Atomic Natural Orbital Research Articles

A simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function.

We devise and apply a simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function. These bonding schemes are close to resonance structures drawn by chemists. Firstly, a CASSCF wave function is computed. Secondly, the CASSCF computation is repeated but now the delocalized complete active space MOs are substituted by Weinhold's localized natural atomic orbitals. In this way the original CASSCF wave function is represented by a sequence of Slater determinants composed of localized natural atomic orbitals. Thus, a standard CASSCF wave function can be reinterpreted in terms of a local picture. To test the method we obtain localized bonding schemes and their weights for the ground and the pi-pi* excited state of ethylene. Moreover, bonding schemes and their weights are derived for the ground, the 1(1)B(u), and the 2(1)Ag pi-pi* excited states of trans-butadiene. The large weight bonding schemes are shown to be a qualitative indicator for the known photochemistry of butadiene. The remarkable stability of the Arduengo carbene is discussed by obtaining bonding schemes that indicate a stabilizing delocalization of the pi electrons. We illustrate that the large weight bonding schemes are in line with the observed reactivity of the Arduengo carbene.

The low-lying excited states of 2,2'-bithiophene: a theoretical analysis.

The low-energy region of the singlet-->singlet, singlet-->triplet, and triplet-->triplet electronic spectra of 2,2'-bithiophene are studied using multiconfigurational second-order perturbation theory (CASPT2) and extended atomic natural orbitals (ANO) basis sets. The computed vertical, adiabatic, and emission transition energies are in agreement with the available experimental data. The two lowest singlet excited states, 1(1)Bu and 2(1)Bu, are computed to be degenerate, a novel feature of the system to be borne in mind during the rationalization of its photophysics. As regards the observed high triplet quantum yield of the molecule, it is concluded that the triplet states 2(3)Ag and 2(3)Bu, separated about 0.4 eV from the two lowest singlet excited states, can be populated by intersystem crossing from nonplanar singlet states.

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be2).

Theoretical Study of Chlorine Nitrates: Implications for Stratospheric Chlorine Chemistry.

Reported here is a theoretical study of possible stratospheric chlorine reservoir species including isomers of chemical formula ClNO(4) and ClNO(5), in addition to the well-known ClONO(2) reservoir species. Density functional theory (DFT) in conjunction with large one-particle basis sets has been used to determine equilibrium structures, dipole moments, rotational constants, harmonic vibrational frequencies, and infrared intensities. The B3LYP functional was used since it has previously been shown to perform well for similar compounds. The equilibrium geometry and vibrational spectra of ClONO(2) are shown to be in good agreement with the experimental data and also with high-level coupled-cluster calculations reported previously. Three stable isomers have been identified for each ClNO(4) and ClNO(5). The vibrational spectrum of O(2)ClONO(2) has been compared with the available experimental data and found to be in good agreement. The relative energetics of the ClNO(4) and ClNO(5) isomers have been determined using large atomic natural orbital (ANO) basis sets in conjunction with the singles and doubles coupled-cluster method that includes a perturbational correction for triple excitations, denoted CCSD(T). Accurate heats of formation have been evaluated by computing energies for isodesmic reactions involving the ClNO(4) and ClNO(5) isomers. The stability of these molecules with respect to thermal dissociation is examined. The present study suggests that isomers of ClNO(4) and ClNO(5) may have no atmospheric chemical relevance because the atmospheric concentrations of the necessary reactants are insufficient, but it is also found that under laboratory conditions the formation of O(2)ClONO(2) cannot be ignored.

Relativistic correlating basis sets for the main group elements from Cs to Ra

Contracted Gaussian-type function sets are developed for correlating functions of the ten main group elements from Cs to Ra. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals or K-orbitals, incorporating the relativistic effect by the third-order Douglas–Kroll approximation. The present basis sets yield more than 98% of atomic correlation energies predicted by accurate natural orbitals of the same size. The use of the present set with the model core potential methods gives more than 99% of the correlation energies obtained by the atomic natural orbitals optimized for the model core potential itself. The present correlating sets applied to relativistic model core potential methods including spin–orbit effects predict the spectroscopic constants of the BiH molecule in excellent agreement with experimental results.

Theoretical Analysis of the Excited States in Maleimide

The electronic excited states of maleimide have been studied using multiconfigurational second-order perturbation theory in its multistate formulation (MS-CASPT2) and extended atomic natural orbital (ANO) basis sets. The calculation of the singlet−singlet and singlet−triplet transition energies comprises 10 valence singlet excited states, four valence triplet states, and the singlet 3s, 3p, and 3d members of the Rydberg series converging to the first four ionization limits. The main features of the absorption spectrum correspond to the 11A1 → 11A2(nπ*), 11A1 → 11B2(ππ*), and 11A1 → 21B2(ππ*) transitions computed at 3.29, 4.44, and 5.59 eV, respectively. The latter corresponds to the most intense band. The lowest Rydberg state is found to be at 5.98 eV in the high-energy side of the main band. A number of additional features are predicted in the higher-energy region of the spectrum, and our assignments follow the same trends as those offered earlier by Robin for N-methyl maleimide. The lowest triplet state is computed of nπ* character in vacuo. However, arguments are given to rationalize the observed phosphorescence of maleimide in solution as being mainly of ππ* nature.

Theoretical study of chlorine nitrates: implications for stratospheric chlorine chemistry.

Reported here is a theoretical study of possible stratospheric chlorine reservoir species including isomers of chemical formula ClNO(4) and ClNO(5), in addition to the well-known ClONO(2) reservoir species. Density functional theory (DFT) in conjunction with large one-particle basis sets has been used to determine equilibrium structures, dipole moments, rotational constants, harmonic vibrational frequencies, and infrared intensities. The B3LYP functional was used since it has previously been shown to perform well for similar compounds. The equilibrium geometry and vibrational spectra of ClONO(2) are shown to be in good agreement with the experimental data and also with high-level coupled-cluster calculations reported previously. Three stable isomers have been identified for each ClNO(4) and ClNO(5). The vibrational spectrum of O(2)ClONO(2) has been compared with the available experimental data and found to be in good agreement. The relative energetics of the ClNO(4) and ClNO(5) isomers have been determined using large atomic natural orbital (ANO) basis sets in conjunction with the singles and doubles coupled-cluster method that includes a perturbational correction for triple excitations, denoted CCSD(T). Accurate heats of formation have been evaluated by computing energies for isodesmic reactions involving the ClNO(4) and ClNO(5) isomers. The stability of these molecules with respect to thermal dissociation is examined. The present study suggests that isomers of ClNO(4) and ClNO(5) may have no atmospheric chemical relevance because the atmospheric concentrations of the necessary reactants are insufficient, but it is also found that under laboratory conditions the formation of O(2)ClONO(2) cannot be ignored.

Theoretical Determination of the Singlet → Singlet and Singlet → Triplet Electronic Spectra, Lowest Ionization Potentials, and Electron Affinity of Cyclooctatetraene

The singlet → singlet and singlet → triplet electronic spectra of cycloocta-1,3,5,7-tetraene are studied using multiconfigurational second-order perturbation theory (CASPT2) and extended atomic natural orbitals (ANOs) basis sets. The observed dipole-allowed features at 4.43, 6.02, and 6.42 eV and the spin-forbidden singlet → triplet bands with maxima at 3.05, 4.05, and 4.84 eV (Frueholz, R. P.; Kuppermann, A. J. Chem. Phys. 1978, 69, 3614) are assigned as the transitions 11A1 → 11A2, 11A1 → 21B2(3pz), 11A1 → 31E, and 11A1 → 13A2, 11A1 → 13E, 11A1 → 13B1, respectively. The lowest (3s) Rydberg singlet and triplet states are placed at 5.58 (21A1) and 5.54 (13A1) eV. New assignments are tentatively suggested for the recorded higher-energy peaks in the singlet manifold. The three lowest ionization potentials are also characterized. At the highest level of theory, the computed adiabatic electron affinity is 0.56 eV, in agreement with experimental determinations. As regards the role of cyclooctatetraene as an efficient triplet quencher of laser dye solutions, the computation supports it could act as acceptor with donors having a triplet excited-state energy equal to or higher than 0.8 eV.

Acrylonitrile (AN)–Cu9(100) interfaces: Electron distribution and nature of bonded interactions

There is a fundamental interest in the investigation of the interfacial interactions and charge migration processes between organic molecules and metallic surfaces from a theoretical standpoint. Quantum mechanical (QM) concepts of bonding are contrasted, and the vital importance of using combined QM methods to explore the nature of the interfacial interactions is established. At the one-electron level, the charge distribution and nature of bonded interactions at the AN–Cu9(100) (neutral and charged (–1)) interfaces are investigated by both the Becke (B) – Vosko (V) – Wilk (W) – Nusair (N)/DZVP density functional theory (DFT) method and the MP2/6–31+G* strategy within the conceptual framework provided by natural bond orbital (NBO) – natural atomic orbital (NAO) population analysis and Atoms-In-Molecules (AIM) theory. By this approach, the interfacial interactions are given physical definitions free of any assumptions and are visualized by using the topological features of the total electron density. A natural link between the electron density on the one side and the shapes (not energies) of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) on the other side is clarified. The question of whether the spatial extents of the HOMO and LUMO resemble the corresponding spatial maps of the negative (charge locally concentrated) and positive (charge locally depleted) Laplacian of the total electron density in [AN–Cu9(100)]–1 is addressed.Key words: AN–Cu9(100) interfaces, NBO–NAO population, electron distribution, AIM, bonded interactions.

The Transoid, Ortho, and Gauche Conformers of Decamethyl-n-tetrasilane, n-Si4Me10: Electronic Transitions in the Multistate Complete Active Space Second-Order Perturbation Theory Description

Multistate complete active space second-order perturbation theory (MS-CASPT2) is used to improve earlier descriptions of the low-energy valence excited states of the transoid, ortho, and gauche conformers of decamethyl-n-tetrasilane, n-Si4Me10, using a generally contracted basis set of atomic natural orbitals (ANOs) at a ground-state geometry optimized in the second-order Møller−Plesset perturbation theory (MP2) approximation with Dunning's correlation consistent triple-ζ basis set (cc-pVTZ) on the silicon atoms and the 6-31G* and 6-31G basis sets on the carbon and hydrogen atoms, respectively. Relative energies, relative free energies, and mole fractions of the transoid, ortho, and gauche conformers are reported at various temperatures. CASPT2 ionization potentials for the three conformers are calculated and found to agree with photoelectron spectra. The first eight valence excited states of each conformer are computed and analyzed in terms of natural orbitals. Most of the important excitations are due to electron promotions from the σ1 HOMO orbital. However, in the ortho and gauche conformers, promotions from the σ2 HOMO-1 orbital play a significant and previously unrecognized role. The MS-CASPT2 simulation of the low-energy region of the absorption spectra of the transoid, ortho, and gauche conformers agrees with the UV absorption spectrum of the transoid conformer of n-Si4Me10 and with the conformationally constrained models of the ortho and gauche tetrasilanes, MeSi[(CH2)5]2Si−Si[(CH2)5]2SiMe and (SiMe2)4(CH2)3, respectively. The UV absorption spectra of n-Si4Me10 conformer equilibrium mixtures at room temperature and 77 K are interpreted. An analysis of the dependence of the nature of electronic excitation on the skeletal dihedral angle confirms the main features of the previously developed picture, which described it in terms of avoided crossings of both B and A symmetry states. These cause the states to interchange their σσ* and σπ* character upon going between the two planar limits, syn and anti. However, the new results show that at small dihedral angles the situation is more complicated because of additional avoided crossings.

Comparing electron (de)localization in the through benzene and anthracene charge transfer

Abstract The contrasting behavior of benzene and anthracene in the through π-system passing of a (+) charge is examined by considering para -diethynylbenzene and para -diethynylanthracene spacers. The (de)localization of their bonds in both neutral and cationic forms are compared by means of a two-electron population analysis; the electron-pair distributions are calculated in orbital spaces appropriate for population analysis, as the natural atomic orbitals, in which two-electron correlations are also investigated. When the spacer involves benzene, then its oxidation causes a re-organization of electron pairs towards a pronounced quinoid bond (de)localization, which induces analogous bond deformations; on the contrary, in the case of anthracene, a similar quinoid (de)localization (and the corresponding bond deformation) is impeded, due to the possibility of additional delocalization on its central ring. As shown, these electron-pair re-organizations are the ‘driving force’ for the corresponding geometrical deformations.

Vertical spectrum of the C2H2+ system. An open shell (SC)2-CAS-SDCI study.

The open shell (SC)(2)-CAS-SDCI method along with a basis set of atomic natural orbitals (ANO) has been applied for calculating the main ionization potentials of acetylene, as well as the manifold of excited states of the different symmetries up to 32 eV. In this method, the single and double excitations of a CAS space are generated and the corresponding CI matrix is corrected by means of the (SC)(2) procedure that cancels the size-extensivity error and adds some high order contributions. The mean absolute error for the outer-valence X (2)Pi(u)(1pi(u) (-1)), A (2)Sigma(g) (+)(3sigma(g) (-1)), and B (2)Sigma(u) (+)(2sigma(u) (-1)) states, and the inner-valence C (2)Sigma(g) (+)(2sigma(g) (-1)) state is 0.1 eV. The excited states of C(2)H(2) (+) corresponding to the Sigma(g) (+), Sigma(u) (+), Pi(g), Pi(u), Delta(g), and Delta(u) symmetries are reported and their composition is discussed. The results are thoroughly compared to the best available multireference CI calculations. Recent multichannel CI results by Wells and Lucchese [J Chem Phys 1999, 110, 6365] have been used also as a guide for the discussion of the results. Discrepancies in the description of many multiconfigurational states by means of the (SC)(2)-CAS-SDCI wave function as compared to previous large MR-CI calculations are significant and are, consequently, remarked on. A large mixing of the 3sigma(g) (-1) and 2sigma(g) (-1) processes is found in the A (2)Sigma(g) (+) and C (2)Sigma(g) (+) states, provided that the basis set is augmented with Rydberg functions.

The vertical spectrum of H2CO revisited: (SC)2-CI and CC calculations

The vertical electronic spectrum of formaldehyde has been studied by means of (SC)2-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchán, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the 2B2 state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)2 dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is satisfactory, in spite of the remarkable reduction in the CI space dimension. The consistency of the (SC)2-MR-SDCI results was tested also against the CCLR and CASPT2 results using the same basis sets and against the CCLR results using Dunning's aug- and daug-cc-pVQZ basis sets. The 3A1(π → π *) state is correctly placed as the second excited triplet while the highly multi-configurational nature of the 1A1(π → π *) state is confirmed as well as its greatly mixed valence-Rydberg nature. This state is predicted as lying under the 10 eV level, on top of the (ny → 3d) Rydberg states that are predicted in the 8.9–9.5eV region. The 5 1B2(ny → 4s) Rydberg state and the 1B2(σy → π*) also are predicted in this region. The triplet states also were calculated with the (SC)2-MR-SDCI method. The vertical ordering of the 2 1A1(ny → 3py) and 2 1B2(ny → 3pz) states is discussed, as well as that of the 1B1(σ → π*) and the Rydberg 1B1(ny → 3dxy) states. This work shows the highly reliable values that may be reached applying the dressing method along with a large basis set. Such a procedure is made possible using an MR-SDCI selection of spaces instead of the CAS-SDCI that was used up to now in most (SC)2 dressing applications.

Valence and correlating basis sets for the second transition-metal atoms from Y to Cd

Contracted Gaussian-type function sets are developed for the valence 5s and 4d orbitals and for correlating functions of the second transition-metal atoms Y through Cd. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation of the target function from the average of accurate atomic natural orbitals for the three lowest LS states arising from the 5s24d n-2, 5s1 4d n-1, and 5s0d n configurations. The present basis sets give a well balanced description for the three configurations at the Hartree—Fock level, and yield more than 97% of the atomic correlation energies predicted by accurate natural orbitals of the same size.

A comparison of polarized double-zeta basis sets and natural orbitals for full configuration interaction benchmarks

We compare several standard polarized double-zeta basis sets for use in full configuration interaction benchmark computations. The 6-31G**, DZP, cc-pVDZ, and Widmark–Malmqvist–Roos atomic natural orbital (ANO) basis sets are assessed on the basis of their ability to provide accurate full configuration interaction spectroscopic constants for several small molecules. Even though highly correlated methods work best with larger basis sets, predicted spectroscopic constants are in good agreement with experiment; bond lengths and harmonic vibrational frequencies have average absolute errors no larger than 0.017 Å and 1.6%, respectively, for all but the ANO basis. For the molecules considered, 6-31G** gives the smallest average errors, while the ANO basis set gives the largest. The use of variationally optimized basis sets and natural orbitals are also explored for improved benchmarking. Although optimized basis sets do not always improve predictions of molecular properties, taking a DZP-sized subset of the natural orbitals from a singles and doubles configuration interaction computation in a larger basis significantly improves results.

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

AbstractA recently proposed perturbational approach to the electron correlation cusp problem Sirbu, I.; King, H. F. J Chem Phys 2002, 117, 6411–6416 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Relativistic correlating basis functions for the Ga–Kr, In–Xe, and Tl–Rn atoms

Generally contracted Gaussian-type function sets were developed for relativistic correlating functions of the Ga–Kr, In–Xe, and Tl–Rn atoms using an atomic natural orbital (ANO) approach. The ANOs were constructed based on configuration interaction calculations of the ground states of respective atoms including the major relativistic effects through model core potentials (MCPs). Both atomic and molecular applications are presented. The use of the present basis sets in conjunction with the MCPs gave the excitation energies, ionization potentials, and electron affinities in good agreement with the observed values for several atoms. The spectroscopic constants of the TlH molecule yielded by relativistic MCP calculations including spin–orbit effects were in excellent agreement with the experimental results.

Multiconfigurational second-order perturbation calculation of the electronic absorption spectrum of trisilane, Si3H8

The low-lying singlet excited states of trisilane have been computed using the complete active space self-consistent field (CASSCF) method, second-order perturbation theory (CASPT2), and the extended multistate CASPT2 (MS-CASPT2) approach, and a generally contracted basis set of atomic natural orbitals (ANOs) including Rydberg functions. The ground state structure was obtained from an ab initio optimization at the second-order Møller-Plesset perturbation theory (MP2) level using Dunning's correlation-consistent triple-zeta basis set (cc-pVTZ) and agrees well with experiment. The calculation of the electronic transitions included the lower valence excited states and two Rydberg series converging to the first two ionization potentials. Only the MS-CASPT2 method gave an accurate description of the observed electronic excitations since it provided an effective separation of the valence and Rydberg states. In contrast with previous assignments, three states of valence character were found below the first Rydberg state, located at 7.20eV. As a consequence, the first broad band observed in the spectrum is entirely of valence character. Vertical dipole-allowed valence transition energies are calculated at 6.55, 7.09, 7.32, 7.60, 8.07 and 8.18eV (excitations to 11B2, 21A1, 31A1, 11B1, 51B2 and 21B1, states, respectively). Two vertical dipole-forbidden valence transitions assigned to the 11A2 and 41A2 states are found at 6.89 and 8.52eV, respectively. The 4s, 4p and 3d members of the Rydberg series converging to the first and second ionization potentials are found at 7.20–8.62 eV and 7.82–9.61 eV, respectively. A detailed theoretical interpretation of the absorption spectrum of trisilane based on the new assignments has been proposed, and comments on the ability of the CASSCF, CASPT2 and MS-CASPT2 approaches to describe accurately the absorption spectrum of oligosilanes are made.

Electronic Spectra of 2,2‘-Bithiophene and 2,2‘:5‘,2‘ ‘-Terthiophene Radical Cations: A Theoretical Analysis

Analysis of the electronic spectra of 2,2‘-bithiophene and 2,2‘:5‘,2‘ ‘-terthiophene radical cations has been performed by using multiconfigurational second-order perturbation theory (CASPT2). Atomic natural orbital (ANO) type basis sets of split valence quality, including polarization functions on all heavy atoms, have been used. In agreement with experimental data, in the energy range below the lowest optically allowed transition of the respective neutral system, theoretical results predict two main absorption bands for both cations. The 22Au and 32Au states computed at 1.94 and 2.80 eV, respectively, are related to the corresponding band maxima recorded for bithiophene cation. The 12B1 state of terthiophene cation placed at 1.31 eV is assigned to the observed lowest-energy band. Nevertheless, according to the present results, the highest-energy band observed in terthiophene cation stems from two electronic transitions. They involve the 22B1(1.94 eV) and 32B1(2.12 eV) excited states.

Contracted polarization functions for the atoms Ca, Ga-Kr, Sr, and In-Xe

Contracted Gaussian-type function sets are proposed for polarization functions of the atoms Ga–Kr and In–Xe. We also report polarization functions for Ca and Sr. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are fully optimized to minimize the deviation from accurate atomic natural orbitals. The present polarization functions yield more than 99% of atomic correlation energies predicted by accurate natural orbitals of the same size.