Localized optimized orbitals, coupled cluster theory, and chiroptical response properties

The impact of orbital localization on the efficiency and accuracy of the optimized-orbital coupled cluster model is examined for the prediction of chiroptical properties, in particular optical rotation. The specific rotations of several test cases-(P)-[4]triangulane, (S)-1-phenylethanol, and chiral conformers of 1-fluoropentane, heptane, and nonane-were computed using an approach in which localization is enforced throughout the orbital optimization and subsequent linear response computation. This method provides a robust local-correlation scheme for future production-level implementation. Although the cross-over point between the canonical and localized coupled cluster approach lies at larger molecules than for ground-state energies, the scheme presented should still provide reduced scaling sufficient to investigate much larger molecules than are presently accessible.     

Ab initio calculation of optical rotation in (P)-(+)-[4]triangulane

Optical rotation, the angle through which plane-polarized light rotates when passed through an enantiomerically pure medium, plays a vital role in the determination of the absolute configurations of chiral molecules such as natural products. We describe new quantum mechanical methodology designed to assist in this endeavor by providing high-accuracy computational optical rotatory dispersion data for matching to experimental results. Comparison between theory and experiment for the rigid, helical molecule trispiro[2.0.0.2.1.1]nonane [also known as (P)-(+)-[4]triangulane], recently synthesized with enantiomeric purity, shows that the coupled cluster quantum chemical model provides superb agreement for optical rotation across a wide range of wavelengths (589-365 nm), with errors averaging only 1%.     

Ab initio calculation of molecular chiroptical properties

This review describes the first-principles calculation of chiroptical properties such as optical rotation, electronic and vibrational circular dichroism, and Raman optical activity. Recent years have witnessed a flurry of activity in this area, especially in the advancement of density-functional and coupled cluster methods, with two ultimate goals: the elucidation of the fundamental relationship between chiroptical properties and detailed molecular structure, and the development of a suite of computational tools for the assignment of the absolute configurations of chiral molecules. The underlying theory and the basic principles of such calculations are given for each property, and a number of representative applications are discussed.     

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.     

Coupled cluster and density functional theory studies of the vibrational contribution to the optical rotation of (S)-propylene oxide

In a previous study (Chemical Physics Letters 2005, 401 , 385) we computed the optical rotatory dispersion of (S)-propylene oxide in gas phase and solution using the hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3. Even for the highly correlated CC3 model combined with a flexible basis set, the theoretical gas-phase specific rotation at 355 nm was found to be negative in contrast to the experimental result. We argued that vibrational contributions could be crucial for obtaining a complete understanding of the experimental result. Here, we show that this indeed is the case by using coupled cluster models and density functional theory methods to calculate the vibrational contributions to the gas-phase specific rotation at 355, 589.3, and 633 nm. While density functional theory (B3LYP and SAOP functionals) overestimates the specific rotation at 355 nm by approximately 1 order of magnitude and yields an incorrect sign at 589.3 and 633 nm, the coupled cluster results are in excellent agreement with the experimentally measured optical rotations. We find that all vibrational modes contribute significantly to the optical rotation and that temperature effects must be taken into account.     

Vibronic coupling simulations for linear and nonlinear optical processes: simulation results

A vibronic coupling model based on time-dependent wavepacket approach is applied to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering, on a series of small molecules. Simulations employing both the long-range corrected approach in density functional theory and coupled cluster are compared and also examined based on available experimental data. Although many of the small molecules are prone to anharmonicity in their potential energy surfaces, the harmonic approach performs adequately. A detailed discussion of the non-Condon effects is illustrated by the molecules presented in this work. Linear and nonlinear Raman scattering simulations allow for the quantification of interference between the Franck-Condon and Herzberg-Teller terms for different molecules.     

Spectroscopic investigation of the structures of dialkyl tartrates and their cyclodextrin complexes

Structures of three dialkyl tartrates, namely, dimethyl tartrate, diethyl tartrate, and diisopropyl tartrate, in CCl4, dimethyl sulfoxide (DMSO)/DMSO-d6, and H2O/D2O solvents have been investigated using vibrational absorption (VA), vibrational circular dichroism (VCD), and optical rotatory dispersion (ORD). VA, VCD, and ORD spectra are found to be dependent on the solvent used. Density functional theory (DFT) calculations are used to interpret the experimental data in CCl4 and DMSO. The trans-COOR conformer with hydrogen bonding between the OH group and the C=O group attached to the same chiral carbon is dominant for dialkyl tartrates both in vacuum and in CCl4. The experimental VA, VCD, and ORD data of dialkyl-D-tartrates in CCl4 correlated well with those predicted for dimethyl-(S,S)-tartrate molecule as both isolated and solvated in CCl4. In DMSO solvent, dialkyl tartrate molecules favor formation of intermolecular hydrogen bonding with DMSO molecules. Clusters of dimethyl-(S,S)-tartrate, with one molecule of dimethyl-(S,S)-tartrate hydrogen bonded to two DMSO molecules, are used for the DFT calculations. A trans-COOR cluster and a trans-H cluster are needed to obtain a reasonable agreement between the predicted and experimental data of dimethyl tartrate in DMSO solvent. VA, VCD, and optical rotations are also measured for dialkyl tartrate-cyclodextrin complexes. It is noted that these properties are barely affected by complexation of dialkyl tartrates with cyclodextrins, indicating weak interaction between tartrates and cyclodextrin. Binding constants of alpha-CD and beta-CD with diethyl L-tartrate in both H2O and DMSO have been determined using isothermal titration calorimetry technique. The smaller binding constants (less than 100) confirmed the weak interaction between tartrates and cyclodextrin in the solution state.     

Accurate adsorption energies for small molecules on oxide surfaces: CH4/MgO(001) and C2H6/MgO(001)

A hybrid method is applied that combines second order Møller–Plesset perturbation theory (MP2) for cluster models with density functional theory for periodic (slab) models to obtain structures and energies for methane and ethane molecules adsorbed on the MgO(001) surface. Single point calculations are performed to estimate the effect of increasing the cluster size on the MP2 energies and to evaluate the difference between coupled cluster (CCSD(T)) and MP2 energies. The final estimates of the adsorption energies are 12.9 ± 1.3 and 18.9 ± 1.8 kJ/mol for CH₄ and C₂H₆, respectively. © 2016 Wiley Periodicals, Inc.     

Quantum mechanics/molecular mechanics study of the catalytic cycle of water splitting in photosystem II

This paper investigates the mechanism of water splitting in photosystem II (PSII) as described by chemically sensible models of the oxygen-evolving complex (OEC) in the S0-S4 states. The reaction is the paradigm for engineering direct solar fuel production systems since it is driven by solar light and the catalyst involves inexpensive and abundant metals (calcium and manganese). Molecular models of the OEC Mn3CaO4Mn catalytic cluster are constructed by explicitly considering the perturbational influence of the surrounding protein environment according to state-of-the-art quantum mechanics/molecular mechanics (QM/MM) hybrid methods, in conjunction with the X-ray diffraction (XRD) structure of PSII from the cyanobacterium Thermosynechococcus elongatus. The resulting models are validated through direct comparisons with high-resolution extended X-ray absorption fine structure spectroscopic data. Structures of the S3, S4, and S0 states include an additional mu-oxo bridge between Mn(3) and Mn(4), not present in XRD structures, found to be essential for the deprotonation of substrate water molecules. The structures of reaction intermediates suggest a detailed mechanism of dioxygen evolution based on changes in oxidization and protonation states and structural rearrangements of the oxomanganese cluster and surrounding water molecules. The catalytic reaction is consistent with substrate water molecules coordinated as terminal ligands to Mn(4) and calcium and requires the formation of an oxyl radical by deprotonation of the substrate water molecule ligated to Mn(4) and the accumulation of four oxidizing equivalents. The oxyl radical is susceptible to nucleophilic attack by a substrate water molecule initially coordinated to calcium and activated by two basic species, including CP43-R357 and the mu-oxo bridge between Mn(3) and Mn(4). The reaction is concerted with water ligand exchange, swapping the activated water by a water molecule in the second coordination shell of calcium.     

Approximate inclusion of four-mode couplings in vibrational coupled-cluster theory

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo?ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.     

Focal point analysis of the singlet-triplet energy gap of octacene and larger acenes

A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet (ST) excitation energies of n-acenes (C(4n+2)H(2n+4)) ranging from octacene (n = 8) to undecacene (n = 11) is presented. The T1 diagnostics of coupled cluster theory and further energy-based criteria demonstrate that all investigated systems exhibit predominantly a (1)A(g) singlet closed-shell electronic ground state. Singlet-triplet (S(0)-T(1)) energy gaps can therefore be very accurately determined by applying the principle of a focal point analysis (FPA) onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets (X = D, T, Q, 5) and single-reference methods [HF, MP2, MP3, MP4SDQ, CCSD, and CCSD(T)] of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations [CCSD(T)] in the limit of an asymptotically complete basis set (cc-pV∞Z), the S(0)-T(1) vertical (adiabatic) excitation energies of these compounds amount to 13.40 (8.21), 10.72 (6.05), 8.05 (3.67), and 7.10 (2.58) kcal/mol, respectively. In line with the absence of Peierls distortions (bond length alternations), extrapolations of results obtained at this level for benzene (n = 1) and all studied n-acenes so far (n = 2-11) indicate a vanishing S(0)-T(1) energy gap, in the limit of an infinitely large polyacene, within an uncertainty of 1.5 kcal/mol (0.06 eV). Lacking experimental values for the S(0)-T(1) energy gaps of n-acenes larger than hexacene, comparison is made with recent optical and electrochemical determinations of the HOMO-LUMO band gap. Further issues such as scalar relativistic, core correlation, and diagonal Born-Oppenheimer corrections (DBOCs) are tentatively examined.     

Large Solvation Effect in the Optical Rotatory Dispersion of Norbornenone

The anomalously large chiroptical response of (1R,4R)‐norbornenone has been probed under complementary vapor‐phase and solution‐phase conditions to assess the putative roles of environmental perturbations. Measurements of the specific rotation for isolated (gas‐phase) molecules could not be reproduced quantitatively by comprehensive quantum‐chemical calculations based on density‐functional or coupled‐cluster levels of linear‐response theory, which suggests that higher‐order treatments may be needed to accurately predict such intrinsic behavior. A substantial, yet unexpected, dependence of the dispersive optical activity on the nature (phase) of the surrounding medium has been uncovered, with the venerable Lorentz local‐field correction reproducing solvent‐mediated trends in rotatory dispersion surprisingly well, whereas more modern polarizable continuum models for implicit solvation performed less satisfactorily.     

Comparison of time-dependent density-functional theory and coupled cluster theory for the calculation of the optical rotations of chiral molecules

A comparison of the abilities of time-dependent density-functional theory (TDDFT) and coupled cluster (CC) theory to reproduce experimental sodium D-line specific rotations for 13 conformationally rigid organic molecules is reported. The test set includes alkanes, alkenes, and ketones with known absolute configurations. TDDFT calculations make use of gauge-including atomic orbitals and give origin-independent specific rotations. CC rotations are computed using both the origin-independent dipole-velocity and origin-dependent dipole-length representations. The mean absolute deviations of calculated and experimental rotations are of comparable magnitudes for all three methods. The origin-independent DFT and CC methods give the same sign of [alpha]D for every molecule except norbornanone. For every large-rotation ketone and alkene for which DFT and CC yield the incorrect sign as compared to liquid-phase experimental data, the corresponding optical rotatory dispersion (ORD) curve is bisignate, suggesting that the two models cannot reliably reproduce the relative excitation energies and antagonistic rotational strengths of multiple competing electronic states that contribute to the total long-wavelength rotation. Several potential sources of error in the theoretical treatments are considered, including basis set incompleteness, vibrational and temperature effects, electron correlation, and solvent effects.     

Basis set dependence of coupled cluster optical rotation computations

Specific rotations for five notoriously difficult molecules, (S)-methyloxirane, (S)-methythiirane, (S)-2-chloropropionitrile, (1S,4S)-norbornenone, and (1R,5R)-β-pinene, have been computed using coupled cluster (CC) and density functional theory (DFT). The performance of the recently developed LPol basis sets compared to the correlation-consistent sets of Dunning and co-workers has been examined at four wavelengths: 355, 436, 589, and 633 nm. We find that the LPol basis sets are an efficient choice, often outperforming the more commonly used correlation-consistent basis sets of comparable size. The smallest of the four, LPol-ds, performs nearly as well as the rest of the series and often yields results closer to the basis set limit than appreciably larger basis sets. While the performance of the LPol bases is admirable, they still do not alleviate the need for high levels of electron correlation, vibrational corrections, and the inclusion of solvent effects to accurately reproduce experimental rotations. In particular in the case of β-pinene we find that they do not produce agreement between DFT and experiment as was previously suggested.     

Vibrational coupled cluster theory

The theory and first implementation of a vibrational coupled cluster (VCC) method for calculations of the vibrational structure of molecules is presented. Different methods for introducing approximate VCC methods are discussed including truncation according to a maximum number of simultaneous mode excitations as well as an interaction space order concept is introduced. The theory is tested on calculation of anharmonic frequencies for a three-mode model system and a formaldehyde quartic force field. The VCC method is compared to vibrational self-consistent-field, vibrational M?ller-Plesset perturbation theory, and vibrational configuration interaction (VCI). A VCC calculation typically gives higher accuracy than a corresponding VCI calculation with the same number of parameters and the same formal operation count.     

Sub-nanometer Au monolayer-protected clusters exhibiting molecule-like electronic behavior: quantitative high-angle annular dark-field scanning transmission electron microscopy and electrochemical characterization of clusters with precise atomic stoichiometry

The synthesis and characterization of the clusters Au13[PPh3]4[S(CH2)11CH3]2Cl2 (1) and Au13[PPh3]4[S(CH2)11CH3]4 (2) are described. These mixed-ligand, sub-nanometer clusters, prepared via exchange of dodecanethiol onto phosphine-halide gold clusters, show enhanced stability relative to the parent. The characterization of these clusters features the precise determination of the number of gold atoms in the cluster cores using high-angle annular dark-field scanning transmission electron microscopy, allowing the assignment of 13 gold atoms (+/-3 atoms) to the composition of both cluster molecules. Electrochemical and optical measurements reveal discrete molecular orbital levels and apparent energy gaps of 1.6-1.7 eV for the two cluster molecules. The electrochemical measurements further indicate that the Au13[PPh3]4[S(CH2)11CH3]2Cl2 cluster undergoes an overall two-electron reduction. The electrochemical and spectroscopic properties of the two Au13 cluster molecules are compared with those of a secondary synthetic product, which proved to be larger Au thiolate-derivatized monolayer-protected clusters with an average core of Au180. The latter shows behavior fully consistent with the adoption of metallic-like properties.     

Computational study of the ion-molecule reactions involving fluxional cations: CH4+ + H2--> CH5+ + H and isotope effect

Potential energy surfaces for the reactions of CH4+ with H2, HD, and D2 have been calculated using high-level ab initio methods, including coupled cluster theory, complete active space self-consistent field, and multireference configuration interaction. The energies are extrapolated to the complete basis set limit using the basis sets aug-cc-pVXZ (X = D, T, Q, 5, 6). The CH4+ + H2 reaction produces CH5+ and H exclusively. Three types of reaction mechanisms have been found, namely, complex-forming abstraction, scrambling, and S(N)2 displacement. The abstraction occurs via a very minor barrier and it is dominant. The other two mechanisms are negligible because of the significant barriers involved. Quantum phase space theory and variational transition state theory are used to calculate the rate coefficients as a function of temperatures in the range of 5-1000 K. The theoretical rate coefficients are compared with the available experimental data and the discrepancy is discussed. The significance of isotope effect, tunneling effect, and nuclear spin effect is investigated. The title reaction is predicted to be slightly exothermic with DeltaHr = -12.7 +/- 5.2 kJ/mol at 0 K.     

Fluorescence properties of organic dyes: quantum chemical studies on the green/blue neutral and protonated DMA-DPH emitters in polymer matrices

The absorption and fluorescence spectra of the green emitter DMA-DPH {1-[4-(dimethylamino)phenyl]-6-phenylhexa-1,3,5-triene} and its protonated blue-emitter form have been studied theoretically through time-dependent density functional theory (TD-DFT) and resolution-of-identity 2nd order perturbative coupled cluster (RI-CC2) calculations with basis sets up to augmented triple-ζ quality, in the gas phase and in solvents of different polarity. These systems dispersed in a polymer matrix are of interest for applications in organic light emitting diode devices (OLEDs). Calculations show that the observed absorption and emission spectra correspond to transitions between the S(0) and S(1) states, in both systems. The nature and characteristics of these transitions are discussed. Excellent agreement with experimental data is obtained, both for absorption and emission, provided that the state-specific polarized continuum model (SS-PCM) method is employed for the inclusion of the solvent.