Atomic Natural Orbital Basis Sets Research Articles

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

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

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

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

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 Cr 2 potential energy curve studied with multiconfigurational second-order perturbation theory

The potential energy curve of the Cr 2 ground state has been obtained by multiconfigurational second-order perturbation theory. In this study 6–8 singularities appear in the potential curve for bond distances ranging from 1.5 to 2.2 Å. However, these singularities are weak enough to allow the determination of approximate spectroscopic constants. By employing a large atomic natural orbital (ANO) basis set of the size 8s7p6d4f and by including 3s, 3p correlation effects and relativistic corrections, the following values were obtained (experimental data within parentheses): equilibrium bond length r e = 1.71 Å (1.68 Å), harmonic vibrational frequency ω e = 625 cm −1 (481 cm −1) and dissociation energy D 0 = 1.54 eV (1.44±0.06 eV).

An electronic structure study of acetone by electron momentum spectroscopy: a comparison with SCF, MRSD-CI and density functional theory

Abstract The binding energy spectra and momentum distributions of all valence orbitals of acetone have been studied by electron momentum spectroscopy (EMS) and SCF, MRSD-CI, and density functional theory (DFT) calculations. The experiment was performed using a multichannel EMS spectrometer at a total energy of 1200 eV. Binding energy spectra measured in the energy range of 6–60 eV are compared with the results of OVGF and 2ph-TDA many-body Green's function calculations. In the inner valence region strong splitting of the 5a1 and 4a1 orbitals due to final state electron correlation is observed. The distribution of energies and pole strengths predicted by the Green's function calculations deviates considerably from the measured ionization energies and strengths in the innervalence region. The measured momentum distributions are compared with calculations at the level of the target Hartree-Fock approximation (THFA) using the SCF method and the target Kohn-Sham approximation (TKSA) using DFT and the local-density approximation. Basis sets used for the SCF calculations ranged from the simplest (STO-3G) to large (204-GTO) and for the DFT calculations very large atomic natural orbital (ANO) basis sets were used. The effects of electron correlation and relaxation are also investigated in MRSD-CI calculations of the full ion-neutral overlap amplitude using large and saturated basis sets. In general, the THFA model with an intermediate basis set and very diffuse functions (6-311 + +G∗∗) and with a near Hartree-Fock limit SCF wavefunction (204-GTO), and the TKSA-DFT model with an ANO basis set all provide reasonable predictions of momentum distributions for most orbitals. However, none of these calculations gives a completely satisfactory description of the momentum distribution of the HOMO (5b2) orbital.

The singlet with a C 3 ring: The probable candidate of HC 6N and C 7H 2

The geometrical structures of various stationary points in the HC 6N and C 7H 2 molecules were investigated using the second-order Moller-Plesset perturbation method with the Huzinaga-Dunning D95** basis set. The relative stability ladder to the most stable structure was determined using the SDCI + Q method with the general contraction scheme of the [4s2pld/2slp] atomic natural orbital basis set. Within 1 eV, eleven and eight stationary points were found for the HC 6N and C 7H 2 molecules, respectively. For each molecule the two singlets containing a C3 ring are very stable. Only a linear structure was obtained for the triplet. Both the skelton structures and the energy relationships of the HC 6N and C 7H 2 molecules are similar to each other. The most stable singlets in both molecules lie about 7 kcal mol −1 below the corresponding linear triplets. The skeletons of the HC 6N and C 7H 2 molecules and the relative energy relationships of the isomers are similar to those of HC 4N and C 5H 2, where the most stable isomer is also a singlet containing a C 3 ring.

The singlet with a C 3 ring: the probable candidate of HC 6N and C 7H 2

The geometrical structures of various stationary points in the HC 6N and C 7H 2 molecules were investigated using the second-order Møller-Plesset perturbation method with the Huzinaga-Dunning D95** basis set. The relative stability ladder to the most stable structure was determined using the SDCI + Q method with the general contraction scheme of the [4s2p1d/2s1p] atomic natural orbital basis set. Within 1 eV, eleven and eight stationary points were found for the HC 6N and C 7H 2 molecules, respectively. For each molecule the two singlets containing a C 3 ring are very stable. Only a linear structure was obtained for the triplet. Both the skelton structures and the energy relationships of the HC 6N and C 7H 2 molecules are similar to each other. The most stable singlets in both molecules lie about 7 kcal mol −1 below the corresponding linear triplets. The skeletons of the HC 6N and C 7H 2 molecules and the relative energy relationships of the isomers are similar to those of HC 4N and C 5H 2, where the most stable isomer is also a singlet containing a C 3 ring.

Ab Initio Study of the Bergman Reaction: The Autoaromatization of Hex-3-ene-1,5-diyne

The Bergman reaction of the hex-3-ene-1,5-diyne molecule (enediyne) to form the singlet biradical p-benzyne structure under ring closure has been studied by ab initio methods. The complete active space (CAS) SCF method was used for geometry optimizations at five points along the reaction path of the Bergman reaction. Subsequent calculations using the multireference second-order perturbation theory based on a CASSCF reference (CASPT2) established the energetics along the reaction path, especially for the reactant, transition state, and product. The energetics were further corrected for zero point vibrational energy at the CASSCF level of theory. The study incorporated four different basis sets: a double-zeta plus polarization (DZP), a triple-zeta plus double polarization (TZ2P), and two different average atomic natural orbital (ANO) basis sets. The study predicts the energy barrier to ring closure to be 25.0 +/- 3.1 kcal/mol and the enthalpy of reaction to be 4.9 +/- 3.2 kcal/mol. The latter value deviates significantly from the value estimated on the basis of group additivity and the Born-Haber cycle. The enediyne moiety is the main functional group of a new class of anticancer agents. The activation of the Bergman reaction in these drugs has been argued to be due to a small structural change in the terminal-terminal carbon distance of about -0.5 Angstrom originating from an epoxide conversion in the rest of the drug. The present study indicates that such a structural change is not sufficient for the Bergman autoaromatization to proceed at an appreciable rate. A new reaction path involving no biradical formation, resulting in the same products, is suggested.

Ab initio MO study on C 4O: structures and electron affinities

The geometrical structures of four conformers of the C 4O molecule were surveyed with second- and third-order Møller-Plesset perturbation theory and complete active space SCF methods using the Huzinaga-Dunning double zeta plus polarization basis set. The relative stability of the conformers and the electron affinity of C 4O were calculated by the configuration interaction method (including single and double excitations) with the Davidson correction. The general contraction scheme of the [5s4p2d1f] atomic natural orbital basis set, based on the (14s9p4d3f) primative Gaussian functions, was applied. The linear structure is most stable in both neutral and anionic C 4O. The electron affinity of C 4O was calculated to be 2.77 eV, 0.72 eV larger than the experimental value.

Characterization of the potential energy surface for CH 3+O 2→products

Complete active space SCF/internally contracted configuration interaction calculations using large atomic natural orbital basis sets are reported for CH 3+O 2. Two potential energy surfaces are found to be important in the CH 3+O 2 reaction. In C s symmetry, the lower 2A″ surface correlates with CH 3+O 2( 3Σ − g) and connects to a bound CH 3OO species with no barrier, but leads only to CH 3O+O products. A higher surface of 2A′ symmetry correlates with CH 3+O 2( 1Δ − g and leads to CH 2+OH with a computed barrier of 13.7 kcal/mol (with respect to CH 3+O 2( 3Σ − g)). Even in lower symmetry, two surfaces are involved leading to a more complex model for this reaction than had been previously considered.

Stability ladder of various HC2N conformers and their excitation energies

The molecular structure of various stationary points of HC2N has been studied using the quadratic configuration interaction including single and double substitutions with triples contributions (QCISD(T)). A Huzinaga–Dunning double-zeta plus polarization (D95**) basis set was used. A stability ladder of these species is calculated using the configuration interaction including single and double substitutions (SDCI) with the Davidson correction (SDCI+Q). The general contraction scheme of the [5s3p2d1f(C and N)/3s2p1d(H)] atomic natural orbital basis set was chosen. The natural orbitals obtained in the preceding complete active space self-consistent field (CASSCF) calculations were applied to the open-shell SDCI. The triplet cyanomethylene is bent, and the barrier to linearity is 1.4 kcal/mol at the single-reference SDCI+Q level of theory in accord with the Schaefer and Roos’ values (0.8–1.0 kcal/mol). The nine-reference SDCI+Q calculation increases the energy separation by 0.7 kcal/mol. The thermal energy change between the two (1 and 2) including the calculated zero-point vibrational energies is 1.4 kcal/mol. The enthalpy barrier (ΔH≠) to linearize 1 to transition state 2 in a (hypothetical) reaction is predicted to be 0.0 kcal/mol using the single-reference SDCI+Q bent-linear energy separation. As a result, experiments might find no barrier to inversion of bent triplet 1. The most stable singlet species 6 (ring form of HC2N) lies 7.7 kcal/mol above the triplet bent cyanomethylene. Vertical excitation energies from the ground-state (3A″) of triplet bent cyanomethylene to 1A′ and 1A″ are studied using the CASSCF and SDCI methods; the SDCI+Q energies are 0.93 and 1.11 eV, respectively. These excitation energies are compared with those in the methylene and oxygen molecules having a qualitatively similar electronic structure to the present HCCN species, where two electrons occupy near-degenerate π-like (or degenerate π) highest occupied molecular orbitals (HOMO) forming a triplet ground-state. The excitation energies of 0.93 and 1.11 eV are close to the relative energies of the 3, 8, and 9 to the most stable triplet bent cyanomethylene.

Accurate quartic force fields and vibrational frequencies for hydrogen cyanide and hydrogen isocyanide

The quartic force fields of HCN and HNC are determined using atomic natural orbital one-particle basis sets of spdf/spd and spdfg/spdf quality in conjunction with the CCSD(T) electron correlation method (singles and doubles coupled-cluster theory plus a perturbation estimate of the effects of connected triple excitations). The HCN force field is in good agreement with a recent experimentally derived force field and also with the force field recently computed by Wong and Bacskay. On the basis of the good agreement obtained for HCN, it is argued that the ab initio quartic force field for HNC is superior to a prior force field derived from experiment. The harmonic frequencies of HNC are predicted to be 3822 +/- 10, 472 +/- 5, and 2051 +/- 10 cm(exp -1) for omega(sub 1), omega(sub 2), and omega(sub 3), respectively; the experimentally derived values are above these values and fall outside the estimated uncertainties. Using the quartic force field, spectroscopic constants are predicted for HNC based on a vibrational second-order perturbation theory analysis. It is also asserted that the gas-phase fundamental nu(sub 3) for HNC is slightly lower than the matrix isolation value. The range of validity of the quartic force fields is investigated by comparison of variational vibrational energies computed with the quartic force fields to those obtained from our recently reported global HCN/HNC potential energy surface and also to experimental data.

Atomic natural orbital basis sets for transition metals

We show that atomic natural orbitals are an excellent way to contract transition-metal basis sets, even though the different low-lying electronic states may have very different basis set requirements.

A theoretical study of the collinear reaction F+H 2→HF+H using multiconfigurational second-order perturbation theory (CASPT2)

The second-order perturbation method (CASPT2) with a single state multiconfigurational reference function generated in complete active self-consistent field (CASSCF) calculations has been used to compute the collinear barrier height, saddle point geometry, and exothermicity of the reaction F+H 2→HF+H. Comparison with full configuration (FCI) calculations with small basis sets shows that the CASPT2 method is capable of reproducing accurately the exact benchmark results correlating seven electrons. Large atomic natural orbital basis sets are used at the seven- and nine-electron level of correlation. With the largest ANO basis set used, F[7s6p5d4f2g]/H[6s5p4d2f], the computed nine-electron barrier height, 2.47 kcal/mol, is about 0.5 kcal/mol higher than results obtained using MRCI+Q and CCSD(T) methods employing basis sets of similar quality. The nine-electron exothermicity obtained with this basis set is 31.25 kcal/mol, about 0.5 kcal/mol below the experimental value.

Striking similarities between elementary silicon and aluminum compounds: monobridged, dibridged, trans-bent, and vinylidene isomers of aluminum hydride (Al2H2)

Ab initio quantum mechanical methods five been used to study the singlet potential energy surface of Al 2 H 2 . Optimum geometries and harmonic vibrational frequencies were obtained for four geometrical isomers using the self-consistent-field (SCF), configuration interaction (CI), and coupled cluster (CC) methods. Both correlation methods including single and double excitations (CISD, CCSD) were employed, and all wave functions were determined with both DZP and TZ2P basis sets. Final energy predictions are obtained using large atomic natural orbital basis sets, and including the effects of triple excitations perturbatively using CCSD(T) methods. We found the planar dibridged structure to be the global minimum, as predicted earlier by Baird

Towards an accurate molecular orbital theory for excited states: Ethene, butadiene, and hexatriene

A newly proposed quantum chemical approach for ab initio calculations of electronic spectra of molecular systems is applied to the molecules ethene, trans-1,3-butadiene, and trans-trans-1,3,5-hexatriene. The method has the aim of being accurate to better than 0.5 eV for excitation energies and is expected to provide structural and physical data for the excited states with good reliability. The approach is based on the complete active space (CAS) SCF method, which gives a proper description of the major features in the electronic structure of the excited state, independent of its complexity, accounts for all near degeneracy effects, and includes full orbital relaxation. Remaining dynamic electron correlation effects are in a subsequent step added using second order perturbation theory with the CASSCF wave function as the reference state. The approach is here tested in a calculation of the valence and Rydberg excited singlet and triplet states of the title molecules, using extended atomic natural orbital (ANO) basis sets. The ethene calculations comprised the two valence states plus all singlet and triplet Rydberg states of 3s, 3p, and 3d character, with errors in computed excitation energies smaller than 0.13 eV in all cases except the V state, for which the vertical excitation energy was about 0.4 eV too large. The two lowest triplet states and nine singlet states were studied in butadiene. The largest error (0.37 eV) was found for the 2 1Bu state. The two lowest triplet and seven lowest singlet states in hexatriene had excitation energies in error with less than 0.17 eV.

Thermochemistry of CHn, SiHn (n=0–4), and the cations SiH+, SiH2+, and SiH3+: A converged quantum mechanical approach

We have determined 0 K heats of formation of CHn and SiHn (n=0–4) as well as the cations SiH+, SiH2+, and SiH3+ using large atomic natural orbital basis sets and coupled cluster methods including all single, double, and (perturbatively) triple excitations [CCSD(T)]. Core-correlation effects on the bond dissociation energies have been explicitly evaluated. For the intermediate hydrides CHn and SiHn (n=1–3), heats of formation are determined from theoretical bond dissociation energies in two ways: using experimental heats of formation of the H and C (or Si) atoms; and using experimental heats of formation of the H atom and the parent hydrides CH4 (or SiH4). In principle, this procedure allows us to place rigorous upper and lower bounds on the heats of formation of the intermediate hydrides. Because our theoretically predicted atomization energies are already of high quality, estimation of remaining deficiencies in the one-particle basis sets can be obtained from extrapolation of observed trends in atomization energies upon basis set expansion. These extrapolated results are in outstanding agreement with experimental values where they are known to high accuracy. For the SiHn compounds, a serious problem occurs: our predicted atomization energy of SiH4 is larger than that obtained from experimental heats of formation for the silicon atom and silane. Thus either relativistic effects on the atomization energy of SiH4 are large, or the experimental heats of formation of Si and SiH4 are incompatible. Excepting the atomization energy of SiH4, and thus the heats of formation of Si and SiH4, none of our other SiHn thermochemical predictions (properly interpreted) are clearly incompatible with experiment. Furthermore, our theoretical predictions are again in outstanding agreement with experimental determinations that are most certain.

An extensive ab initio study of the structures, vibrational spectra, quadratic force fields, and relative energetics of three isomers of Cl2O2

The three lowest-lying isomers of Cl2O2 have been investigated using state-of-the-art ab initio quantum-mechanical methods. Electron correlation methods that have been used include second-order Mo/ller–Plesset perturbation theory, singles and doubles coupled-cluster (CCSD) theory, and the CCSD(T) method, which incorporates a perturbational estimate of the effects of connected triple excitations. Accurate relative energies have been obtained using the CCSD(T) method in conjunction with large atomic natural orbital basis sets that include up to g-type functions. Our best estimate is that the ClClO2 and ClOClO isomers lie 0.9±2.0 and 10.1±4.0 kcal/mol higher in energy (0 K), respectively, than the more stable ClOOCl peroxide form. In order to obtain accurate equilibrium geometries it is necessary to include f-type functions in the one-particle basis set. The vibrational spectra (including IR intensities) of all three isomers are computed and compared with experimental data for ClOOCl and ClClO2. The theoretical and experimental vibrational frequencies agree very well except for the symmetric combination of Cl–O stretches in ClOOCl, where it is concluded that the experimental band is most likely due to the antisymmetric Cl–O stretch. The heat of formation of ClOOCl is computed using an isodesmic reaction involving Cl2O, H2O, and HOOH, and determined to be 34.2 kcal/mol (0 K). The largest uncertainty in this value is due to potential errors in the experimental heat of formation of Cl2O. Using the experimental heat of formation of ClO, the dissociation energy of ClOOCl relative to 2 ClO is computed to be 14.9 kcal/mol at 298 K. The equilibrium structures and vibrational spectra of Cl2O, H2O, and HOOH from our highest-level calculations are found to be in excellent agreement with the available experimental data.

Ab initio multireference study of the BN molecule

The lowest 1Σ+ and 3Π states of the BN molecule have been studied using multireference configuration interaction (MRCI) and averaged coupled-pair functional (ACPF) methods and large atomic natural orbital (ANO) basis sets, as well as several coupled cluster methods. Our best calculations strongly support a 3Π ground state, but the a 1Σ+ state lies only 381±100 cm−1 higher. The a 1Σ+ state wave function exhibits strong multireference character and, consequently, the predictions of the perturbationally-based single-reference CCSD(T) coupled cluster method are not as reliable in this case as the multireference results. The best theoretical predictions for the spectroscopic constants of BN are in good agreement with experiment for the X 3Π state, but strongly suggest a misassignment of the fundamental vibrational frequency for the a 1Σ+ state.