Performance of Property-Optimized Basis Sets for Optical Rotation with Coupled Cluster Theory

Reduced Scaling Real-Time Coupled Cluster Theory

Real-time coupled cluster (CC) methods have several advantages over their frequency-domain counterparts, namely, response and equation of motion CC theories. Broadband spectra, strong fields, and pulse manipulation allow for the simulation of complex spectroscopies that are unreachable using frequency-domain approaches. Due to the high-order polynomial scaling, the required numerical time propagation of the CC residual expressions is a computationally demanding process. This scaling may be reduced by local correlation schemes, which aim to reduce the size of the (virtual) orbital space by truncation according to user-defined parameters. We present the first application of local correlation to real-time CC. As in previous studies of locally correlated frequency-domain CC, traditional local correlation schemes are of limited utility for field-dependent properties; however, a perturbation-aware scheme proves promising. A detailed analysis of the amplitude dynamics suggests that the main challenge is a strong time dependence of the wave function sparsity.

On the choice of coordinate origin in length gauge optical rotation calculations

In this work, we explore the issue of origin dependence in optical rotation (OR) calculations in the length dipole gauge (LG) using standard approximate methods belonging to density functional theory (DFT) and coupled cluster (CC) theory. We use the origin-invariant LG approach, LG(OI), that we recently proposed as reference for the calculations, and we study whether a proper choice of coordinate origin and molecular orientation can be made such that diagonal elements of the LG-OR tensor match those of the LG(OI) tensor. Using a numerical search algorithm, we show that multiple spatial orientations can be found where the LG and LG(OI) results match. However, a simple analytical procedure provides a spatial orientation where the origin of the coordinate system is close to the center of mass of the molecule. At the same time, we also show that putting the origin at the center of mass is not an ideal choice for every molecule (relative errors in the OR up to 70% can be obtained in out test set). Finally, we show that the choice of coordinate origin based on the analytical procedure is transferable across different methods and it is superior to putting the origin in the center of mass or center of nuclear charge. This is important because the LG(OI) approach is trivial to implement for DFT, but not necessarily for nonvariational methods in the CC family. Therefore, one can determine an optimal coordinate origin at DFT level and use it for standard LG-CC response calculations.

A computational approach for modeling electronic circular dichroism of solvated chromophores

The present study consists in a novel computational protocol to model the UV-circular dichroism spectra of solvated species. It makes use of quantum-chemical calculations on a series of conformations of a flexible chromophore or on a series of chromophore/solvent clusters extracted from molecular dynamic simulations. The protocol is described and applied to the aqueous cationic tripeptide GAG⁺ and to the aqueous neutral decapeptide (GVGVP)₂ . The protocol has proven able to: (i) properly consider the conformational motion of solute in the given environment; (ii) give the actual statistical weight of each conformational state; (iii) provide a reliable quantum mechanical method able to reproduce the spectral features. Temperature effects on conformations and spectral properties are properly taken into account. The role of explicit solvent on the conformational analysis and the spectra calculation is discussed. The comparison of the calculated circular dichroism spectra with experimental ones recorded at different temperatures represents a strict validation test of the method.

Finding reliable methodology for optical rotation and correct predictions of (s)-methyloxirane and (1R,5R)-β-pinene

Theoretical calculations of optical rotation (OR), although important to predict absolute configurations (ACs) and corroborate experiments, require efficient methodology able to reproduce enantiomer specificity and real OR values. Also, troublesome molecules are recurring in the literature, such as (S)-methyloxirane and (1R,5R)-β-pinene. This study evaluates DFT functionals B3LYP, CAM-B3LYP, ωB97X-D, M06-2X, and PBE0 considering basis sets aug-cc-pVDZ, aug-cc-pVTZ, 6-311++G(2d,p), and 6-311++G(3df,2p) in OR prediction of 42 rigid organic molecules assessing cases with wrong enantiomeric determination comparing to available experimental data at wavelengths 355, 589, and 633 nm. Functionals CAM-B3LYP and ωB97X-D with aug-cc-pVTZ are indicated here to reproduce experimental values more accurately considering fewer number of wrong AC predictions, normalized RMSD values below 0.70, and a good approximation to experimental values in hierarchical cluster analysis. Methyloxirane AC was reproduced in CAM-B3LYP and PBE0, with [ α ] 355 = 6 . 94 $$ {\left[\alpha \right]}_{355}=6.94 $$ for CAM-B3LYP/aug-cc-pVTZ close to experimental value [ α ] 355 = 7 . 49 ± 0 . 30 $$ {\left[\alpha \right]}_{355}=7.49\pm 0.30 $$ . Good results were found for AC of β-pinene in M06-2X, CAM-B3LYP, and ωB97X-D while the latter in 6-311++G(3df,2p) obtained OR values of [ α ] 589 = 3 . 44 $$ {\left[\alpha \right]}_{589}=3.44 $$ and [ α ] 689 = 4 . 20 $$ {\left[\alpha \right]}_{689}=4.20 $$ close to experimental values [ α ] 589 = 2 . 8 $$ {\left[\alpha \right]}_{589}=2.8 $$ and [ α ] 689 = 4 . 66 ± 0 . 60 $$ {\left[\alpha \right]}_{689}=4.66\pm 0.60 $$ . The two molecules aforementioned are, for the first time, reported to give valid theoretical OR values in such simple methodologies. OR calculations were all performed after geometry optimization at the same level of theory, and analysis of different functional combinations for each step in β-pinene showed it can interfere with AC prediction even in rigid molecules.

Comparative Study of Vibrational Raman Optical Activity with Different Time-Dependent Density Functional Approximations: The VROA36 Database

A new database, VROA36, is introduced to investigate the performance of computational approaches for vibrational Raman optical activity (VROA) calculations. The database is composed of 36 molecules with known experimental VROA spectra. It includes 93 conformers. Normal modes calculated with B3LYP-D3(BJ)/def2-TZVP are used to compute the VROA spectra with four functionals, B3LYP-D3(BJ), ωB97X-D, M11, and optimally tuned LC-PBE, as well as several basis sets. SimROA indices and frequency scaling factors are used to compare calculated spectra with each other and with experimental data. The four functionals perform equally well independently of the basis set and usually achieve good agreement with the experimental data. For molecules in near- or at-resonance conditions, the inclusion of a complex (damped) linear response approach is important to obtain physically meaningful VROA intensities. The use of any of the tested functional approximations with the def2-SVPD Gaussian-type basis set, or a basis of similar flexibility, can be recommended for efficient and reliable theoretical VROA studies.

Basis Set Dependence of Optical Rotation Calculations with Different Choices of Gauge

In this work, the basis set dependence of optical rotation (OR) calculations is examined for various choices of gauge/level of theory. The OR is calculated for a set of 50 molecules using B3LYP and CAM-B3LYP and 17 molecules using coupled cluster with single and double excitations (CCSD). The calculations employ the correlation-consistent basis sets, aug-cc-pVζZ with ζ = D, T, Q. An inverse-power extrapolation formula is then utilized to obtain OR values at the complete basis set (CBS) limit. We investigate the basis set convergence for these methods and three choices of gauge: length gauge (with gauge-including atomic orbitals, LG(GIAOs), for DFT), the origin-invariant length gauge [LG(OI)], and the modified velocity gauge (MVG). The results show that all methods converge smoothly to the CBS limit and that the LG(OI) approach has a slightly faster convergence rate than the other choices of gauge. While the DFT methods reach gauge invariance at the CBS limit, CCSD does not. The significant difference between the MVG and LG(OI) results at the CBS limit, 26%, indicates that CCSD is not quite at convergence in the description of electron correlation for this property. On the other hand, gauge invariance at the CBS limit for DFT does not lead to the same OR values for the two density functionals, which is also due to electron correlation incompleteness. A limited comparison to gas-phase experimental OR values for the DFT methods shows that CAM-B3LYP seems more accurate than B3LYP. Overall, this study shows that the LG(OI) approach with the aug-cc-pVTZ basis set for DFT, and with the CBS(DT) extrapolation for CCSD, provides a good cost/accuracy balance.

A Density Functional Theory Study of Optical Rotation in Some Aziridine and Oxirane Derivatives

We present time-dependent density functional theory (TDDFT) calculations of the electronic optical rotation (ORP) for seven oxirane and two aziridine derivatives in the gas phase and in solution and compare the results with the available experimental values. For seven of the studied molecules it is the first time that their optical rotation was studied theoretically and we have therefore investigated the influence of several settings in the TDDFT calculations on the results. This includes the choice of the one-electron basis set, the exchange-correlation functional or the particular polarizable continuum model (PCM). We can confirm that polarized quadruple zeta basis sets augmented with diffuse functions are necessary for converged results and find that the aug-pc-3 basis set is a viable alternative to the frequently employed aug-cc-pVQZ basis set. Based on our study, we cannot recommend the generalized gradient functional KT3 for calculations of the ORP in these compounds, whereas the hybrid functional PBE0 gives results quite similar to the long-range correct CAM-B3LYP functional. Finally, we observe large differences in the solvent effects predicted by the integral equation formalism of PCM and the SMD variant of PCM. For the majority of solute/solvent combinations in this study, we find that the SMD model in combination with the PBE0 functional and the aug-pc-3 basis set gives the best agreement with the experimental values.

Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge

This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10%-20% with CAM-B3LYP and 20%-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(-)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistent with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials.

Chiroptical Sensing: A Conceptual Introduction

Chiroptical responses have been an essential tool over the last decades for chemical structural elucidation due to their exceptional sensitivity to geometry and intermolecular interactions. In recent times, there has been an increasing interest in the search for more efficient sensing by the rational design of tailored chiroptical systems. In this review article, advances made in chiroptical systems towards their implementation in sensing applications are summarized. Strategies to generate chiroptical responses are illustrated. Theoretical approaches to assist in the design of these systems are discussed. The development of efficient chiroptical reporters in different states of matter, essential for the implementation in sensing devises, is reviewed. In the last part, remarkable examples of chiroptical sensing applications are highlighted.

Accurate calculation of optically induced birefringences in chiral systems using efficient polarized basis sets

Using state-of-the-art ab initio methodology, we evaluate universal molecular parameters entering the expressions for various optically induced birefringences in chiral fluids. For this, we use the single and double excitation coupled cluster (CCSD) theory together with Dunning's augmented correlation consistent polarized basis sets of increasing size. As this is the first time these parameters are evaluated for chiral molecules using the CCSD approach, we choose possibly small test systems: a model asymmetric methane molecule, and (R)-fluoro-oxirane. With this choice, the convergence of the molecular parameters with the increase of the basis set size is investigated in detail. The results are compared to those obtained with the LPol-n (n = ds, dl, fs) and the ORP basis sets, and to the corresponding Density Functional Theory (DFT) counterparts. We can conclude that the DFT medium constant values are considerably far from coupled cluster, and therefore, aware of the known excellent performance of the CCSD method in the evaluation of various dynamic responses, we do not recommend the former methodology for accurate evaluation of the present properties. Regarding basis set convergence, the performace of the LPol-ds basis set is more efficient than that of the d-aug-cc-pVDZ set, and therefore, the former basis set can be a good choice when dealing with the study of larger systems.

Assessment of DFT for endohedral complexes' dipole moment: PNO-LCCSD-F12 as a reference method

We present a systematic evaluation of the performance of a wide range of exchange-correlation functionals and related dispersion correction schemes for the computation of dipole moments of endohedral complexes, formed through the encapsulation of an AB molecule (AB = LiF, HCl) inside carbon nanotubes (CNTs) of different diameter. The consistency and accuracy of (i) generalized gradient approximation, (ii) meta GGA, (iii) global hybrid, and (iv) range-separated hybrid density functionals are assessed. In total, 37 density functionals are tested. The results obtained using the highly accurate pair natural orbitals based explicitly correlated local coupled cluster singles doubles (PNO-LCCSD-F12) method of Werner and co-workers [Schwilk et al., J. Chem. Theory Comput., 2017, 13, 3650; Ma et al., J. Chem. Theory Comput., 2017, 13, 4871] with the aug-cc-pVTZ basis set serve as a reference. The static electric dipole moment is computed via the finite field response or, when possible, as the expectation value of the dipole operator. Among others, it is shown that functionals belonging to the class of range-separated hybrids, provide results closest to the coupled cluster reference data. In particular, the ωB97X as well as the M11 functional may be considered as a promising choice for computing electric properties of noncovalent endohedral complexes. On the other hand, the worst performance was found for the functionals which do not include the Hartree-Fock exchange. The analysis of both the coupled cluster and the DFT results indicates a strong coupling of dispersion and polarization that may also explain why lower level DFT methods, as well as Hartree-Fock and MP2, cannot yield dipole moments beyond a qualitative agreement with the higher order reference data. Interestingly, the much smaller and less systematically constructed basis sets of Pople of moderate size provide results of accuracy at least comparable with the extended Dunning's aug-cc-pVTZ basis set.