Density functional calculations on electronic circular dichroism spectra of chiral transition metal complexes

Excitation and circular dichroism spectra of (−)-(3aS, 7aS)-2-chalcogena-trans-hydrindans(Ch = S, Se, Te): SAC and SAC-CI calculations

The ground and several electronic excited states of (3aS,7aS)-2-chalcogena-trans-hydrindans were calculated by the symmetry adapted cluster (SAC) and SAC-configuration interaction (SAC-CI) methods. Theoretical electronic excitation spectra and natural circular dichroism (CD) spectra were obtained for these compounds, and the calculated spectra showed good agreement with the experimental ones reported by Laur (Proceedings of the Third International Symposium on Organic Selenium and Tellurium compounds, Metz, France, 1979, pp. 219-299). For all the chalcogen compounds, the first singlet excited states are assigned to n-sigma* and the other states are assigned to n-Rydberg in our calculations. It indicates that the spectra for the sulfide, selenide, and telluride are almost regarded as the analogues except for the red shifts of the band positions from the sulfide to the telluride. For the telluride, however, the experimental spectra have shapes that cannot be interpreted by the singlet excitations solely. Our calculations predict the triplet states that account for the spectral shapes, indicating importance of the spin-orbit interaction effects for the accurate reproduction of the experimental spectra of the telluride.

Absolute Configuration of Conformationally Flexiblecis-Dihydrodiol Metabolites by the Method of Confrontation of Experimental and Calculated Electronic CD Spectra and Optical Rotations

We have determined the absolute configurations of conformationally flexible cis-dihydrodiol metabolites (cis-1,2-dihydroxy-3,5-cyclohexadienes), bearing different substituents (e.g., Br, F, CF3, CN, Me) in 3- and 5-positions, by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations. Convergent results were obtained by both methods in eight out of ten cases. For the difficult cases, where either conformer population and/or chiroptical properties (calculated rotational strengths of the long-wavelength Cotton effect or optical rotations) of contributing conformers remain inconclusive, the absolute configuration could still be correctly assigned based on one of the biased properties (either ECD or optical rotation). This approach appears well-suited for a broad spectrum of conformationally flexible chiral molecules.

Chiroptical Properties of (R)-3-Chloro-1-butene and (R)-2-Chlorobutane

Coupled cluster and density functional models of specific rotation and vacuum UV (VUV) absorption and circular dichroism spectra are reported for the conformationally flexible molecules (R)-3-chloro-1-butene and (R)-2-chlorobutane. Coupled cluster length- and modified-velocity-gauge representations of the Rosenfeld optical activity tensor yield significantly different specific rotations for (R)-3-chloro-1-butene, with the latter providing much closer comparison (within 3%) to the available gas-phase experimental data at 355 and 633 nm. Density functional theory overestimates the experimental rotations for (R)-3-chloro-1-butene by approximately 80%. For (R)-2-chlorobutane, on the other hand, all three models give reasonable comparison to experiment. The theoretical specific rotations of the individual conformers of (R)-3-chloro-1-butene are much larger than those of (R)-2-chlorobutane, in disagreement with previous studies of the temperature dependence of the experimental rotations in solution. Simulations of VUV absorption and circular dichroism spectra reveal large differences between the coupled cluster and density functional excitation energies and the rotational strengths. However, while these differences lead to very different specific rotations for (R)-3-chloro-1-butene, they have much less impact on the computed specific rotations for (R)-2-chlorobutane. In addition, the coupled cluster VUV absorption spectrum of (R)-2-chlorobutane compares well to experiment.

Electronic circular dichroism spectra from the complex polarization propagator

The complex linear polarization propagator approach has been applied to the calculation of electronic circular dichroism spectra of 3R-chloro-1-butyne, 3R-methylcyclopentanone, 3S-methylcyclohexanone, 4R-1,1-dimethyl-[3]-(1,2)ferrocenophan-2-on, S-3,3,3',3'-tetramethyl-1,1'-spirobi[3H,2,1]-benzoxaselenole, and the fullerene C84. Using time-dependent Kohn-Sham density functional theory, it is shown that a direct and efficient evaluation of the circular dichroism spectrum can be achieved. The approach allows for the determination of the circular dichroism at an arbitrary wavelength thereby, in a common formulation and implementation, covering the visible, ultraviolet, and x-ray regions of the spectrum. In contrast to traditional methods, the entire manifold of excited states is taken into account in the calculation of the circular dichroism at a given wavelength.

SAC and SAC−CI Calculations of Excitation and Circular Dichroism Spectra of Straight-Chain and Cyclic Dichalcogens

Accurate quantum-chemical calculations of the excitation energies and the rotatory strengths of dichalcogens R-Ch-Ch-R (Ch = S, Se, Te) were carried out with the symmetry adapted cluster (SAC) and SAC-configuration interaction (CI) methods. A series of straight-chain molecules (dihydrogen dichalcogenide, dimethyl dichalcogenide, and (+)-bis(2-methylbutyl) dichalcogenide) and one cyclic molecule (2,3-(R,R)-dichalcogenadecalin) were adopted for comparative analysis. The calculated excitation and circular dichroism (CD) spectra were in good agreement with experimental ones (Laur, P. H. A. In Proceedings of the Third International Symposium on Organic Selenium and Tellurium Compounds; Cagniant, D., Kirsch, G., Eds.; Universite de Metz: Metz, 1979; pp 219-299) within 0.3 eV. The fitting CD spectra also reasonably reproduced the experimental ones. In all the molecules adopted, the first and second lowest bands were assigned to the n-sigma(Ch-Ch) transition and the third and fourth lowest bands to the n-sigma(Ch-R) transition. The first and second lowest bands apparently depended on the R-Ch-Ch-R dihedral angle, suggesting that the orbital energies of two sigma(Ch-Ch) change with the R-Ch-Ch-R dihedral angle. This calculated trend agrees with two empirical rules: the C(2) rule and the quadrant rule.

Ab Initio Optical Rotatory Dispersion and Electronic Circular Dichroism Spectra of (S)-2-Chloropropionitrile

Coupled-cluster and density-functional methods have been used to determine specific rotations and electronic circular dichroism (ECD) rotational strengths for (S)-2-chloropropionitrile. Coupled-cluster specific rotations using both the length- and velocity-gauge representations of the electric-dipole operator, computed with basis sets of triple-zeta quality containing up to 326 functions, compare very well with recently reported gas-phase cavity-ring-down polarimetry data. ECD rotational strengths for the six lowest-lying excited states are found to vary in sign, and the second excited state, which has a larger rotational strength than the first by a factor of 4, was found to yield a much larger contribution (by a factor of 10) to the overall negative specific rotation observed both experimentally and theoretically. However, both valence and Rydberg states appear to make substantial contributions to the total rotation, often of opposite sign from the converged/linear-response result. Furthermore, the sum-over-states approach was found to be inadequate for reproducing the specific rotations derived from the linear-response approach, even when 100 excited states (well beyond the estimated ionization limit) were included in the summation. Density-functional specific rotations using the B3LYP functional with basis sets of quadruple-zeta quality containing up to 588 functions are found to be too large compared to experiment by approximately a factor of 2. This error appears to be related to both the underestimation of the electronic excitation energies, as well as concomitant overestimation of the corresponding ECD rotational strengths. Although earlier studies reported good agreement between density-functional specific rotations and experiment when electric-field-dependent functions were used in conjunction with a double-zeta-quality basis set, the results reported here, which are near the basis-set limit, suggest that this agreement may be fortuitous.

Time-Dependent Density Functional Calculations of Optical Rotatory Dispersion Including Resonance Wavelengths as a Potentially Useful Tool for Determining Absolute Configurations of Chiral Molecules

The optical rotations for six organic molecules (verbenone, fenchone, camphor, nopinone, Tröger's base, dimethyl-cyclopropane) and the transition metal complex [Co(en)(3)](3+) were calculated as a function of wavelength using time-dependent density functional theory (TDDFT). In the calculations, a realistic behavior of the optical rotation in the vicinity of an electronic transition was obtained by using a phenomenological damping parameter of the order of 0.2 eV (0.007 au). In comparison with experiment, for the molecules studied here the sign and order of magnitude of the optical rotation as well as the excitation energies were reasonably well reproduced in most computations. These findings apply to the investigated wavelength ranges typically between about 200 and 650 nm even when using comparatively small basis sets. Such calculations might therefore routinely be applied to help assigning the absolute configurations of chiral molecules. Supplementary calculations of the circular dichroism (CD) and comparison with experimental CD were used for further assessment of the optical rotation calculations. In particular, a combined study of optical rotation and CD turned out to be useful in cases where the optical rotatory dispersion in a specific energy range exhibits a considerable blue or red shift or where it is difficult to reproduce because of an interplay of several competing Cotton effects. The influence of basis set, density functional, and the damping parameter was also investigated.

The electronic structure and spectra of spin-triplet ground state bis(biuretato)cobalt(iii) coordination compounds

The planar coordination compounds of cobalt(III) with bis(biuretato) ligands are highly unusual due to their intermediate spin triplet ground state. Density functional theory (DFT) and time-dependent DFT have been applied in a study of the structure and electronic spectroscopy of this type of coordination compounds. The investigations included prediction and spectroscopic measurements of the absorption and circular dichroism (CD), as well as an experimental study of the magnetic CD. The results obtained by TD-DFT were in excellent agreement with the observed spectral features, both regarding the d-d and the charge transfer regions. There was noted a systematic blue-shift of the TD-DFT results compared to experiment, corresponding to an offset of ca. 0.5 microm(-1) and a scaling factor of 1.25 for the transition energies. The DFT results are rationalized in terms of a qualitative MO analysis.

Density Functional Calculation of the Electronic Circular Dichroism Spectra of the Transition Metal Complexes [M(phen)3]2+ (M = Fe, Ru, Os)

The circular dichroism spectra of the tris-bidentate metal complexes Lambda-[M(phen)3]2+, with M = Fe, Ru, Os and phen = 1,10-tris-phenanthroline, are investigated computationally, employing time-dependent density functional theory. Good agreement with experimental spectra is obtained for Ru and Os. The Lambda-[Os(phen)3]2+ spectrum is analyzed in detail. It is shown how relativistic effects red shift CD bands where the Os 5d-orbital participates to a large extent in the excitations. Further, the participation of the metal in the ligand pi --> pi exciton CD is determined to be of the order of 10%. Though solvent effects can have a noticeable effect on individual transitions and rotatory strengths, they are demonstrated to have only a very small overall effect on the resulting simulated CD spectra. For Lambda-[Fe(phen)3]2+, the results are shown to be rather sensitive to the choice of the applied hybrid and nonhybrid density functionals, and the optimized geometries based thereupon. In particular, the sign pattern of the lower-energy part (up to 33 x 10(3) cm(-1)) of the Lambda-[Fe(phen)3]2+ CD spectrum is difficult to reproduce. Some combinations of functionals and geometries yield good agreement with experiment, but no "best" approach can be devised based on the available results. Possible sources of errors in the spectrum of Lambda-[Fe(phen)3]2+ due to deficiencies in the functionals and the exchange-correlation kernels are investigated.

Absolute Configuration, Conformation, and Circular Dichroism of Monocyclic Arene Dihydrodiol Metabolites: It is All Due to the Heteroatom Substituents

Absolute configurations and conformations of selected cis-1,2-dihydrodiols, isolated from bacterial enzyme-catalyzed arene dihydroxylation, have been examined by comparison of experimental and DFT-calculated CD spectra and confrontation with the results of X-ray diffraction studies in the crystalline phase. The equilibrium between the diene P and M conformers in cis-dihydrodiols is strongly dependent on the intramolecular OH-OH, OH-pi, and OH-F hydrogen bonding pattern and is crucial in determining the sign and magnitude of the long-wavelength diene pi-pi transition Cotton effect. The differences originate from a dominant contribution of either P-helical (1b, X=Me) or M-helical conformers (1d, X=F), or are due to M and P low-energy conformers, both contributing a positive rotational strength (1c, X=Br). Computations show that cis-dihydrodiol 1e (X=CF3) has only one M conformer stabilized by an intramolecular O-H...F hydrogen bond. cis-Dihydrodiol 1f (X=CN) shows a Cotton effect of the sign opposite to the sense of helicity of the dominating conformer. The results of the computations highlight the inadequacy of the Diene Helicity Rule and the Allylic Chirality Rule to correlate observed Cotton effects with dihydrodiol absolute configuration. A reliable model is presented to predict the absolute configuration of substituted benzene dihydrodiol derivatives from CD spectra, based on the confrontation of DFT-computed and experimental CD spectra. For 3-alkyl derivatives, a simple noncomputational model is offered, which is based on the contributions of the allylic hydroxy groups and the diene core in P and M conformers.

On the Origin of Optical Activity in Tris-diamine Complexes of Co(III) and Rh(III): A Simple Model Based on Time-Dependent Density Function Theory

Time-dependent density functional theory (TD-DFT) is applied to the CD spectra of Lambda(deltadeltadelta)-(+)-[Co(S-pn)n(en)(3-n)]3+ (n = 1, 2, 3) and Lambda(deltadeltadelta)-(+)-[Co(en)3]3+ as well as the stereoisomers Delta-((delta)n(lambda)(3-n))-(-)-[Co(S-pn)n(en)(3-n)]3+ (n = 1, 2, 3) and Delta(deltadeltadelta)-(-)-[Co(en)3]3+. Theory is able to reproduce the major differences in the CD spectra of the species with a Lambda-configuration and their isomers with a Delta-configuration in both the d-d and ligand-to-metal CT region. It is further possible to rationalize the trend in terms of a larger azimuthal distortion away from the octahedral geometry in the Lambda-conformation compared to the Delta-configuration. Considerations were also given to the CD spectra of the lel3-isomer, Delta(lambdalambdalambda)-(-)-[Rh(R-pn)3]3+ and the ob-isomer, Lambda(lambdalambdalambda)-(+)-[Rh(S-pn)3]3+.

CD Spectra of d−f Heterobimetallic Helicates with Segmental Di-Imine Ligands

We have investigated the CD spectra of a series of enantiomerically pure heterobimetallic helicates, Lambda,Lambda-[LnCr(1)(3)](6+) (Ln = Eu, Gd, Tb), which contain segmental di-imine ligands. For the mononuclear precursor of these helicates, Lambda-[Cr(1)(3)](3+), a positive exciton couplet was observed around 330 nm, as expected for a tris(di-imine) complex with this absolute configuration. The titration of Ln(III) ions into a solution of this complex leads to the formation of Lambda,Lambda-[LnCr(1)(3)](6+). During this process, the CD signal was observed to invert to give a signal which was negative at lower energies. We investigated the observed changes in the CD spectra using a ZINDO-based computational method which we have previously developed. We were able to show that the exciton coupling of the chromophores coordinated to the Cr and Ln ions give rise to CD signals of opposite phase, despite having the same nominal absolute configuration. Exciton coupling between chromophores located on different metal centers ("internuclear" exciton coupling) is also predicted to have a significant impact on the observed spectrum. We were able to "deconstruct" the observed CD spectra into a set of competing exciton coupling effects and show that the sign of these spectra does not correlate with the absolute configuration of the individual metal centers.

Calculation of the A term of magnetic circular dichroism based on time dependent-density functional theory I. Formulation and implementation

A procedure for calculating the A term and the A/D ratio of magnetic circular dichroism (MCD) within time-dependent density functional theory (TD-DFT) is described. Utilizing an implementation of the MCD theory within the Amsterdam Density Functional program, the A term contributions to the MCD spectra of MnO(4) (-), CrO(4) (2-), VO(4) (3-), MoO(4) (2-), VO(4) (3-), MoS(4) (2-), Se(4) (2+), Te(4) (2+), Fe(CN)(6) (4-), Ni(CN)(4) (2-), trichlorobenzene, hexachlorobenzene, tribromobenzene, and hexabromobenzene are calculated. For the most part, agreement between theory and experiment for A/D ratios and the relative magnitude of A terms is found to be good, leading to simulated spectra that are similar in appearance to those derived from measurements. The A terms are found to be too small whenever comparison with experiment was possible, probably due to the neglect of environment effects on the incident radiation and the relative low accuracy of dipole strengths calculated within TD-DFT.

On the Origin of the Optical Activity in the d−d Transition Region of Tris-Bidentate Co(III) and Rh(III) Complexes

Time-dependent density functional theory (TD-DFT) has been employed to calculate the rotatory strengths in the d-d transition region for various tris-bidentate Co(III) and Rh(III) complexes. Optimized structural parameters are also reported. Our results confirm a previously proposed relationship between the azimuthal distortion of a complex containing saturated tris(diamine) and its optical activity. Formally d-d transitions are forbidden and should not exhibit optical activity. However, it is shown here that the intensity of these bands originates from a coupling of even ligand combination (participating in the e(g) type LUMO) and an odd ligand combination (participating in the t(2)(g) HOMO). For complexes containing planar unsaturated ligands, the signs of the d-d bands observed from the single-crystal circular and linear dichroisms are in accordance with the TD-DFT predictions. It is shown that by using hypothetical Co(NH(3))(6)(3+) complexes it is possible to estimate the contribution from the azimuthal distortion to the total rotatory strengths of the saturated tris(diamine) complexes. A discussion is also provided of previous theoretical studies and the way in which these investigations rationalized the optical activity.