Excited state dipole moments and geometries of the bases of nucleic acids

CNDO/s-CI and VE-PPP methods have been employed to calculate the dipole moments of the bases of nucleic acids in the ground and excited states. A component analysis in terms of μ_hyb^(σ), μ_ch and μ_π has been done using the CNDO/s-CI method and these results have been compared with those obtained by the CNDO/2 and IEHT methods. It is observed that while the CNDO/2 and CNDO/s-CI methods give almost the same total dipole moments, component-wise their predictions are very different.Dipole moments of the molecules have also been studied for the lowest excited singlet and triplet π^* ← π states. It is observed that the conventional method of calculating dipole moments using changes of only the net charges in the excited state does not give correct results for uracil and thymine, for which experimental results are available. Considering deformed non-planar excited state geometries for these molecules, the observed excited state dipole moments have been explained. A method has been suggested to include the effects of non-planarity while calculating the properties of a complex molecule in a π^* ← π excited state. For adenine, guanine and cytosine, the excited state dipole moments are found to be smaller than the ground state values.     

Perturbation theories and wave functions for calculation of electronic polarizabilities application to DNA bases

Three different forms of perturbation theories, variational perturbation, finite perturbation and second-order, are evaluated regarding their value for calculation of electronic polarizabilities of small and intermediate size molecules. It is concluded that with the practical constraint of a small basis set the variational perturbation method is the most promising alternative for calculation of polarizabilities. For several small molecules, our calculated polarizabilities indicate that both IEHT and ab initio wave functions give values in close agreement with each other. Variational perturbation calculations of polarizabilities with IEHT wave functions also include the DNA bases.     

Elastic forward scattering of high-energy electrons and molecular electron density

The elastic forward scattering of high-energy electrons from molecules has been studied in the second Born approximation. An integral transformation has been adopted to evaluate the second Born integrals analytically without explicit use of molecular wave functions. In the high-energy limit, the differential cross section for the forward scattering is expressed in terms of electric dipole and quadrupole moments, the second moment of charge distribution with respect to the molecular center, and transition dipole moments. All these quantities are shown to be computable from molecular electron densities in the ground state.     

Core model calculation of the electric field gradient: Projection operator formalism with application to NH3

A core model approach to the calculation of deuteron quadrupole coupling constants is investigated using NH₃ as an example. First the deuteron quadrupole coupling constant is calculated from a CNDO wave function. This result is subsequently improved by recomputing the N—D bond orbital by means of a variational calculation using the CNDO function to construct a core potential for the bond Hamiltonian. In order to simplify integrations a single-center basis is chosen to represent the variational wave function. A projection operator formalism is used as a computational scheme to maintain orthogonality of the bond orbital to core orbitals. Excellent agreement with experiment is obtained. The procedure is applicable to more complicated molecules.     

Atomic dipole moments calculated using analytical molecular second-moment gradients

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.     

Calculation of polarizabilities by the CNDO method

The polarizabilities of a number of small and medium size molecules are calculated using CNDO/2 wave functions. The first-order and the second-order perturbation equations are solved by variational procedures. The results are encouraging for the component along the internuclear axes and in the molecular plane. The effect of deorthogonalization of the CNDO/2 orbitals is discussed.     

Topological analysis of the molecular charge density and impact sensitivy models of energetic molecules

Important explosives of practical use are composed of nitroaromatic molecules. In this work, we optimized geometries and calculated the electron density of 17 nitroaromatic molecules using the Density Functional Theory (DFT) method. From the DFT one-electron density matrix, we computed the molecular charge densities, thus the electron densities, which were then decomposed into electric multipoles located at the atomic sites of the molecules using the distributed multipole analysis (DMA). The multipoles, which have a direct chemical interpretation, were then used to analyze in details the ground state charge structure of the molecules and to seek for correlations between charge properties and sensitivity of the corresponding energetic material. The DMA multipole moments do not present large variations when the size of the Gaussian basis set is changed; the largest variations occurred in the range 10-15% for the dipole and quadrupole moments of oxygen atoms. The charges on the carbon atoms of the aromatic ring of each molecule become more positive when the number of nitro groups increases and saturate when there are five and six nitro groups. The magnitude and the direction of the dipole moments of the carbon atoms, indicators of site polarization, also depend on the nature of adjacent groups, with the largest dipole value being for C-H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbon atoms indicates a decrease in the delocalized electron density due to an electron-withdrawing effect. Three models for sensitivity of the materials based on the DMA multipoles were proposed. Explosives with large delocalized electron densities in the aromatic ring of the component molecule, expressed by large quadrupole values on the ring carbon atoms, correspond to more insensitive materials. Furthermore, the charges on the nitro groups also influence the impact sensitivity.     

SCF Deformation densities and electrostatic potentials of purines and pyrimidines

4-31G wave functions have been computed for five purines and pyrimidines. The calculated deformation densities have been partitioned into atomic fragments, which were integrated to yield atomic multipole moments. The transferability of atomic fragments between related molecules was verified by constructing model maps for uracil and guanine from appropriate fragments of cytosine and adenine. Model electrostatic potentials calculated from the moments of model atoms are similar to the corresponding 4-31G potentials. Comparison of 4-31G and 4-31G** deformation densities of cytosine provides simple rules for estimating the effects of polarization functions on the atomic multipole moments of most atom types occurring in the purines and pyrimidines. These rules were applied to the other molecules and yielded reasonable approximations for their molecular dipole moments. Substituting CH₃ for H has little effect on the deformation density beyond the substitution center.     

A Continuum Reaction Field Theory of Polarizable, Nondipolar, Quadrupolar Solvents: Ab Initio Study of Equilibrium Solvation in Benzene

A continuum theory to describe solvation in nondipolar quadrupolar solvents is developed by accounting for electronic polarizability. A general Hamiltonian for a solute–solvent system in an arbitrary nonequilibrium configuration is obtained in terms of two field variables—densities of the solvent quadrupole and induced dipole moments. Equilibrium solvation is studied by optimizing this Hamiltonian with account of cavity boundaries. As an application, electronic structures and free energies of small molecules in benzene are examined with ab initio methods. Solvation stabilization due to solvent quadrupole moments is found to be substantial; for the solutes considered here, it is comparable to and often in excess of that arising from solvent-induced dipole moments.     

Electric polarization effects on the electronic spectral shift of centrosymmetric compounds

The classic dielectric dipolar Onsager model was extended to include quadrupolar interactions between solute molecules and solvents with different polarities. A multiparametric solvatochromic expression, based on the point quadrupole moment inside a spherical cavity embedded in a dielectric continuum, is applied to centrosymmetric sulfonamide porphyrins, zinc tetraphenyl porphyrin, squaraine and 9,10-dicyanoanthracene, in order to account for the quadrupolar polarization effect of solute molecules. The reaction field polarity functions created respectively by dipole and quadrupole moments are compared and found to be linearly correlated.     

Deorthogonalization of atomic originals in the CNDO approach

The procedure for deorthogonalization (D) of atomic orbitals in the semiempirical CNDO approach is reviewed. For comparative studies, CNDO/2, CNDO/2D, and STO -3G calculations of molecular dipole moments and Mulliken populations are carried out on 35 prototype molecules containing H, C, N, O, and F atoms. The calculated values are assessed on the basis of how well they agree with experimental trends, chemical bonding theories, and ab initio molecular orbital (MO) values. Results of analyses indicate that the CNDO/2D values for dipole moments are in reasonable agreement with experimental values, and those for net atomic charges and electron populations bear greater resemblance to the ab initio (STO -3G and 6-31G**) values than the original CNDO/2 values. These findings, together with those of previous investigators, demonstrate unequivocally the advantages of incorporating deorthogonalization into routine CNDO/2 or INDO calculations as a means to obtain reasonable estimates of charge distributions.     

An application of the CNDO/2 and INDO theories to the calculation of molecular quadrupole moments

Values of molecular quadrupole moments are calculated using the CNDO/2 and INDO methods and compared with experiment and other calculations. The agreement is good, except for π systems both linear and planar. Consideration of this disagreement suggests that use of π AO's which are less compressed perpendicular to the molecular plane or the internuclear axis may produce better results. A preliminary method of this type is adopted to obtain satisfactory theoretical results for π systems, too.     

A Hirshfeld-I interpretation of the charge distribution, dipole and quadrupole moments of the halogenated acetylenes FCCH, ClCCH, BrCCH, and ICCH

We report the dipole and quadrupole moments of the halogenated acetylenes calculated using large basis sets and the SCF, DFT(B3LYP), and CCSD methods, and we analyze the charge density using the Hirshfeld and Hirshfeld-I techniques. The atomic charges, dipoles, and quadrupoles resulting from the Hirshfeld-I analysis are used to interpret the unusually small molecular dipole moments in the sequence as well as the molecular quadrupole moments. The very small dipoles obtain for two reasons. First, the dipole moment associated with the σ and π electron densities is comparable in magnitude and opposite in direction. Second, the charge and induced dipole contributions for ClCCH, BrCCH, and ICCH have opposite signs further reducing the molecular dipoles. The molecular quadrupole moments are the sum of a charge, atomic dipole, and in situ quadrupole terms, and are dominated by the atomic dipoles and in situ quadrupoles with the charge contributions playing an unexpectedly minor role.     

On the representation of molecular quadrupole moments in terms of atomic moments

The magnitude and algebraic sign of the molecular quadrupole moments of the homonuclear diatomic molecules N2, O2, F2, P2, S2 and Cl2 are analyzed by expressing them as a sum of the quadrupole moments of the free atoms and an induced molecular quadrupole due to bond formation. This induced molecular quadrupole is further analyzed in terms of in situ atomic dipole and quadrupole moments constructed following the electron partitioning method suggested by Hirshfeld. These in situ moments are interpreted in terms of the sigma and pi character of the chemical bonds and are compared with those predicted by the DMA method of Stone (The Theory of Intermolecular Forces; Clarendon: Oxford, 1996).     

CNDO calculations of diamagnetic shielding in molecules

An approximate procedure for the calculation of diamagnetic shielding in molecules is presented. The method proposed is based on the ‘complete neglect of differential overlap’ (CNDO) molecular wave functions and is formulated according to the zero differential overlap (ZDO) approximation. The results obtained with several CNDO-type wave functions for diatomic and polyatomic molecules are in very good agreement with non-empirical SCF calculations. The ¹⁴N diamagnetic shielding constants in several molecules were computed and some approximations usually adopted in the interpretation of ¹⁴N chemical shifts are critically discussed. It was shown that in some cases the observed ¹⁴N chemical shifts cannot be interpreted solely in terms of the paramagnetic contribution to the shielding constant.     

Properties of atoms in molecules

Atomic charges calculated by the population analysis method for three types of semi-empirical wave functions have been compared with charges obtained by integrating the corresponding electronic density functions over individual atomic regions. It was found that the two sets of charges compare quite well for CNDO wave functions and for extended-Hückel functions which are in terms of orthogonalized basis orbitals. However only the CNDO charges are reasonably close to those obtained by integrating near-Hartree-Fock electronic density functions.     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

Atomic properties of selected biomolecules: quantum topological atom types of carbon occurring in natural amino acids and derived molecules

We seek to recover rigorous atom types from amino acid wave functions. The atom types emerge from a cluster analysis operating on a set of seven atomic properties, including kinetic energy, volume, population, and dipole, quadrupole, octupole, and hexadecapole moments. These properties are acquired by partitioning the molecular electron density into quantum topological atoms. Wave functions are generated at the B3LYP/6-311+G(2d,p)//HF/6-31G(d) level for a sensible conformation of each of the 20 naturally occurring amino acids and smaller derived molecules, which together constitute a data set of 57 molecules. From this set 213 unique quantum topological carbons are obtained, which are linked according to the similarity of their properties. After introducing a statistical separation criterion, our cluster analysis proposes two representations: a cruder one with 5 atom types and a finer one with 21 atom types. The immediate coordination of the central carbon plays a major role in labeling the atom types.     

Subshell fitting of relativistic atomic core electron densities for use in QTAIM analyses of ECP-based wave functions

Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in particular cases. For molecules containing atoms of any elements of the periodic table, the production of extended wave function files that include the appropriate atomic core densities for ECP-based calculations, and the use of these wave functions for QTAIM analyses, has been automated.