3P). All-electron CASSCF+CI calculations have been made with averaged atomic natural orbital basis sets. Spectroscopic constants are calculated for the bound states but are in disagreement with an experimental analysis in the literature of a 2Πr → X 2Σ+ system. It is suggested that a re-examination of the spectroscopy of this species would be worthwhile.

A theoretical study of the excited electronic states of the molecular ion BBr

A comprehensive theoretical treatment is presented of the low-lying electronic states of the molecular ion BBr+ correlating with the two lowest dissociation asymptotes B+(1S) Br(2P) and B(2P)+Br+(3P). All-electron CASSCF+CI calculations have been made with averaged atomic natural orbital basis sets. Spectroscopic constants are calculated for the bound states but are in disagreement with an experimental analysis in the literature of a 2Πr → X 2Σ+ system. It is suggested that a re-examination of the spectroscopy of this species would be worthwhile.

The varying nature of fluorine oxygen bonds

The singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T), together with a triple zeta double polarized (TZ2P) one-particle basis set is used to determine the geometries, harmonic frequencies, infrared intensities, and dipole moments of HOF, F2O, HOOF, FOOF, C1OOF. Agreement with experiment is very good, with the exception that the currently accepted experimental assignment of the symmetric and antisymmetric O–F stretches in FOOF is shown to be reversed (and to be consistent with an earlier experimental study). Very accurate heats of formation of HOOF, FOOF and C1OOF are also computed using the CCSD(T) method in conjunction with large atomic natural orbital basis sets. The F–O bond distances, quadratic force constants, bond energies, and fluorine and oxygen atomic charges from the above five molecules and six previously studied molecules (FONO2, trans-FONO cis-FONO, FOC1, FOBr and FON) are compared and used to deduce a simple model of F–O bonding. The unusual relationship between the F–O bond distance and quadratic force constant shows that F–O bonding is a function of at least three effects, which are degree of covalent character, degree of ionic character, and extent of lone electron-pair repulsions. All of the data are qualitatively consistent with this simple model The bonding in cis-FONO is even more complicated, involving also dispersion interactions between fluorine and the terminal oxygen. It is suggested that the general importance of lone pair repulsions in F–O bonding and the additional importance of intra-molecular dispersion interactions explains why many density functionals have difficulty in describing the geometry of cis-FONO.

The proton affinity of HOBr

The proton affinity (PA) of HOBr is determined to be 161.5 ± 1.0 kcal/mol (298.15 K). The single and double coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), was used in conjunction with large spdfg atomic natural orbital basis sets to arrive at this value. The PA of HOBr is 7.0 kcal/mol larger than a recent prediction for HOCl. The most stable form of protonated HOBr is H 2OBr + with HOBrH + determined to be 17.4 ± 1.0 kcal/mol (298.15 K) higher in energy.

A CASPT2 calculation of the lowest excited states of H 2Fe(CO) 4

CASPT2 calculations based on CASSCF reference wavefunctions, using large atomic natural orbital basis sets, are reported for the lowest excited states of H 2Fe(CO) 4. The excitation energies obtained with this accurate method are compared to the values from multireference contracted CI calculations based on a unique CASSCF wavefunction. This computational strategy is usually employed for the calculation of the one-electron properties, spin-orbit interaction or costly potential energy surfaces describing the photochemistry of organometallic molecules. The relative order of the excited states is not affected by this more refined treatment and the largest excitation energy differences are of the order of 0.25 eV for the lowest excited states. However, the computational strategy seems to have a dramatic influence on the results obtained for the highest excited states pointing out the limit of less accurate methods. The theoretical spectra obtained for this family of molecules must be compared with poorly resolved experimental spectra.

Ab Initio Characterization of Triatomic Bromine Molecules of Potential Interest in Stratospheric Chemistry

The equilibrium structures, harmonic vibrational frequencies, quadratic force fields, dipole moments, and IR intensities of several triatomic bromine compounds of known or potential importance in stratospheric ozone depletion chemistry have been determined using the CCSD(T) electron correlation method in conjunction with a basis set of triple zeta double polarized (TZ2P) quality. Specifically, the molecules included in the present study are HOBr, HBrO, FOBr, FBrO, BrNO, BrON, Br2O, BrBrO, BrCN, BrNC, ClOBr, ClBrO, and BrClO. Very accurate isomeric energy differences have also been determined at the CCSD(T) level with atomic natural orbital basis sets that include through g-type functions. In most cases, the isomer with a normal neutral Lewis dot structure is the lowest energy form, with the single exception that FBrO is predicted to be 11.1 kcal/mol (0 K) lower in energy than FOBr. In all cases, however, the hypervalent isomer is more stable relative to the isomer with a normal Lewis dot structure as compared to the chlorine analogs. Consistent with this observation, the energy of the last three molecules given above increases in the order ClOBr less than ClBrO less than BrClO. The CCSD(T)/TZ2P geometries and vibrational frequencies are in good agreement with the available experimental data. Heats of formation are determined for all species using a combination of theoretical isomeric, homodesmic, and isodesmic reaction energies. The accuracy of these quantities is ultimately dependent on the reliability of the experimental heat of formation of HOBr.

Large atomic natural orbital basis sets for the first transition row atoms

Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu atoms. The primitive sets are taken from the large sets optimized by Partridge, namely (21s13p8d) for Sc and Ti and (20s12p9d) for V to Cu. These primitive sets are supplemented with threep, oned, sixf, and fourg functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d n 4s2 and 3dn+14s1 occupations. For Ni, the1S(3d10) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.

The low-lying electronic states of LiC

The spectroscopic constants for the doublet and quartet states of LiC below about 30000 cm −1 are determined using an internally contracted multireference configuration-interaction approach in conjunction with a [6s5p3d2f] atomic natural orbital basis sets. All of the strongly bound states, X 4 Σ −, (1) 2 Δ, (1) 2 Σ +, and (2) 2Π, are very ionic in character. The only bound-bound quartet transition in this energy range is (2) 4 Σ − − X 4 Σ − and Franck-Condon factors, Einstein A values, and lifetimes are reported for this transition.

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

The electronic spectrum of Cr 2

The electronic spectrum of Cr 2 has been studied using multiconfigurational second-order perturbation theory. Potential curves for 18 electronic states have been computed. By employing an atomic natural orbital (ANO) basis set of the size 8s7p6d4f and by including 3s3p correlation effects and relativistic corrections, the following results were obtained (experimental data within parentheses): First, the location of two 1Σ u + states at 2.86 eV (2.70) and 2.51 eV (2.40) above the ground state. Second, spectroscopic constants for the a′ 3Σ u + state located 1.82 eV (1.76) above the ground state are: r e = 1.67 A ̊ (1.65 ± 0.02) and ΔG 1 2 = 680 cm −1 (574). Third, a plausible candidate for the metastable state detected in 1985 by Moskovits et al. is the 5Σ g + state in the ground state manifold with the vibrational frequency ω e = 148 cm −1 (79 in a matrix). The vertical transition 5Σ u + ← 5Σ g + is 2.07 eV (2.11).

Quantum chemical study on the equilibrium geometries of S3 and S−3, The electron affinity of S3 and the low lying electronic states of S−3

The geometries and relative stabilities of the open, C2v symmetric and closed, D3h symmetric forms of thiozone and its anion, the adiabatic electron affinity of S3 and the energies of the three low-lying excited electronic states of the thiozone anion (Ã 2B2,B̃ 2A1,C̃ 2A2) at the optimized geometry of the X̃ 2B1 ground state are computed employing coupled-cluster [CCSD(T)], second-order multireference perturbation theory (CASPT2), and multireference CI (MRCI and IC-MRCI) methods using large atomic natural orbital basis sets. In addition, the saddle point for the open→closed isomerization on the neutral S3 potential energy surface is being studied. Surprisingly, the calculations do not show the expected underestimation of the experimentally determined electron affinity, in sharp contrast to test calculations on the sulfur atom, the disulfur molecule, and earlier results for ozone. Apart from this, thiozone and its anion behave in many respects qualitatively similar as ozone and O−3, while quantitatively various differences are observed.