Showing papers in "Theoretical Chemistry Accounts in 2008"

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

Role of hydration in determining the structure and vibrational spectra of L-alanine and N-acetyl L-alanine N′-methylamide in aqueous solution: a combined theoretical and experimental approach

Abstract: In this work we have utilized recent density functional theory Born-Oppenheimer molecular dynamics simulations to determine the first principles locations of the water molecules in the first solvation shell which are responsible for stabilizing the zwitterionic structure of L-alanine. Previous works have used chemical intuition or classical molecular dynamics simulations to position the water molecules. In addition, a complete shell of water molecules was not previously used, only the water molecules which were thought to be strongly interacting (H-bonded) with the zwitterionic species. In a previous work by Tajkhorshid et al. (J Phys Chem B 102:5899) the L-alanine zwitterion was stabilized by 4 water molecules, and a subsequent work by Frimand et al. (Chem Phys 255:165) the number was increased to 9 water molecules. Here we found that 20 water molecules are necessary to fully encapsulate the zwitterionic species when the molecule is embedded within a droplet of water, while 11 water molecules are necessary to encapsulate the polar region with the methyl group exposed to the surface, where it migrates during the MD simulation. Here we present our vibrational absorption, vibrational circular dichroism and Raman and Raman optical activity simulations, which we compare to the previous simulations and experimental results. In addition, we report new VA, VCD, Raman and ROA measurements for L-alanine in aqueous solution with the latest commercially available FTIR VA/VCD instrument (Biotools, Jupiter, FL, USA) and Raman/ROA instrument (Biotools). The signal to noise of the spectra of L-alanine measured with these new instruments is significantly better than the previously reported spectra. Finally we reinvestigate the causes for the stability of the Pπ structure of the alanine dipeptide, also called N-acetyl-L-alanine N′-methylamide, in aqueous solution. Previously we utilized the B3LYP/6-31G* + Onsager continuum level of theory to investigate the stability of the NALANMA4WC Han et al. (J Phys Chem B 102:2587) Here we use the B3PW91 and B3LYP hybrid exchange correlation functionals, the aug-cc-pVDZ basis set and the PCM and CPCM (COSMO) continuum solvent models, in addition to the Onsager and no continuum solvent model. Here by the comparison of the VA, VCD, Raman and ROA spectra we can confirm the stability of the NALANMA4WC due to the strong hydrogen bonding between the four water molecules and the peptide polar groups. Hence we advocate the use of explicit water molecules and continuum solvent treatment for all future spectral simulations of amino acids, peptides and proteins in aqueous solution, as even the structure (conformer) present cannot always be found without this level of theory.

Electron localizability indicator for correlated wavefunctions. III: singlet and triplet pairs

Abstract: The electron pair density can be decomposed into the symmetric and antisymmetric parts. The antisymmetric component is connected with the probability that two electrons are coupled to a triplet. On the basis of triplet-coupled electrons the electron localizability indicator is defined, describing the correlation of motion of electrons forming a triplet pair. In case of spin-polarized systems the electron localizability indicator for triplet pairs combines the two spin channels together into a single functional.

A vibrational circular dichroism implementation within a Slater-type-orbital based density functional framework and its application to hexa- and hepta-helicenes

Abstract: We describe the implementation of the rotational strengths for vibrational circular dichroism (VCD) in the Slater-type orbital based Amsterdam Density Functional (ADF) package. We show that our implementation, which makes use of analytical derivative techniques and London atomic orbitals, yields origin independent rotational strengths. The basis set dependence in the particular case of Slater-type basis functions is also discussed. It turns out that the triple zeta STO basis sets with one set of polarization functions (TZP) are adequate for VCD calculations. The origin- dependence of the atomic axial tensors is checked by a distributed origin gauge implementation. The distributed and common origin gauge implementations yield virtually identical atomic axial tensors with the Slater-type basis sets employed here, proving that our implementation yields origin independent rotational strengths. We verify the implementation for a set of benchmark molecules, for which the dependence of the VCD spectra on the particular choice of the exchange–correlation functional is studied. The pure functionals BP86 and OLYP show a particularly good performance. Then, we apply this approach to study the VCD spectra of hexa- and hepta- helicenes. In particular we focus on relationships between the sign of the rotational strengths of the two helicenes.

A combined theoretical and experimental study of the structure and vibrational absorption, vibrational circular dichroism, Raman and Raman optical activity spectra of the L-histidine zwitterion

Abstract: A combined theoretical and experimental study of the vibrational absorption (VA)/IR, vibrational circular dichroism (VCD), Raman and Raman optical activity (ROA) spectra of l-histidine in aqueous solution has been undertaken to answer the questions (i) what are the species present and (ii) which conformers of the species are present under various experimental conditions. The VA spectra of l-histidine have been measured in aqueous solution and the spectral bands which can be used to identify both species (cation, zwitterion, anion) and conformer of the species have been identified and subsequently used to identify the species (zwitterion) and conformer (gauche minus minus, gauche minus plus for the side chain dihedral angles) present in solution at pH 7.6. The VCD spectral intensities have been used subsequently in combination with further theoretical studies to confirm the conclusions that have been arrived at by only analyzing the VA/IR spectra. Finally a comparison of measured Raman and ROA spectra of l-histidine with Raman and ROA spectral simulations for the conformers and species derived from the combined VA/IR and VCD experimental and theoretical work is presented as a validation of the conclusions arrived at from VA/IR and VCD spectroscopy. The combination of VA/IR and VCD with Raman and ROA is clearly superior and both sets of experiments should be performed.

Ab initio modeling of TiO2 nanosheets

Abstract: We present density functional calculations on 1–6 monolayer (ML) thick TiO2 films peeled off from the main low-index surfaces of anatase. The structure of the films is optimized both by constraining the lattice constants to those of bulk anatase, and by allowing them to relax. It is found that the stability order of the films does not follow that of the surfaces from which they are derived, and does not increase monotonously with film thickness. Furthermore, relaxing the lattice constants can induce large modifications in the film structure. In particular, two anomalously stable films are found. One derives from the 2 ML (001) film, and rearranges to a lepidocrocite-TiO2 nanosheet. The other one derives from a 4 ML (101) film, and gives rise to a novel phase, where all the Ti ions are fivefold coordinated.

Technical aspects of quantum chemical modeling of enzymatic reactions: the case of phosphotriesterase

Abstract: Quantum chemical methods are today a powerful tool in the study of enzymatic reaction mechanisms. In this paper we evaluate the adequacy of some of the technical approximations frequently used in t ...

MP2 Study of synergistic effects between X–H/π (X = C,N,O) and π–π interactions

Abstract: In this manuscript we report high level ab initio calculations [RI-MP2(full)/aug-cc-pVDZ] and experimental evidence that demonstrate that important synergistic effects between two relevant non covalent interactions that are omnipresent in biological systems, i.e., π–π and X–H/π interactions (X = C,N,O), occur when the interactions coexist in the same complex. In particular, we study how the π–π interaction influences the X–H/π interaction and vice versa by computing the genuine non additivity energies of the ternary X–H/π–π complexes.

Calculating molecular vibrational spectra beyond the harmonic approximation

Abstract: We present a new approach for calculating anharmonic corrections to vibrational frequency calculations. The vibrational wavefunction is modelled using translated Hermite functions thus allowing anharmonic effects to be incorporated directly into the wavefunction whilst still retaining the simplicity of the Hermite basis. We combine this new method with an optimised finite-difference grid for computing the necessary third and fourth nuclear derivatives of the energy. We compare our combined approach to existing anharmonic models—vibrational self-consistent field theory (VSCF), vibrational perturbation theory (VPT), and vibrational configuration interaction theory (VCI)—and find that it is more cost effective than these alternatives. This makes our method well-suited to computing anharmonic corrections for frequencies in medium-sized molecules.

On the TD-DFT UV/vis spectra accuracy: the azoalkanes

Abstract: Using an ab intio TD-DFT approach systematically accounting for the molecular surroundings effects, we have computed the n → π* absorption wavelength of 22 azoalkane derivatives. For the complete set of molecules, we propose a theoretical procedure able to reproduce the major auxochromic effects, and to deliver a mean absolute error of 5.8 nm (0.056 eV) with maximal deviations limited to 21 nm (0.20 eV). The impact of including in the model explicit solvent molecules is discussed as well. This contribution confirms that PCM-TD-PBE0 is a first-grade method for simulating the vertical absorption spectra of organic dyes.

Density functional studies of coinage metal nanoparticles: scalability of their properties to bulk

Abstract: Density functional plane-wave calculations have been carried out for series of Cu n ,Ag n and Au n particles containing up to 146 (Cu, Ag) and 225 (Au) atoms. Full geometry optimization has been performed for all particles starting from the structures created by cuts from the bulk. In line with previous studies, calculated average nearest-neighbour distances and cohesive energies of the particles linearly depend on such size-derived parameters as the average coordination number of metal atoms and the inverse of the mean particle radius, respectively. Rather accurate linear extrapolation of the observables under scrutiny to the bulk values has been achieved. However, we show that the scalability for particles made of various elements of the same d10s1 electron configuration differs, e.g. for bond lengths in Au n species it is noticeably less perfect than that for Cu n and Ag n ones. Implications of encountered structural peculiarities of the nanoparticles for their reactivity are outlined.

Anharmonic vibrational spectroscopy calculations with electronic structure potentials: comparison of MP2 and DFT for organic molecules

Abstract: Density functional theory (DFT) technique is the most commonly used approach when it comes to computation of vibrational spectra of molecular species. In this study, we compare anharmonic spectra of several organic molecules such as allene, propyne, glycine, and imidazole, computed from ab initio MP2 potentials and DFT potentials based on commonly used BLYP and B3LYP functionals. Anharmonic spectra are obtained using the direct vibrational self-consistent field (VSCF) method and its correlation-corrected extension (CC-VSCF). The results of computations are compared with available experimental data. It is shown that the most accurate vibrational frequencies are obtained with the MP2 method, followed by the DFT/B3LYP method, while DFT/BLYP results are often unsatisfactory.

Elastic and dynamical properties of alkali-silicate glasses from computer simulations techniques

Abstract: This paper shows recent progresses in the field of computer simulations of inorganic glasses. Molecular dynamics simulations and energy minimization methods have been applied to calculate the elastic and transport properties of alkali silicate glasses of compositions xM2O · (100 − x)SiO2 (with x = 0, 10, 15, 20, 25, 30 % mol for M = Li, Na and K) and of a soda-lime glass with composition 15Na2O · 10CaO · 75SiO2, which has been employed to ascertain the effect of the replacement of CaO for Na2O. The excellent agreement of the computed results with the experimental data highlights the important predictive and interpretative role reached by computer simulations techniques.

The excited states of adenine and thymine nucleoside and nucleotide in aqueous solution: a comparative study by time-dependent DFT calculations

Abstract: The effect substitutions at nitrogen atom 1 of thymine and nitrogen atom 9 of adenine have on lowest energy excited electronic states has been studied by means of time-dependent PBE0 calculations in aqueous solution. In agreement with the experimental indications, the vertical excitation energy of the bright state of 1,methyl-thymine, thymine nucleoside and thymine nucleotide is red-shifted with respect to that of thymine. Deoxyribose and deoxyribose-phosphate substituents affect mainly the lowest energy dark state of adenine and thymine, slightly increasing their oscillator strength. The excited states of 9, methyl-adenine and 1, methyl-thymine have also been studied by using the recently developed M052X, CAM-B3LYP and LC-ωPBE density functionals. The computed VEE are in good agreement with those obtained by using PBE0, which, however, provides values closer to the experimental band maximum.

Theoretical study of N–H· · ·O hydrogen bonding properties and cooperativity effects in linear acetamide clusters

Abstract: We investigated geometry, energy, $${ u_{{\text{N--H}}}}$$ harmonic frequencies, 14N nuclear quadrupole coupling tensors, and $${n_{\rm O}\to \sigma _{{\text{N--H}}}^\ast}$$ charge transfer properties of (acetamide) n clusters, with n = 1 − 7, by means of second-order Moller-Plesset perturbation theory (MP2) and DFT method. Dependency of dimer stabilization energies and equilibrium geometries on various levels of theory was examined. B3LYP/6-311++G** calculations revealed that for acetamide clusters, the average hydrogen-bonding energy per monomer increases from −26.85 kJ mol−1 in dimer to −35.12 kJ mol−1 in heptamer; i.e., 31% cooperativity enhancement. The n-dependent trend of $${ u_{{\text{N--H}}}\,{and}\,^{14}}$$ N nuclear quadrupole coupling values were reasonably correlated with cooperative effects in $${r_{{\text{N--H}}}}$$ bond distance. It was also found that intermolecular $${n_{\rm O}\to \sigma_{{\text{N--H}}}^\ast}$$ charge transfer plays a key role in cooperative changes of geometry, binding energy, $${ u_{{\text{N--H}}}}$$ harmonic frequencies, and 14N electric field gradient tensors of acetamide clusters. There is a good linear correlation between 14N quadrupole coupling constants, C Q (14N), and the strength of Fock matrix elements (F ij ). Regarding the $${n_{\rm O}\to \sigma_{{\text{N--H}}}^\ast}$$ interaction, the capability of the acetamide clusters for electron localization, at the N–H· · ·O bond critical point, depends on the cluster size and thereby leads to cooperative changes in the N–H· · ·O length and strength, N–H stretching frequencies, and 14N quadrupole coupling tensors.

Intrinsic local constituents of molecular electronic wave functions. I. Exact representation of the density matrix in terms of chemically deformed and oriented atomic minimal basis set orbitals

Abstract: A coherent, intrinsic, basis-set-independent analysis is developed for the invariants of the first-order density matrix of an accurate molecular electronic wavefunction. From the hierarchical ordering of the natural orbitals, the zeroth-order orbital space is deduced, which generates the zeroth-order wavefunction, typically an MCSCF function in the full valence space. It is shown that intrinsically embedded in such wavefunctions are elements that are local in bond regions and elements that are local in atomic regions. Basis-set-independent methods are given that extract and exhibit the intrinsic bond orbitals and the intrinsic minimal-basis quasi-atomic orbitals in terms of which the wavefunction can be exactly constructed. The quasi-atomic orbitals are furthermore oriented by a basis-set independent method (viz. maximization of the sum of the fourth powers of all off-diagonal density matrix elements) so as to exhibit clearly the chemical interactions. The unbiased nature of the method allows for the adaptation of the localized and directed orbitals to changing geometries.

Theory of Raman scattering and Raman optical activity: near resonance theory and levels of approximation

Abstract: A new level of the theory of Raman scattering and Raman optical activity (ROA) is identified between the general, unrestricted (GU) theory and the far-from-resonance (FFR) theory called the near resonance (NR) theory. In the NR theory, the Raman tensor is not symmetric, and there is nonequivalence between the incident and scattered circular polarization (ICP and SCP) forms of ROA and non-zero intensity for out-of-phase dual circular polarization (DCPII) ROA. Several levels of theory are identified in passing from the GU theory to the FFR theory. The NR theory provides vibronic detail, present in the GU theory but absent from the FFR, by assuming that the vibrational levels of the excited electronic states are the same as those of the ground electronic state. The NR theory obeys time-reversal symmetry and can be expressed in a form that is computationally tractable, thereby providing an improved description of the frequency dependence of Raman and ROA intensities relative to that provided by the FFR theory.

Global warming potential predictions for hydrofluoroethers with two carbon atoms

Abstract: Global warming potentials are predicted using computational chemistry and thermodynamics approaches for four hydrofluoroethers where no data have previously been available. We also compare results with the same methodology for six other species. We combine predictions of radiative forcing values from density functional theory computations at the B3LYP/6-31g* level of theory with previous experimentally determined or newly estimated hydroxyl radical-hydrogen abstraction rate constants to obtain these global warming potentials. We find that many of the HFEs studied have lower global warming potentials than the hydrofluorocarbons and chlorofluorocarbons they may soon replace, although other environmental and technical issues may need to be addressed first.

Characterization of the active site of yeast RNA polymerase II by DFT and ReaxFF calculations

Abstract: Most known DNA-dependent RNA polymerases (RNAPs) share a universal heptapeptide, called the NADFDGD motif. The crystal structures of RNAPs indicate that in all cases this motif forms a loop with an embedded triad of aspartic acid residues. This conserved loop is the key part of the active site. Based on the crystal structures of the yeast RNAP II, we have studied this common active site for three cases: (1) single RNAP, (2) pre-translocation elongation complex, and (3) post-translocation elongation complex. Here we have applied two different modeling methods, the GGA density functional theory method (PBE) of quantum mechanics (QM) and the ReaxFF reactive force field. The QM calculations indicate that the loop shrinks from pre- to post-translocation and expands from post- to pre- translocation. In addition, PBE MD simulations in the gas phase at 310 K shows that the loop in the single-RNAP case is tightly connected to a catalytic Mg 2+ ion and that there is an ordered hydrogen bond network in the loop. The corresponding ReaxFF MD simulation presents a less stable loop structure, suggesting that ReaxFF may underestimate the coordinating interactions between carbonyl oxygen and magnesium ion compared to the gas phase QM. However, with ReaxFF it was practical to study the dynamics for a much more detailed model for the post-translocational case, including the complete loop and solvent. This leads to a plausible reactant-side model that may explain the large difference in efficiency of NTP polymerization between RNA and DNA polymerases.

On the properties of natural orbitals for chemical valence

Abstract: Natural orbitals for chemical valence (NOCV) were recently introduced as descriptors of chemical bond. They were shown to provide a valuable bond diagnosis in transition metal complexes (Mitoraj and Michalak in J Mol Model 13:347–355, 2007). The present paper treats the mathematical basis for the proposed method. In particular, the algebraic properties of NOCV, on which this methodology relies, are rigorously proven.

On the nature of the interaction between H2 and metal-organic frameworks

Abstract: The mechanism of adsorption of molecular hydrogen (H2) on IRMOF-1 is studied at the MP2 level. The role of the two principal MOF components, the inorganic connector and the organic linker, for H2 adsorption is evaluated. Correlation methods and large basis sets are necessary to describe correctly the weak interactions (London dispersion) and to account for the polarisability of H2. We proof that the electrostatic interactions have a negligible contribution to the interaction energy and the adsorption mechanism is governed by London dispersion (3–5 kJ mol−1).

An electron localization function and catastrophe theory analysis on the molecular mechanism of gas-phase identity SN2 reactions

Abstract: A set of four reactions, XCH3+X− (X=F, Cl, Br) and ClSiH3+Cl−, is investigated by means of the joint use of the electron localization function (ELF) and catastrophe theory (CT) analysis in order to obtain new insights into the bond breaking/forming processes for identity SN2 gas-phase reactions. Using DFT calculations at the OLYP/6-311++G(d,p) level, the effect of nucleophile (F, Cl, and Br anions) and the role of reacting centers (C or Si) on the reaction mechanisms are investigated. The charge-shift character of carbon–halogen bonds is studied by determination of the weights of the Lewis resonance structures. In all SN2 reactions at the carbon atom, there is a progressive reduction on the covalent character of the C–X bond from the reactant complex (0.41, 0.57, 0.58 for F, Cl, and Br, respectively) until the bond-breaking process, occurring before the transition structure is reached. On the other hand, the Si–Cl bond maintains its degree of covalent character (0.51) from the isolated fragments to the formation of a stable transition complex, presenting two silicon–chlorine charge-shifted bonds. The analysis of the ELF topology along the reaction path reveals that all reactions proceed via the same turning points of fold-type but the order is inverted for reactions taking place at C or Si atoms.

Characterizing vibrational motion beyond internal coordinates

Abstract: We present a procedure for the decomposition of the normal modes of a composite system, including its rotations and translations, into those of fragments. The method permits—by the cross-contraction of dyads of mass-weighted displacement vectors, without recourse to valence coordinates—the direct comparison of nuclear motions of structurally similar but otherwise arbitrary fragments of molecules, and it leads to a quantitative definition of the similarity and the overlap of nuclear motions. We illustrate its usefulness by the quantification of the mixing of the normal modes of formic acid monomers upon the formation of a dimer, by the comparison of the overlap of the intermolecular normal vibrations of the water dimer computed with different ab initio schemes, and by the comparison of similarity and overlap of vibrations of (4S,7R)-galaxolide and (4S)-4-methylisochromane. The approach is expected to become a standard tool in vibrational analysis.

Can extrapolation to the basis set limit be an alternative to the counterpoise correction? A study on the helium dimer

Abstract: Configuration interaction and coupled cluster calculations are reported for He2 using various orbital basis sets of the d-aug-AVXZ type, with the results being extrapolated to the one electron basis set limit both with counterpoise and without counterpoise correction. A generalized uniform singlet- and triplet-pair extrapolation scheme has been utilized for such a purpose. Using appropriate corrections to mimic full configuration interaction, the energies were predicted in excellent agreement with the best available estimates. The results also suggest that extrapolation to the complete basis set limit may be a general alternative to the counterpoise correction that yields a more accurate potential energy while being more economical.

An IEF-PCM study of solvent effects on the Faraday $${\mathcal{B}}$$ term of MCD

Abstract: We present the first theoretical investigation of solvent effects on the Faraday $${\mathcal{B}}$$ term of magnetic circular dichroism (MCD) at the density–functional level of theory. In our model, the solvent is described by the polarizable continuum model in its integral-equation formulation. We present the extensions required for including electron correlation effects using density–functional theory (DFT) as well as the necessary extensions for including the effects of a dielectric continuum. The new code is applied to the study of the Faraday $${\mathcal{B}}$$ term of MCD in a series of benzoquinones. It is demonstrated that electron correlation effects, as described by DFT, are essential in order to recover the experimentally observed signs of the $${\mathcal{B}}$$ term. Dielectric continuum effects increase, in general, the magnitude of the $${\mathcal{B}}$$ term, leading to an overestimation of the experimental observations in most cases.

An exponential multi-reference wavefunction ansatz: connectivity analysis and application to N2

Abstract: A connectivity analysis for the exponential multi-reference wavefunction ansatz (MRexpT) (J Chem Phys 123:84102, 2005) is carried out. Assuming a complete model space and separating interactions carrying active labels the cluster operator carrying no active labels is fully connected. The valence (active) part of the MRexpT cluster operator, however remains disconnected. Consequently, the MRexpT correlation energy scales linearly with the number of non-active electrons as single reference coupled cluster does while MRexpT additionally can treat multi reference cases. Therefore, MRexpT should be well suited to be applied to a large number of molecular applications. Its applicability to periodic systems with multi-reference unit cells however seems to be limited. An application to the triple bond breaking of the N2 molecule is presented.

Tight β-turns in peptides. DFT-based study of infrared absorption and vibrational circular dichroism for various conformers including solvent effects

Abstract: Vibrational circular dichroism (VCD) has had a large impact on configurational studies of organic molecules largely due to the theoretical advances made by Philip Stephens and co-workers. For peptides, the structural issue is not one of the configuration, but of conformation, and the flexibility of the oligomeric structure raises major computational challenges. Turns are a vital aspect of peptide and protein conformation that allow such structures to fold into a compact unit. However, unlike helices and sheets, they are not extended repeating structures, but each residue has a different local conformation. Also, when turns are part of larger peptides their termini are connected to completely different structural elements. We have done extended comparative density functional theory (DFT) computations to characterize the expected spectral contributions of selected turn structures to the amide IR and VCD spectra of peptides. The isolated vacuum results for tri-amide turns (Ac-X-Y-NH2) of a few different sequences are compared with calculations involving correction for solvation effects. In particular, we looked at the sequence variation in spectra and structure between Ala-Ala, Aib-Gly and D-Pro-Gly for the turn-specific X–Y residues. The nature of some turn-associated, amide originating, spectral transitions are developed and tested.

A definition for the covalent and ionic bond index in a molecule

Abstract: Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms. The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides, hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion.

Explicitly correlated second-order perturbation theory calculations on molecules containing heavy main-group elements

Abstract: Slater-type geminals (STGs) have been used as explicitly correlated two-electron basis functions for calculations on the hydrides of N–As and Sb (as well as on the hydrides of O–Se and F–Br with similar, not reported results) in various one-electron basis sets of Gaussian atomic orbitals. The performance of the explicitly correlated theory has been assessed with respect to the exponent of the STG, for example, by using different exponents for individual pair correlation functions and pair energies. It is shown that a correlation factor with an exponent of \({\gamma = 1.4 a_{0}^{-1}}\) can give reliable results within 1% from the basis-set limit for all investigated molecules in an aug-cc-pVQZ basis set for the valence shells, using fixed amplitudes for the STGs in a diagonal orbital-invariant formulation of the theory. The use of relativistic effective core potentials (RECPs) in explicitly correlated second-order perturbation theory has been investigated.