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.     

Atomic Properties of Amino Acids: Computed Atom Types as a Guide for Future Force‐Field Design

The quantum chemical topology (QCT) is able to propose atom types by direct computation rather than by chemical intuition. In previous work, molecular electron densities of 20 amino acids and smaller derived molecules were partitioned into a set of 760 topological atoms. Each atom was characterised by seven atomic properties and subjected to cluster analysis element by element, that is, C, H, O, N, and S. From the respective dendrograms, 21 carbon atom types were distinguished, 7 hydrogen, 2 nitrogen, 6 oxygen, and 6 sulfur atom types. Herein, we contrast the QCT atom types with those of the assisted model building with energy refinement (AMBER) force field. We conclude that in spite of fair agreement between QCT and AMBER atom types, the latter are sometimes underdifferentiated and sometimes overdifferentiated. In summary, we suggest that QCT is a useful guide in designing new force fields or improving existing ones. The computational origin of QCT atom types makes their determination unbiased compared to atom type determination by chemical intuition and a priori assumptions. We provide a list of specific recommendations.     

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.     

Analytical method for the representation of atoms-in-molecules densities

We present analytic refinements and applications of the deformed atomic densities method [Fernández Rico, J.; López, R.; Ramírez, G. J Chem Phys 1999, 110, 4213-4220]. In this method the molecular electron density is partitioned into atomic contributions, using a minimal deformation criterion for every two-center distributions, and the atomic contributions are expanded in spherical harmonics times radial factors. Recurrence relations are introduced for the partition of the two-center distributions, and the final radial factors are expressed in terms of exponential functions multiplied by polynomials. Algorithms for the practical implementation are developed and tested, showing excellent performances. The usefulness of the present approach is illustrated by examining its ability to describe the deformation of atoms in different molecular environments and the relationship between these atomic densities and some chemical properties of molecules.     

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.     

An ab initio evaluation of the role of p,π interaction: II. Molecules of the CH3COX series

The RHF/6-311G(d) and MP2/6-311G(d) calculations with full geometry optimization were performed for CH₃COX molecules (X = F, Cl, Br, CH₃). Variations in the populations of the p _y orbitals of their halogen and carbon atoms (orbitals whose symmetry axes are perpendicular to the molecular plane) from X = F to X = Cl, Br, and CH₃ are not associated with variations in the extent of the p,π conjugation between the lone electron pair of the halogen atom and the π-electron system of the carbonyl group. The bonding molecular orbitals formed by these atomic p _y orbitals are not determined by this interaction. The RHF/6-311G(d) and MP2/6-311G(d) calculations give similar results.     

Topological Analysis of Electron Densities: Is the Presence of an Atomic Interaction Line in an Equilibrium Geometry a Sufficient Condition for the Existence of a Chemical Bond?

The structure, energetics, and electron density in the inclusion complex of He in adamantane, C10H16, have been studied by density functional theory calculations at the B3LYP6-311++G(2p,2d) level. Topological analysis of the electron density shows that the He atom is connected to the four tertiary tC atoms in the cage by atomic interaction lines with (3,-1) critical points. The calculated dissociation energy of the complex He@adamantane(g)=adamantane(g) + He(g) of DeltaE=-645 kJ mol(-1) nevertheless shows that the He-tC interactions are antibonding.     

Density functional theory study of the reaction mechanism and energetics of the reduction of hydrogen peroxide by ebselen, ebselen diselenide, and ebselen selenol

Density functional theory calculations at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G(d,p) level have been performed to elucidate the mechanism and reaction energetics for the reduction of hydrogen peroxide by ebselen, ebselen diselenide, ebselen selenol, and their sulfur analogues. The effects of solvation have been included with the CPCM model, and in the case of the selenol anion reaction, diffuse functions were used on heavy atoms for the geometry optimizations and thermochemical calculations. The topology of the electron density in each system was investigated using the quantum theory of atoms in molecules, and a detailed interpretation of the electronic charge and population data as well as the atomic energies is presented. Reaction free energy barriers for the oxidation of ebselen, ebselen diselenide, and ebselen selenol are 36.8, 38.4, and 32.5 kcal/mol, respectively, in good qualitative agreement with experiment. It is demonstrated that the oxidized selenium atom is significantly destabilized in all cases and that the exothermicity of the reactions is attributed to the peroxide oxygen atoms via reduction. The lower barrier to oxidation exhibited by the selenol is largely due to entropic effects in the reactant complex.     

Toward universal substituent constants: Model chemistry sensitivity of descriptors from the quantum theory of atoms in molecules

The quantum theory of atoms in molecules (QTAIM) provides a theoretical foundation to determine the properties of functional groups through additive atomic contributions. Many studies have used QTAIM in their analyses with a variety of electronic structure methods, but it is unknown if the properties measured using one model chemistry, the combination of the electronic structure method and basis set, can be compared to those measured by another. Here, we evaluate the sensitivity of QTAIM functional group and bond critical point properties using six functionals and seven basis sets. High-level B2PLYPD3-BJ/aug-cc-pV5Z reference values are provided for 116 functional groups and the property sensitivity with respect to these values are evaluated based on absolute deviations and by assessing linear relationships. Functional group properties, including charges, dipoles, quadrupoles and volumes, were found to be mostly insensitive to choice of computational model chemistry. However, due to structural and topological inconsistencies, the 6-31G(d) basis set is not recommended for use. Bond critical point properties varied with choice of model chemistry, but models incorporating hybrid functionals and triple-ζ basis sets provided values suitable for use in regression studies.     

Effect of dimerization and racemization processes on the electron density and the optical rotatory power of hydrogen peroxide derivatives

The variation of the electron density properties and optical rotatory power of the monomers and dimers of seven monosubstituted hydrogen peroxide derivatives, HOOX (X = CCH, CH(3), CF(3), t-Bu, CN, F, Cl), upon racemization has been studied using DFT (B3LYP/6-31+G) and MP2 (MP2/6-311+G) methods. The geometrical results have been rationalized on the basis of natural bond orbital (NBO) analysis. The atomic partition of the electron density properties within the atoms in molecules (AIM) methodology has allowed investigating the energy and charge redistribution in the different structures considered. The calculated optical rotatory power (ORP) of the dimers are, in general, twice of the values obtained for the monomers.     

To What Extent are “Atoms in Molecules” Structures of Hydrocarbons Reproducible from the Promolecule Electron Densities?

The “atoms in molecules” structures of 225 unsubstituted hydrocarbons are derived from both the optimized and the promolecule electron densities. A comparative analysis demonstrates that the molecular graphs derived from these two types of electron densities at the same geometry are equivalent for almost 90 % of the hydrocarbons containing the same number and types of critical points. For the remaining 10 % of molecules, it is demonstrated that by inducing small perturbations, through the variation of the used basis set or slight changes in the used geometry, the emerging molecular graphs from both densities are also equivalent. Interestingly, the (3, ?1) critical point between two “non‐bonded” hydrogen atoms, which triggered “H?H bonding” controversy is also observed in the promolecule densities of certain hydrocarbons. Evidently, the topology of the electron density is not dictated by chemical bonds or strong interactions and deformations induced by the interactions of atoms in molecules have a quite marginal role, virtually null, in shaping the general traits of the topology of molecular electron densities of the studied hydrocarbons, whereas the key factor is the underlying atomic densities.     

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.     

Computational study about through-bond and through-space interactions in [2.2]cyclophanes

An analysis of the electron density, obtained by B3PW91/6-31+G(d,p), B3LYP/6-31+G(d,p), and MP2/6-31+G(d,p) for [2,2]cyclophanes isomers, [2.2]paracyclophane, anti-[2.2]metacyclophane, syn-[2.2]metacyclophane, and [2.2]metaparacyclophane, was made through natural bond orbitals (NBO), natural steric analysis (NSA), and atoms in molecules (AIM) methods and through analysis of frontier molecular orbitals (MOs). NBO indicates that all compounds present through-bond interactions, but only the conformers of [2.2]metacyclophane present significant through-space interactions. The last interactions are observed in AIM analysis and by the plots of MOs. AIM indicates that these through-space interactions are closed-shell ones, and they stabilize the conformers. In contrast, all isomers present through-bond and through-space repulsive interactions. In addition, the atomic properties, computed over the atomic basins, showed that the position of the bridges and the relative displacement of the rings can affect the atomic charges, the first atomic moments, and the atomic volumes.     

QTAIM charge-charge flux-dipole flux interpretation of electronegativity and potential models of the fluorochloromethane mean dipole moment derivatives

Infrared fundamental vibrational intensities and quantum theory atoms in molecules (QTAIM) charge-charge flux-dipole flux (CCFDF) contributions to the polar tensors of the fluorochloromethanes have been calculated at the QCISD/cc-pVTZ level. A root-mean-square error of 20.0 km mol(-1) has been found compared to an experimental error estimate of 14.4 and 21.1 km mol(-1) for MP2/6-311++G(3d,3p) results. The errors in the QCISD polar tensor elements and mean dipole moment derivatives are 0.059 e when compared with the experimental values. Both theoretical levels provide results showing that the dynamical charge and dipole fluxes provide significant contributions to the mean dipole moment derivatives and tend to be of opposite signs canceling one another. Although the experimental mean dipole moment derivative values suggest that all the fluorochloromethane molecules have electronic structures consistent with a simple electronegativity model with transferable atomic charges for their terminal atoms, the QTAIM/CCFDF models confirm this only for the fluoromethanes. Whereas the fluorine atom does not suffer a saturation effect in its capacity to drain electronic charge from carbon atoms that are attached to other fluorine and chlorine atoms, the zero flux electronic charge of the chlorine atom depends on the number and kind of the other substituent atoms. Both the QTAIM carbon charges (r = 0.990) and mean dipole moment derivatives (r = 0.996) are found to obey Siegbahn's potential model for carbon 1s electron ionization energies at the QCISD/cc-pVTZ level. The latter is a consequence of the carbon mean derivatives obeying the electronegativity model and not necessarily to their similarities with atomic charges. Atomic dipole contributions to the neighboring atom electrostatic potentials of the fluorochloromethanes are found to be of comparable size to the atomic charge contributions and increase the accuracy of Siegbahn's model for the QTAIM charge model results. Substitution effects of the hydrogen, fluorine, and chlorine atoms on the charge and dipole flux QTAIM contributions are found to be additive for the mean dipole derivatives of the fluorochloromethanes.     

胸腺嘧啶-BH3构型与性质的DFT和MP2研究

Geometries and combination energies are predicated at B3LYP / 6-31G（d）and MP2 / 6-31G（d）level for thymine-BH3 complexes and 5 geometries have been obtained. Then single point energy calculations using larger basis sets（6-311 + G（2df）and aug-cc-pVDZ）and vibrational analysis and natural bond orbital analysis are carried out on the 5 optimized conformers. The outcome indicates that the conformers with the boron atom combined with O directly are relatively stable ones,（a）and（b）,with the combination energies of 90. 4 and 88. 0 kJ / mol （B3LYP / 6-31G（d）,BSSE corrected）. The fact is that the nitrogen atom offers electron to the empty atomic orbital of boron which produces the conformers（c）and（d）. Only one conformer is found which is formed because two carbon atoms offer π electron to the empty orbital of boron. The charge transference exists in all the conformers. The combination energies have a good line relation with their charge transference. The calculated results show that when the complex forms their IR spectrum moved to the red side and the frequency shifts are relative to the stabilities of the complexes.     

Quantum theory of atoms in molecules charge-charge flux-dipole flux models for the infrared intensities of X(2)CY (X = H, F, Cl; Y = O, S) molecules

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the X2CY (X = H, F, Cl; Y = O, S) molecules are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square errors of +/-0.03 D and +/-1.4 km mol(-1) are found for the molecular dipole moments and fundamental IR intensities calculated using quantum theory of atoms in molecules (QTAIM) parameters when compared with those obtained directly from the MP2/6-311++G(3d,3p) calculations and +/-0.05 D and 51.2 km mol(-1) when compared with the experimental values. Charge (C), charge flux (CF), and dipole flux (DF) contributions are reported for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.83 is calculated between the charge flux and dipole flux contributions and indicates that electronic charge transfer from one side of the molecule to the other during vibrations is accompanied by a relaxation effect with electron density polarization in the opposite direction. The characteristic substituent effect that has been observed for experimental infrared intensity parameters and core electron ionization energies has been applied to the CCFDF/QTAIM parameters of F2CO, Cl2CO, F2CS, and Cl2CS. The individual atomic charge, atomic charge flux, and atomic dipole flux contributions are seen to obey the characteristic substituent effect equation just as accurately as the total dipole moment derivative. The CH, CF, and CCl stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions.     

Resonance structures of the amide bond: the advantages of planarity

Delocalization indexes based on magnitudes derived from electron-pair densities are demonstrated to be useful indicators of electron resonance in amides. These indexes, based on the integration of the two-electron density matrix over the atomic basins defined through the zero-flux condition, have been calculated for a series of amides at the B3LYP/6-31+G* level of theory. These quantities, which can be viewed as a measure of the sharing of electrons between atoms, behave in concordance with the traditional resonance model, even though they are integrated in Bader atomic basins. Thus, the use of these quantities overcomes contradictory results from analyses of atomic charges, yet keeps the theoretical appeal of using nonarbitrary atomic partitions and unambiguously defined functions such as densities and pair densities. Moreover, for a large data set consisting of 24 amides plus their corresponding rotational transition states, a linear relation was found between the rotational barrier for the amide and the delocalization index between the nitrogen and oxygen atoms, indicating that this parameter can be used as an ideal physical-chemical indicator of the electron resonance in amides.     

原子构造原理与过渡元素原子的价电子组态

众所周知,元素周期系过渡元素基态原子价电子组态的多样化是已往的原子构造理论无论是从定性还是从定量方面都是迄今难以给出圆满理论解释的原子构造现象之一^[1-11]。本文介绍新近提出的原子构造的对称性原理以及依据这一原理对上述原子构造现象所作的系统理论解释。     

The substituent effect in ethylenes and acetylenes – AIM analysis

The calculations on disubstituted ethylenes YCHCHX with Y = Li, H, F and X = H, F, Li, Na, OH, BeH, NH₂, BH₂, NO₂ were performed at MP2/6-311++G(d,p) level of theory. The analysis of bond lengths and atoms in molecules based theory (AIM) topological parameters such as the characteristics of bond critical points (electron densities and their Laplacians) and atomic radii leads to the conclusion that the AIM parameters are much more sensitive to the action of intramolecular perturbations like substituents than traditional structural parameters such as bond lengths. A comparison of substituted ethylenes with the previously analyzed substituted acetylenes is also given.     

N, P, and As ylides and aza- and arsa-Wittig reactions from topological analyses of electron density

The nature of bonding between N, P, and As constituent atoms in ylide systems with the R(3)XYR' formula (X = N, P, As; Y = N, P, As; R = F, H; R' = H, CH(3)) has been characterized by ab initio (MP2/6-311++G**) and density functional theory (B3LYP/6-311++G**) calculations. Its electronic structure has been analyzed through electron density with the quantum theory of atoms in molecules and the electron localization function (ELF). The characteristics of the central bond are inspected with the calculated rotational barriers. The results show that N has a behavior different from that of the remaining pnicogen atoms (P, As), where the bond is much stronger. Fluorine substituents strengthen the X-Y bond, reduce the bond distance, and increase the electron density in the central bond so that the substituent pulls charge from the bond in the pnicogen X atom. For the N-pnicogen ylides, the results showed different bonding characters between F and X atoms; depending on the position of the F atom, the difference of the bond character is sensed by the basin synaptic order, as it is deduced from the analysis of the ELF basins. The energy profiles of the rotational barriers have been calculated at the MP2/6-311++G** level, indicating that the electronegativity of the substituents is a relevant factor that has consequences in the characteristics of the X-Y bond.