Atomic Natural Orbital Research Articles

Electronic spectrum of F2CO: theoretical calculations of vertical excitation energies and intensities

In this work, the linear response formalism with a triples-corrected CCSD reference wave function, LR-CCSDR(3), is applied to the calculation of vertical excitation energies of singlet states of the F2CO molecule. A basis set of atomic natural orbitals augmented with a series of Rydberg functions has been used in the calculations. A large number of electronically excited states were calculated, and the valence, Rydberg, or mixed character of the states were investigated. In addition, the molecular quantum defect orbital (MQDO) method has been used to determine transition intensities involving Rydberg states. Excitation energies and transition intensities for Rydberg states with n > 3 are reported for the first time.

Björn O. Roos (1937-2010)

Björn O. Roos (1937-2010)

Cl-loss and F-loss dissociations in low-lying electronic states of the [formula omitted] ion studied using multiconfiguration second-order perturbation theory

Complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with an atomic natural orbital (ANO-L) basis were performed for Cl- and F-loss dissociations of the CF 2 Cl 2 + ion in the 1 2B 2 (X 2B 2), 1 2A 2, 1 2B 1, and 1 2A 1 states. The electronic states of the CF 2Cl + and CF Cl 2 + ions produced by Cl-loss and F-loss dissociation, respectively, were carefully determined. Our predicted appearance potential values are in good agreement with experimental findings for CF 2Cl + (X 1A 1) and CF Cl 2 + (X 1A 1).

Origin and Nature of Transmission Modes of Anomalous Effects of meta-Substituents on the 13C Chemical Shift of the Carboxyl Carbon (δCO) of Benzoic Acid

Studies of substituent effects on NMR chemical shifts are of great benefit in determining fine details of electron distribution in molecules. Interestingly, NMR substituent effects are often different and even opposite to those associated with chemical reactivity. Among molecules exhibiting anomalous (reverse) substituent effects is benzoic acid, the standard model for studying substituent effects. The substituent effect on the 13C chemical shift of its carboxyl carbon (δ CO) is just the opposite of that on its acid strength or reactivity. To develop insights into the origin of the anomalous effect of a substituent on δ CO, occupancies of natural atomic orbitals at the carboxyl and ring carbons of a set of 10 meta-substituted benzoic acids have been calculated at the density functional theory level using the B3LYP function with split valance 6–311G++** basis set. Statistical correlations obtained for the 13C chemical shifts, δ CO and δ C-ring of these benzoic acids with the natural atomic orbital occupancies calculated for respective carbon atoms on one hand and with Taft’s inductive and resonance parameters (σ I and σ R BA ) of the substituents on the other hand have been critically analyzed. The findings have established firmly that a meta-substituent’s anomalous effect on δ CO is caused by the substituent-induced changes in the total occupancy of only the p z natural atomic orbitals at the carboxyl carbon. The study has demonstrated further that the transmission of the anomalous effect can be successfully interpreted by a 5.5:–2.5:1 combination of the localized, extended, and resonance-induced π-polarization effects.

Molecular acidity: A quantitative conceptual density functional theory description

Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar.

Theoretical study on HBO+ and HOB+ cations using multiconfiguration second‐order perturbation theory

The HBO(+) and HOB(+) cations have been reinvestigated using the CASSCF and CASPT2 methods in conjunction with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points in the potential energy surfaces were optimized at the CASSCF/ANO and CASPT2/ANO levels. The ground and the first excited states of HBO(+) are predicted to be X(2)Pi and A(2)Sigma(+) states, respectively. It was predicted that the ground state of HOB(+) is X(2)Sigma(+) state. The A(2)Pi state of HOB(+) has unique imaginary frequency. A bending local minimum M1 was found for the first time along the 1(2)A'' potential energy surface and the A(2)Pi state of HOB(+) should be the transition state of the isomerization reactions for M1<--> M1. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions were calculated as functions of the HBO bond angle. Many of the CASSCF and CASPT2 calculated results were different from the previously published QCISD(T) results.

Theoretical prediction on HBeN− and HNBe− anions using multiconfiguration second-order perturbation theory

The HBeN− and HNBe− anions have been investigated for the first time using the CASSCF, CASPT2, and DFT/B3LYP methods with the contracted atomic natural orbital (ANO) and cc-pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces were optimized at the CASSCF/ANO and B3LYP/cc-pVTZ levels. The ground and the first excited states of HBeN− are predicted to be X2Π and A2Σ+ states, respectively. It was predicted that the ground state of HNBe− is X2Σ+ state. The A2Π state of HNBe− has unique imaginary frequency. A bend local minimum M1 was found along the 12A″ potential energy surface and the A2Π state of HNBe− should be the transition state of the isomerization reactions for M1 ↔ M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HBeN bond angle. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Shannon information entropy of fractional occupation probability as an electron correlation measure in atoms and molecules

A new method to determine electron correlation energy is presented for atoms and molecules. This method is based on Shannon information entropy that is obtained by fractional occupation probabilities of natural atomic orbitals. It is indicated that the Shannon entropy increases as the number of electrons increases and thus can be considered as a possible measure for the electron correlation in atomic and molecular systems. For neutral atoms and singly charged positive ions we proposed an expression for correlation energy with explicit dependence on the Shannon entropy and atomic number. The obtained correlation energies have been used to compute the first ionization potentials of the ground state of the main group elements from hydrogen through krypton. The calculated ionization potentials are in reasonably good agreement with their corresponding experimental values.We also developed the additivity scheme to find a connection between Shannon entropy and molecular correlation energy. The estimated molecular correlation energies show an excellent agreement with those obtained by elaborate G3 method with R2=0.990.

An efficient generalized polyelectron population analysis in orbital spaces: The hole-expansion methodology

We present relations leading to an efficient generalized population analysis in orbital spaces of usual delocalized molecular orbital wave functions. Besides the calculation of the diagonal elements of the reduced density matrices of any order, one can also calculate efficiently the probabilities (or, in general, the weights) of various occupation schemes of local electronic structures, by using generalized density operators referring to both electrons and electron holes. Within this population analysis, correlated molecular orbital wave functions can be used, and there are no restrictions to the number of the analyzed electrons and electron holes. It is based on the hole-expansion methodology, according to which a given electronic population is expanded in terms involving only electron holes, which as shown, can be calculated very efficiently; usual difficulties arising from the necessity to handle extremely large local determinantal basis sets are avoided, without introducing approximations. Although an emphasis is given for populations in the basis of orthogonal orbital spaces (providing probabilities), the case of nonorthogonal ones is also considered in order to show the connection of the generalized populations and the traditional weights obtained from valence-bond wave functions. Physically meaningful populations can be obtained by using natural orbitals, such as the natural atomic orbitals (NAOs) (orthogonal orbitals) or the pre-NAO's (nonorthogonal orbitals); numerical applications for pyrrole molecule are presented in the basis of these natural orbitals.

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.

Estimation of Molecular Acidity via Electrostatic Potential at the Nucleus and Valence Natural Atomic Orbitals

An effective approach of estimating molecular pK(a) values from simple density functional calculations is proposed in this work. Both the molecular electrostatic potential (MEP) at the nucleus of the acidic atom and the sum of valence natural atomic orbitals are employed for three categories of compounds, amines and anilines, carbonyl acids and alcohols, and sulfonic acids and thiols. A strong correlation between experimental pK(a) values and each of these two quantities for each of the three categories has been discovered. Moreover, if the MEP is subtracted by the isolated atomic MEP for each category of compounds, we observe a single unique linear relationship between the resultant MEP difference and experimental pK(a) data of amines, anilines, carbonyl acids, alcohols, sulfonic acids, thiols, and their substituents. These results can generally be utilized to simultaneously estimate pK(a) values at multiple sites with a single calculation for either relatively small molecules in drug design or amino acids in proteins and macromolecules.

Estimation of Molecular Acidity via Electrostatic Potential at the Nucleus and Valence Natural Atomic Orbitals

Estimation of Molecular Acidity via Electrostatic Potential at the Nucleus and Valence Natural Atomic Orbitals

Theoretical study on HBC− and HCB− anions using multiconfiguration second‐order perturbation theory

AbstractThe HBC− and HCB− anions have been studied using the complete active space self‐consistent field, CASPT2, and DFT/B3LYP methods with the contracted atomic natural orbital (ANO) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces were optimized at the CASSCF/ANO and B3LYP/cc‐pVTZ levels. The ground state of HBC− is predicted to be X2ϕ state, which is different from the previously published results. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions were calculated as a function of HBC bond angle and the PECs also show the 2ϕ state is the ground state of HBC− anion. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

New Relativistic Atomic Natural Orbital Basis Sets for Lanthanide Atoms with Applications to the Ce Diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess 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 ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are included as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.

Extracting Covalent and Ionic Structures from Usual Delocalized Wave Functions: The Electron-Expansion Methodology

We present easily programmable expansions, allowing the calculation of the weights of local covalent and ionic structures of a chemical bond from usual delocalized wave functions; they are obtained in the framework of the electron-expansion methodology, in which the hole conditions (involved by definition in a covalent or ionic structure) are expanded in terms involving only electrons. From the derived relations, true for both HF and correlated levels, one can also express the covalency/ionicity and the localization of a usual two-electron two-center (2e/2c) bond in terms of electronic populations. The three-electron populations are crucial for bond localization. On the contrary, in 2e/2c bonding, and particularly in Charge-Shift bonds (which show enhanced covalent-ionic interactions) although the three-electron populations can be non-negligible, they are not important for the covalency/ionicity of these bonds. Numerical applications and discussion are given for correlated MO wave functions of butadiene, hexatriene, and pyrrole molecules on the basis of both natural atomic orbitals (NAOs) (orthogonal orbitals) and pre-NAOs (nonorthogonal orbitals).

Full configuration interaction calculation of BeH adiabatic states

An all-electron full configuration interaction (FCI) calculation of the adiabatic potential energy curves of some of the lower states of BeH molecule is presented. A moderately large ANO basis set of atomic natural orbitals (ANO) augmented with Rydberg functions has been used in order to describe the valence and Rydberg states and their interactions. The Rydberg set of ANOs has been placed on the Be at all bond distances. So, the basis set can be described as 4s3p2d1f3s2p1d(BeH)+4s4p2d(Be). The dipole moments of several states and transition dipole strengths from the ground state are also reported as a function of the R(Be-H) distance. The position and the number of states involved in several avoided crossings present in this system have been discussed. Spectroscopic parameters have been calculated from a number of the vibrational states that result from the adiabatic curves except for some states in which this would be completely nonsense, as it is the case for the very distorted curves of the 3s and 3p (2)Sigma(+) states or the double-well potential of the 4p (2)Pi state. The so-called "D complex" at 54 050 cm(-1) (185.0 nm) is resolved into the three 3d substates ((2)Sigma(+),(2)Pi,(2)Delta). A diexcited valence state is calculated as the lowest state of (2)Sigma(-) symmetry and its spectroscopic parameters are reported, as well as those of the 2 (2)Delta (4d) state The adiabatic curve of the 4 (2)Sigma(+) state shows a swallow well at large distances (around 4.1 A) as a result of an avoided crossing with the 3 (2)Sigma(+) state. The probability that some vibrational levels of this well could be populated is discussed within an approached Landau-Zerner model and is found to be high. No evidence is found of the E(4ssigma) (2)Sigma(+) state in the region of the "D complex". Instead, the spectroscopic properties obtained from the (4ssigma) 6 (2)Sigma(+) adiabatic curve of the present work seem to agree with those of the experimental F(4psigma) (2)Sigma(+) state. The FCI calculations provide benchmark results for other correlation models for the open-shell BeH system and evidence both the limitations and capabilities of the basis set.

Density Functional and Basis Set Dependence of Hydrated Ln(III) Properties

Benchmark studies of Ln(H2O)1,8-9(3+) (Ln = La, Lu) have been performed to assess the calculated properties obtained with local density approximation, generalized gradient approximation (GGA), meta-GGA, and hybrid functionals, when used with small- and large-core relativistic effective core potentials and their associated bases. Basis set dependence and the importance of specific functions to adequately describe the Ln atomic orbitals have been determined. The lanthanide contraction has been found to be an insufficient metric for characterizing the quality of a method/basis set combination due to cancellation of the errors. The electrostatic description obtained by natural population analysis has been examined, and an alternative partitioning of the valence space, which includes the 6s6p5d4f natural atomic orbitals, has been proposed.

”Developing paradigms of chemical bonding: adaptive natural density partitioning

A method of description of the chemical bonding combining the compactness and intuitive simplicity of Lewis theory with the flexibility and generality of canonical molecular orbital theory is presented, which is called adaptive natural density partitioning. The objects of chemical bonding in this method are n-center 2-electron bonds, where n goes from one (lone-pair) to the maximum number of atoms in the system (completely delocalized bonding). The algorithm is a generalization of the natural bonding orbital analysis and is based on the diagonalization of the blocks of the first-order density matrix in the basis of natural atomic orbitals. The results obtained by the application of the algorithm to the systems with non-classical bonding can be readily interpreted from the point of view of aromaticity/antiaromaticity concepts. The considered examples include Li4 cluster and a family of planar boron clusters observed in molecular beams.

The role of ionic structures in the response of a non-polar molecule to an electric field

Going beyond one- and two- electron distributions, we investigate the behavior of ionic structures of chemical bonds, and the role that play in the response of a non-polar molecule to an electric field. We use as model non-polar molecule the cis-butadiene, and we examine the behavior of its ionic structures with respect to a longitudinal and a perpendicular electric field direction. The probabilities (weights) of various types of ionic structures are estimated by means of poly-electron population analysis in the basis of natural atomic orbitals, and their behavior is explained and rationalized by means of a Field Component Analysis. The electric field polarizes the bond dipoles according to its direction, and in this framework, the relative orientations of these local dipoles, which can be favorable or unfavorable to the chemical bonding, control the overall response of the molecular system to the external stimulus.

Theoretical study of the electronic structure of HXY/XYH radicals (XC,Si;YO,S)

The electronic structures of the HXY/XYH compounds (X[Double Bond]C,Si;Y[Double Bond]O,S) on the (2)A(') electronic ground state were investigated by applying the natural bond orbital (NBO) method to the computed B3LYP6-311G(**) wave functions. Different localized structures are proposed for the HXY and XYH isomers and the central XY unit is described as intermediate between a double and a triple bond in HCO, HCS, HSiO, and HSiS, similar to a double bond in COH, CSH, and SiSH, and clearly a single bond in SiOH. Through the comparison between the NBO results for the diatomic and hydrogenated compounds, the energy preferences on each pair of isomers and the computed geometrical parameters are explained. According to the structures proposed, the HXY compounds are sigma radicals with the spin density distributed along the molecular framework, while the XYH compounds are pi radicals with most of the unpaired spin located on an almost pure p orbital of the X atom. Finally, the amounts of spin density on natural atomic orbitals provided by the NBO method are used to explain the computed values of the isotropic and anisotropic hyperfine coupling constants.