Time-dependent density functional theory for calculating origin-independent optical rotation and rotatory strength tensors

An approach to calculate origin-independent electronic chiroptical property tensors using time-dependent density functional theory (TDDFT) and gauge-including atomic orbital (GIAO) basis sets is evaluated. Computations of origin-dependent optical rotation tensors and of rotatory strengths needed to simulate circular dichroism spectra are presented. The optical rotation tensor computations employ solutions of coupled perturbed Kohn-Sham equations for a dynamic electric field and a static magnetic field. Because the magnetic field is time independent, the GIAO treatment is somewhat simplified compared to a previously reported method, at some added computational cost if hybrid functionals are employed. GIAO rotatory strengths are also calculated, using transition density matrices from a standard TDDFT excitation energy module. A new implementation in the NWChem quantum chemistry package is employed for representative computations of origin-invariant chiroptical response tensors for methyloxirane, norbornenone, and the ketosteroid androstadienone. For the steroid molecule the vibrational structure of the CD spectrum is modeled explicitly by using calculated Franck-Condon factors. The agreement with experiment is favorable.     

Non-empirical assignment of the absolute configuration of (-)-naringenin, by coupling the exciton analysis of the circular dichroism spectrum and the ab initio calculation of the optical rotatory power

The non-empirical assignment of the absolute configuration of (-)-naringenin, the aglycone of (-)-naringin, a flavanone glycoside abundant in the albedo of immature grapefruits and showing several interesting biological properties, has been approached by two different methods: (a) the exciton analysis of the circular dichroism (CD) spectrum and (b) the ab initio calculation of the optical rotatory power. Both the methods indicate the configurational correlation (-)/(S), as empirically suggested by Gaffield. A comparison of advantages and limitations of the two methods of analysis is also presented.     

The current state of ab initio calculations of optical rotation and electronic circular dichroism spectra

The current ability of ab initio models to compute chiroptical properties such as optical rotatory dispersion and electronic circular dichroism spectra is reviewed. Comparison between coupled cluster linear response theory and experimental data (both gas and liquid phase) yields encouraging results for small to medium-sized chiral molecules including rigid species such as (S)-2-chloropropionitrile and (P)-[4]triangulane, as well as conformationally flexible molecules such as (R)-epichlorohydrin. More problematic comparisons are offered by (S)-methyloxirane, (S)-methylthiirane, and (1S,4S)-norbornenone, for which the comparison between theory and experiment is much poorer. The impact of basis-set incompleteness, electron correlation, zero-point vibration, and temperature are discussed. In addition, future prospects and obstacles for the development of efficient and reliable quantum chemical models of optical activity are discussed, including the problem of gauge invariance, scaling of the coupled cluster approach with system size, and solvation.     

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.     

Determination of the absolute configuration of flexible molecules by ab initio ORD calculations: a case study with cytoxazones and isocytoxazones

Ab initio calculations of the optical rotatory power of the natural cytokine modulator cytoxazone 1 and its trans-diastereomer 2, as well as the structural isomers cis-3 and trans-4 isocytoxazones, have been performed at four different wavelengths (589, 546, 435, and 405 nm) by Density Functional Theory. The calculation of ORD curves provides a reliable method for the assignment of absolute configuration of these conformationally flexible molecules. The absolute configurations of isocytoxazones has been established as (+)-(4R,5S)-cis-3 and (+)-(4S,5S)-trans-4.     

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。     

Ab initio calculation of optical rotatory dispersion (ORD) curves: a simple and reliable approach to the assignment of the molecular absolute configuration

In this paper, both Hartree-Fock (HF) and density functional theory (DFT) methods have been used to make ab initio calculations of the optical rotatory power of selected molecules at several wavelengths; that is, part of the optical rotatory dispersion (ORD) curve has been predicted. This approach constitutes a new, simple, and reliable method to assign the molecular absolute configuration, at least for rigid molecules such as those studied in the present work. In fact, in this way, it is possible to overcome the difficulties connected to some relevant cases, in particular that of (-)-beta-pinene, for which even a very high-level (DFT/B3LYP/6-311++G(2d,2p)) calculation affords the wrong sign of the optical rotation at 633 nm. On the contrary, the predicted ORD curve, even using small basis sets, reproduces (below 400 nm) the experimental trend well, allowing for the correct configurational assignment. This result clearly shows that to have a reliable configurational assignment the comparison between experimental and predicted rotation values must be carried out at different wavelengths and not at a single frequency. The reason for this is that working at wavelengths approaching the absorption maximum the [alpha](lambda) values become larger and their prediction becomes more reliable. Coupling the use of an inexpensive instrument (a polarimeter working at a few wavelengths) with the use of a DFT-calculation package can also allow the experimental organic chemist to arrive, quickly and reliably, at the assignment of the molecular absolute configuration.     

The optical activity of carvone: a theoretical and experimental investigation

The optical rotatory dispersion (ORD) and circular dichroism of the conformationally flexible carvone molecule has been investigated in 17 solvents and compared with results from calculations for the "free" (gas phase) molecule. The G3 method was used to determine the relative energies of the six conformers. The optical rotation of (R)-(-)-carvone at 589 nm was calculated using coupled cluster and density functional methods, including temperature-dependent vibrational corrections. Vibrational corrections are significant and are primarily associated with normal modes involving the stereogenic carbon atom and the carbonyl group, whose n → π? excitation plays a significant role in the chiroptical response of carvone. Without the inclusion of vibrational corrections the optical rotation calculated with CCSD and DFT has the opposite sign of experimental data. Calculations of optical rotation performed in solution using the polarizable continuum model were also opposite in sign when compared to that of the experiment.     

Calculation of the fine structure and intensity of the singlet-triplet transitions in the imidogen radical

The singlet-triplet transition moments are calculated for the NH radical by multiconfiguration self-consistent field (MCSCF) method with a quadratic response (QR) technique. The band systems in the visible region (b(1)Sigma(+)-->X(3)Sigma(-) and a(1)Delta-->X(3)Sigma(-)) of the NH radical are analyzed in comparison with previous ab initio treatments and with the recent experimental data in attempt to solve some discrepancies. The b(1)Sigma(+)-->X(3)Sigma(Omega)(-) transition moments ratio for the two spin sublevels Omega = 1 and Omega=0 of the ground state is well reproduced and the radiative lifetime of the b(1)Sigma(+) state (tau(b)=58 ms) is obtained in a good agreement with the experimental value tau(b)=53((-13)(+17)) ms. The A(3)Pi<--a(1)Delta transition probability is calculated for the first time and found to be in an excellent agreement with the recent optical pumping measurements of the NH radical in a molecular beam, where population transfer from the metastable a(1)Delta state to the ground X(3)Sigma(-) state is achieved. For the a(1)Delta-->X(3)Sigma(-) transition some improvement is achieved in comparison with the previous ab initio results, but the calculated radiative lifetime (tau(a)=3.9 s) is still much lower than the recent measurement provides (tau(a)=12.5 s). The zero field splitting and spin-rotation coupling constants are calculated for the ground state by different methods and advantage of the density functional theory is stressed.     

Optical properties of large molecules and clusters in the frenkel exciton picture

Frenkel exciton theory is reviewed. This theory yields general formulas relating the absorption and circular dichroism spectra of large molecules or clusters to the optical properties of their subunits. It is shown that for weakly interacting systems, the circular dichroism associated with a band of exciton states is proportional to tr( FH ), where F is an “optical matrix” constructed from the positions and transition dipole moments of the subunits, and H is an interaction-energy matrix. It is shown that if a system expnds isotropically, then tr( FH ) falls off as the inverse square of the linear dimensions. This result is compared with experimental measurements of the low-temperature optical rotatory dispersion of proteins as a function of temperature. The optical properties of helical polymers are also discussed as a function of their geometrical parameters.     

Anisotropic dipole polarizability of transition metal atoms: Sc(2D), Ti(3F,3P), V(4F,4P,6D), Ni(3F) and ions: Sc2+(2D), Ti2+(3F,3P)

Dipole polarizability tensor components and quadrupole moments of transition-metal atoms Sc, Ti, V, Ni, and Cu and ions Sc2+ and Ti2+ are computed using finite field complete active space self-consistent field and multireference configuration interaction ab initio methods. Perpendicular components of the dipole polarizability tensor are calculated from equations involving only parallel components of the polarizability tensor and its average value. Mean polarizability and polarizability anisotropy decrease in the Sc-Ni series. Relativistic effects are accounted for with the Douglas-Kroll Hamiltonian. The consequences of the anisotropic properties of these atoms to their interactions with spherically symmetric rare gases are also discussed.     

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.     

Assignment of the absolute configuration of (+)-diplopyrone, the main phytotoxin produced by Diplodia mutila, the pathogen of the cork oak decline, by a nonempirical analysis of its chiroptical properties

The nonempirical assignment of the absolute configuration of (+)-diplopyrone, the main phytotoxin of Diplodia mutila, i.e., an endophytic fungus, widespread in Sardinian oak forests, and considered one of the main causes of cork oak decline, has been approached by two different methods: (a) the exciton analysis of the circular dichroism (CD) spectrum and (b) the ab initio calculation of the optical rotatory power. Both methods indicate that (+)-diplopyrone is 6-[(1S)-1-hydroxyethyl]-2,4a(S),6(R),8a(S)-tetrahydropyrano[3,2-b]pyran-2-one, so the stereostructure of this important biomolecule is safely determined for the first time. A comparison of advantages and limitations of the two methods of analysis is also presented.     

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.     

Binding Energies of Proton-Bound Dimers of Imidazole and n-Acetylalanine Methyl Ester Obtained by Blackbody Infrared Radiative Dissociation

The dissociation kinetics of protonated n-acetyl-L-alanine methyl ester dimer (AcAlaME(d)), imidazole dimer, and their cross dimer were measured using blackbody infrared radiative dissociation (BIRD). Master equation modeling of these data was used to extract threshold dissociation energies (E(o)) for the dimers. Values of 1.18 +/- 0.06, 1.11 +/- 0.04, and 1.12 +/- 0.08 eV were obtained for AcAlaME(d), imidazole dimer, and the cross dimer, respectively. Assuming that the reverse activation barrier for dissociation of the ion-molecule complex is negligible, the value of E(o) can be compared to the dissociation enthalpy (DeltaH(d) degrees ) from HPMS data. The E(o) values obtained for the imidazole dimer and the cross dimer are in agreement with HPMS values; the value for AcAlaME(d) is somewhat lower. Radiative rate constants used in the master equation modeling were determined using transition dipole moments calculated at the semiempirical (AM1) level for all dimers and compared to ab initio (RHF/3-21G*) calculations where possible. To reproduce the experimentally measured dissociation rates using master equation modeling, it was necessary to multiply semiempirical transition dipole moments by a factor between 2 and 3. Values for transition dipole moments from the ab initio calculations could be used for two of the dimers but appear to be too low for AcAlaME(d). These results demonstrate that BIRD, in combination with master equation modeling, can be used to determine threshold dissociation energies for intermediate size ions that are in neither the truncated Boltzmann nor the rapid energy exchange limit.     

Optical rotation of achiral pentaerythritol

The optical rotatory power of achiral crystals of achiral pentaerythritol molecules was measured. The maximum rotations were found to be +/-6 degrees /mm. The quantum mechanically computed rotation of pentaerythritol molecules using linear response theory was 6 times larger although the experimental and theoretical tensors were similarly oriented to within 5 degrees .     

Theoretical study of the 1:1 and 2:1 (homo- and heterochiral) complexes of XOOX' (X, X' = H, CH3) with lithium cation

A theoretical study of the 1:1 and 2:1 complexes of XOOX' (X, X' = H, CH(3)) with the lithium cation has been carried out by means of ab initio computational methods up to the MP2/aug-cc-pVTZ level. The optical rotatory power and NMR parameters (absolute chemical shielding and indirect coupling constants) have been calculated. In addition, the racemization barriers within the complexes formed have been evaluated. Special attention has been paid concerning the differences between the 2:1 homo- and heterochiral complexes.     

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)