Rationalization of the optical rotatory power of chiral molecules into atomic terms: a study of N<Subscript>2</Subscript>H<Subscript>4</Subscript>

We applied a strategy to assign the individual contributions that atoms make to the optical rotation angle and, more generally, to the molecular chirality. The method resolves the optical rotatory power tensor into atomic contributions employing the formalism of the acceleration gauge for the electric dipole and the torque formalism for the magnetic dipolar moment. The gross atomic isotropic contributions have been evaluated for nitrogen and hydrogen in hydrazine, employing Gaussian basis sets of very good quality, in order to achieve the Hartree–Fock limit.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002)     

Molecular Exciton Approach to Anisotropic Absorption and Circular Dichroism II. The Partial Optic Axis and its Application in Molecular Exciton Theory

The first part of the present communication develops the general theory of the partial optic axis, which is an excitation specific structural feature first proposed as an aid to the choice of chromophoric reference points in a molecular exciton approach to optical rotatory power, and discusses its applicability to symmetry analyses in the light of the distinction between the three categories for anisotropic optical rotatory power, i.e. chiral, achiral optically active, and achiral optically inactive molecular structures. The second part of the communication discusses the special role played by the concept of the partial optic axis in the evaluation of the anisotropic chromophoric intensity contributions in a molecular exciton approach, in particular in relation to the use of the chromophoric symmetry for the systematic selection and characterization of the intensity contributions.     

Molecular Exciton Approach to Anisotropic Absorption and Circular Dichroism II. The Partial Optic Axis and its Application in Molecular Exciton Theory

Summary. The first part of the present communication develops the general theory of the partial optic axis, which is an excitation specific structural feature first proposed as an aid to the choice of chromophoric reference points in a molecular exciton approach to optical rotatory power, and discusses its applicability to symmetry analyses in the light of the distinction between the three categories for anisotropic optical rotatory power, i.e. chiral, achiral optically active, and achiral optically inactive molecular structures. The second part of the communication discusses the special role played by the concept of the partial optic axis in the evaluation of the anisotropic chromophoric intensity contributions in a molecular exciton approach, in particular in relation to the use of the chromophoric symmetry for the systematic selection and characterization of the intensity contributions.Permanent address: Holmebjerg 5, DK-2950 Vedbæk, Denmark     

Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals

Summary The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.Dedicated to Prof. Jan Linderberg     

Bond orbital approach for optical rotatory strength calculations

Directly determined localized approximate molecular Orbitals are used in excitation energy and optical rotatory strength calculations within the CNDO/2 scheme. Using strictly localized bond orbitals one obtains qualitatively good excitation energies, but quantitative agreement can be found only by considering delocalization effects, which have been proved to be crucial in determining the optical rotatory strength. The delocalization interactions are classified as through space and through bond ones and even the latter is found to have significant contributions. The chiroptical properties of the lowest lying transitions in the twisted glyoxal molecule are analysed in terms of localized molecular orbital contributions.     

Analytic calculations of vibrational hyperpolarizabilities in the atomic orbital basis

We present an analytic scheme for the calculation of pure vibrational contributions to linear and nonlinear optical properties such as the polarizability and the first and second hyperpolarizabilities. The formalism is fully expressed in terms of a perturbation- and time-dependent atomic orbital basis, using the elements of the density matrix in the atomic orbital basis as the basic variables. We calculate perturbed densities up to third order with respect to the electric field in accordance with the n + 1 rule, and the approach is therefore applicable for the calculation of pure vibrational contributions involving all vibrational coordinates in large molecular complexes. In the case of static electric fields, we therefore only need to calculate 19 response equations, independent of the size of the molecule. If we can determine the molecular energy and force field, the calculation of pure vibrational contributions to the nonlinear optical properties of the molecule is therefore a rather straightforward task. We illustrate the implementation by calculating pure vibrational contributions to the first and second hyperpolarizabilities of molecules containing up to 66 atoms using basis sets of good quality.     

Quantitative determination of linear and second-harmonic generation optical effective responses of achiral or chiral materials in planar structures: theory and materials

A theoretical formalism designed to quantify linear optical and second-order nonlinear optical responses of achiral or chiral anisotropic materials in planar structure is presented. In particular, the theory includes linear optical activity that is governed by the gyrotropic components and second-harmonic generation optical rotatory dispersion, the magnitude of which depends on the ratio of chiral and achiral chi((2)) components. Examples are given which reproduce complex interference effects and other subtle optical effects that are encountered in layered structures. Detailed experimental second harmonic generation studies of quartz and dihydrogen phosphate that quantify linear and nonlinear optical activities of these materials are reported.     

An atomic charge study of highly ionic diatomic molecular systems

Four atomic charge formalisms are compared using highly ionic diatomic molecules, such as LiF, NaF, KF, LiCl, NaCl, KCl, BF, AlF, GaF, BeO, and MgO. All calculations were done at the QCISD/6‐311G(2df) level. The only formalism consistent with the characteristics of all these systems is Quantum theory of atoms in molecules (QTAIM). Absolute Mulliken charge values are small. ChelpG charges are not reliable for systems in which the atoms are largely anisotropic. Generalized atomic polar tensor values are contaminated with charge fluxes and atomic dipole fluxes and fail when these contributions are important and do not cancel each other. Finally, the charge–charge flux–dipole flux model was applied to dipole moment derivatives with QTAIM. This analysis shows that charge flux and atomic dipole flux contributions during bond stretching are almost null, except for oxides. There are also evidences that the lone electron pair at Group 13 elements in fluorides becomes less localized as the bond is stretched. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Applications of fourier transforms in molecular orbital theory. Calculation of optical properties and tables of two-center one-electron integrals

Fourier transform methods initiated by Geller and Harris are applied to the calculation of optical properties of molecules. Tables of one-electron two-center integrals needed for the accurate computation of molecular absorption and optical activity are calculated by the Fourier transform method. A general theorem is derived which allows the angular part of the integrals to be treated by means of projection operators. The radial parts of the integrals are treated by the methods of Harris. The results are obtained in a simple closed form which avoids the usual transformation to local coordinates. The two-center integrals evaluated include matrix elements of the momentum operator, the dipole moment operator, the tensor operator , the quadrupole moment operator, and the angular momentum operator. These are evaluated between 1s, 2s, and 2p Slater-type atomic orbitals located on different atoms. The results are expressed as functions of the Slater exponents and of the relative coordinates of the two atoms.     

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.     

A free-electron theory of optical activity

The Schrödinger equation is derived for an electron moving in the field of a potential supported by a space curve, and an approximate solution is found which becomes exact as the potential binds the electron more and more tightly to the curve but otherwise does not restrict the electron's motion along the curve. These so-called free-electron wavefunctions and energy levels are used to obtain a general expression for the optical rotatory power associated with an arbitrary space curve. Calculations of the specific rotatory power are carried out for three different curves.     

Modeling diamagnetic and magnetooptic properties of organic compounds with the TOSS-MODE approach

The topological substructural molecular design (TOSS-MODE) approach is used to describe the diamagnetic susceptibility of organic compounds. Two data sets composed of 233 aliphatic and 85 aromatic compounds were studied for which good linear correlations were found. The contributions of many different structural fragments and atomic groups were computed by the current approach. The predictive ability of the models developed was tested by using external prediction sets of compounds of different classes than those used in training. A quantitative model based on the current approach was developed to compute the diamagnetic susceptibility exaltation of aromatic compounds, which is exemplified by the study of polycyclic aromatic hydrocarbons. The rotatory power of organic compounds in a magnetic field was also described by the TOSS-MODE approach. Good linear correlations were obtained for this property in aliphatic and aromatic compounds. The predictive abilities of the models found were tested by external prediction sets for which good correlations between calculated and experimental values are found.     

An analysis of the through bond interaction using the localised molecular orbitals—III : Long range effect of lone pair orbital to the optical rotatory strength of the carbonyl n-π* transition in 3-ketopiperidines

The optical rotatory strengths of the carbonyl n-π^* transitions of (1R)-3-ketopiperidine and (1S)-3-ketopiperidine were subjected to the analysis in terms of the through-space and the through-bond interactions according to the procedure using localised molecular orbitals we proposed in the preceding papers. As a result of the present analysis, the optical rotatory strengths of the molecules were found to be influenced by the direction of the remote nitrogen lone pair orbital. This influence was found to be illustrated by the coupling between the CO group and the nitrogen lone pair orbital as well as the N-H bond localized orbital via a path containing the through-bond and the through-space interactions. That is, the positive coupling and the negative coupling paths were determined by the present analysis and the sign of the optical rotatory strength was found to correspond to the sum of the contributions of both coupling paths.     

The optical rotatory power of water

Ab initio molecular orbital calculations of the optical rotatory response of a single oriented water molecule are described. The unique tensor element g(xy) was computed to be -0.047 bohr(3) with CCSD/6-311+G(d,p). A value of -0.033 was obtained with the minimal valence basis that was better suited to parsing the rotatory response among a limited number of excited states. Transition moments were calculated ab initio and qualitatively derived from the wave functions. Rotations were reckoned from the relative dispositions of the transition moments with respect to the wavevectors. In this way, it was possible to intuitively reckon the form of the optical rotation tensor consistent with that from higher levels of theory and to establish which excitations make the most significant contributions.     

S-(-)-2, 2'-联二萘酚衍生物的合成及其螺旋结构与旋光性的关系

以S-(-)-2,2'-联二萘酚为手性模板分子,合成出了它的两个七元环衍生物。通过对它们的旋光值、X衍射结构及构象的研究,找出了它们的螺旋结构与旋光性的关系,并对其旋光大小进行了比较。此外,首次提出我们建立的螺旋片段判定规则及我们定义的ω值。     

S-(-)-2,2′-联二萘酚衍生物的合成及其螺旋结构与旋光性的关系

以S-(-)-2,2’-联二萘酚为手性模板分子,合成出了它的两个七元环衍生物.通过对它们的旋光值、X衍射结构及构象的研究,找出了它们的螺旋结构与旋光性的关系,并对其族光大小进行了比较.此外,首次提出我们建立的螺旋片段判定规则及我们定义的ω值.     

Optical rotatory strength calculation by evaluating the gradient matrix through the equation of motion

A straightforward generalization of Linderberg's equation-of-motion-based formula for the matrix elements of the linear momentum operator is proposed. The essential feature of the modification is the abandonment of the zero differential overlap (ZDO) approximation for the electric transition integrals. It is expected that this new formula gives better transition moments and, consequently, better optical rotatory strength values. The results of this modification are analysed numerically for the rotatory strengths of the twisted hydrogen peroxide and for the 1,6-diazaspiro[4,4]-nonane-2,7-dione, C₇H₁₀N₂O₂, molecule, using a CNDO Hamiltonian. For both systems a definitive improvement of calculated rotatory strengths resulted.     

Energy partitioning schemes

The paper gives an overview, generalization and systematization of the different energy decomposition schemes we have devised in the last few years by using both the 3-D analysis (the atoms are represented by different parts of the physical space) and the Hilbert space analysis in terms of the basis orbitals assigned to the individual atoms. The so called "atomic decomposition of identity" provides us the most general formalism for analyzing different physical quantities in terms of individual atoms or pairs of atoms. (The "atomic decomposition of identity" means that we present the identity operator as a sum of operators assigned to the individual atoms.) By proper definitions of the atomic operators, both Hilbert-space and the different 3-D decomposition schemes can be treated on an equal footing. Several different but closely related energy decomposition schemes have been proposed for the Hilbert space analysis. They differ by exact or approximate treatment of the three- and four-center integrals and by considering the kinetic energy as a part of the atomic Hamiltonian or as having genuine two-center components, too. (Also, some finite basis correction terms may be treated in different manners.) The exact schemes are obtained by using the "atomic decomposition of identity". In the approximate schemes a projective integral approximation is also introduced, thus the energy components contain only one- and two-center integrals. The diatomic energy contributions have also been decomposed into terms of different physical nature (electrostatic, exchange etc.) The 3-D analysis may be performed either in terms of disjunct atomic domains, as in the case of the AIM formalism, or by using the so called "fuzzy atoms" which do not have sharp boundaries but exhibit a continuous transition from one to another. The different schemes give different numbers, but each is capable of reflecting the most important intramolecular interactions as well as the secondary ones--e.g. intramolecular interactions of type C-H[...]O.     

Structure-property relationships for three-photon absorption in stilbene-based dipolar and quadrupolar chromophores

Based on essential-state models for three-photon absorption (3PA), we have investigated the structure-property relationships for stilbene-based dipolar and quadrupolar chromophores. The emphasis lies on the evolution of the 3PA cross section with the degree of ground-state polarization. For dipolar systems, we find a dominant role played by Deltamu, which expresses the change in dipole moment between the ground state and the 3PA active excited state. Thus, the strategies usually applied to maximize the second-order polarizability beta are also applicable to optimize the 3PA cross section. For quadrupolar systems, the 3PA response is dominated by contributions from channels including various low-lying two-photon allowed states, which limits the applicability of essential-state models. Optimization strategies can be proposed but vary for different ranges of ground-state polarization.     

Chiroptical spectroscopy and the validation of crystal structure stereochemical assignments

The absolute stereochemistry of chiral molecules is ideally established to atomic resolution by X-ray crystallographic analysis. However, chiroptical spectroscopies, namely electronic circular dichroism (ECD), optical rotatory dispersion (ORD), vibrational circular dichroism (VCD) and Raman optical activity (ROA), play important complementary roles in establishing relative and absolute sterochemistries as well as allowing determinations of optical purity. A brief summary of chiroptical spectroscopies is presented, along with guidance to their advantages and disadvantages. The application of ECD to verifying that single crystals selected for crystallographic analysis are indeed representative of bulk material is described.