An official website of the United States government
ABSTRACT In this work, we present simulations of the optical rotation (OR) for five molecular crystals at density functional theory level with periodic boundary conditions (DFT‐PBC). Calculations are compared with experimental measurements and show semi‐quantitative agreement with experimental data for three of the crystals: tartatic acid, benzil, and pentaerythritol. For the other two crystals, aspartic acid and glutamic acid, the calculated data are in qualitative agreement with, but two orders of magnitude smaller than, the experimental data. We provide some arguments that support the theoretical predictions and suggest that the experiments should be revisited. We also find that the position of H centers provided in experimental X‐ray data is not sufficiently reliable for simulating OR, and better results are obtained when H atoms are allowed to relax while keeping heavier elements fixed at the experimental positions. Comparison with molecular cluster calculations with a better functional and a larger basis set indicate that the role of intermolecular interactions (reproduced with the PBC technique) is as or more important than the choice of model chemistry. Despite the current limitations in the level of theory that can be employed, these simulations provide a promising avenue to investigate the effect of intermolecular interactions on this sensitive electronic property of molecules and materials.
more »
« less
Derivation and implementation of the optical rotation tensor for chiral crystals
This paper reports the derivation and implementation of the electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability tensors at the density functional theory level with periodic boundary conditions (DFT-PBC). These tensors are combined to evaluate the Buckingham/Dunn tensor that describes the optical rotation (OR) in oriented chiral systems. We describe several aspects of the derivation of the equations and present test calculations that verify the correctness of the tensor formulation and their implementation. The results show that the full OR tensor is completely origin invariant as for molecules and that PBC calculations match molecular cluster calculations on 1D chains. A preliminary investigation on the choice of density functional, basis set, and gauge indicates a similar dependence as for molecules: the functional is the primary factor that determines the OR magnitude, followed by the basis set and to a much smaller extent the choice of gauge. However, diffuse functions may be problematic for PBC calculations even if they are necessary for the molecular case. A comparison with experimental data of OR for the tartaric acid crystal shows reasonable agreement given the level of theory employed. The development presented in this paper offers the opportunity to simulate the OR of chiral crystalline materials with general-purpose DFT-PBC methods, which, in turn, may help to understand the role of intermolecular interactions on this sensitive electronic property.
more »
« less
- Award ID(s):
- 1650942
- PAR ID:
- 10383283
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 157
- Issue:
- 21
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract 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.more » « less
-
Abstract 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.more » « less
-
Abstract Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction‐basedab initioor density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self‐consistent field Theory (VSCF) and post‐VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode‐coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode‐mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI‐PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post‐VSCF methods to generate more accurate representations of computed infrared spectra.more » « less
-
We present a new implementation for computing spin–orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework in the standard spin-conserving formulation as well in the spin–flip variant (SF-TD-DFT). This approach employs the Breit–Pauli Hamiltonian and Wigner–Eckart’s theorem applied to the reduced one-particle transition density matrices, together with the spin–orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states. Benchmark calculations using several closed-shell organic molecules, diradicals, and a single-molecule magnet illustrate the efficiency of the SOC protocol. The results for organic molecules (described by standard TD-DFT) show that SOCs are insensitive to the choice of the functional or basis sets, as long as the states of the same characters are compared. In contrast, the SF-TD-DFT results for small diradicals (CH 2 , [Formula: see text], SiH 2 , and [Formula: see text]) show strong functional dependence. The spin-reversal energy barrier in a Fe(III) single-molecule magnet computed using non-collinear SF-TD-DFT (PBE0, ωPBEh/cc-pVDZ) agrees well with the experimental estimate.more » « less
