An official website of the United States government
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
Static polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA)
An analytical implementation of static dipole polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic [Formula: see text] scaling of operation count and [Formula: see text] scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree–Fock (HF), semilocal density functional approximations (DFAs), second-order Møller–Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the “overpolarization” problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Na n for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure.
more »
« less
- PAR ID:
- 10417084
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 157
- Issue:
- 16
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 164107
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)A major challenge in density functional theory (DFT) is the development of density functional approximations (DFAs) to overcome errors in existing DFAs, leading to more complex functionals. For such functionals, we consider roles of the noninteracting reference systems. The electron density of the Kohn–Sham (KS) reference with a local potential has been traditionally defined as being equal to the electron density of the physical system. This key idea has been applied in two ways: the inverse calculation of such a local KS potential for the reference from a given density and the direct calculation of density and energy based on given DFAs. By construction, the inverse calculation can yield a KS reference with the density equal to the input density of the physical system. In application of DFT, however, it is the direct calculation of density and energy from a DFA that plays a central role. For direct calculations, we find that the self-consistent density of the KS reference defined by the optimized effective potential (OEP), is not the density of the physical system, when the DFA is dependent on the external potential. This inequality holds also for the density of generalized KS (GKS) or generalized OEP reference, which allows a nonlocal potential, when the DFA is dependent on the external potential. Instead, the density of the physical system, consistent with a given DFA, is given by the linear response of the total energy with respect to the variation of the external potential. This is a paradigm shift in DFT on the use of noninteracting references: the noninteracting KS or GKS references represent the explicit computational variables for energy minimization, but not the density of the physical system for external potential-dependent DFAs. We develop the expressions for the electron density so defined through the linear response for general DFAs, demonstrate the results for orbital functionals and for many-body perturbation theory within the second-order and the random-phase approximation, and explore the connections to developments in DFT.more » « less
-
The temperature dependence of the complex dielectric function [Formula: see text] of bulk Ge near the direct bandgap was investigated with spectroscopic ellipsometry at temperatures between 10 and 710 K. Second derivatives of the dielectric function with respect to energy are obtained using a digital linear filter method. A model that incorporates excitonic effects using the Tanguy model for the Hulthén potential [C. Tanguy, Phys. Rev. B 60, 10660 (1999)] was used to fit the dielectric function and its second derivatives simultaneously. Using [Formula: see text] theory and literature values for effective masses, reasonable agreement with the experiment is obtained for [Formula: see text] up to room temperature using the direct bandgap and its broadening as the only adjustable parameters.more » « less
-
It is demonstrated that a double hybrid density functional approximation, ωB88PTPSS, that incorporates equipartition of density functional theory and the non-local correlation, however with a meta-generalized gradient approximation correlation functional, as well as with the range-separated exchange of ωB2PLYP, provides accurate excitation energies for conventional systems, as well as correct prescription of negative singlet–triplet gaps for non-conventional systems with inverted gaps, without any necessity for parametric scaling of the same-spin and opposite-spin non-local correlation energies. Examined over “safe” excitations of the QUESTDB set, ωB88PTPSS performs quite well for open-shell systems, correctly and fairly accurately [relative to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) reference] predicts negative gaps for 50 systems with inverted singlet–triplet gaps, and is one of the leading performers for intramolecular charge-transfer excitations and achieves near-second-order approximate coupled cluster (CC2) and second-order algebraic diagrammatic construction quality for the Q1 and Q2 subsets. Subsequently, we tested ωB88PTPSS on two sets of real-life examples from recent computational chemistry literature–the low energy bands of chlorophyll a (Chl a) and a set of thermally activated delayed fluorescence (TADF) systems. For Chl a, ωB88PTPSS qualitatively and quantitatively achieves DLPNO-STEOM-CCSD-level performance and provides excellent agreement with experiment. For TADF systems, ωB88PTPSS agrees quite well with spin-component-scaled CC2 (SCS-CC2) excitation energies, as well as experimental values, for the gaps between the S1 and T1 excited states.more » « less
-
Spin-to-charge conversion and the reverse process are now critically important physical processes for a wide range of fundamental and applied studies in spintronics. Here, we experimentally demonstrate effective spin-to-charge conversion in thermally evaporated chromium thin films using the longitudinal spin Seebeck effect (LSSE). We present LSSE results measured near room temperature for Cr films with thicknesses from 2 to 11 nm, deposited at room temperature on bulk polycrystalline yttrium-iron-garnet (YIG) substrates. Comparison of the measured LSSE voltage, [Formula: see text], in Cr to a sputtered Pt film at the same nominal thickness grown on a matched YIG substrate shows that both films show comparably large spin-to-charge conversion. As previously shown for other forms of Cr, the LSSE signal for evaporated Cr/YIG shows the opposite sign compared to Pt, indicating that Cr has a negative spin Hall angle, [Formula: see text]. We also present measured charge resistivity, [Formula: see text], of the same evaporated Cr films on YIG. These values are large compared to Pt and comparable to [Formula: see text]-W at a similar thickness. Non-monotonic behavior of both [Formula: see text] and [Formula: see text] with film thickness suggests that spin-to-charge conversion in evaporated Cr, which we expect has a different strain state than previously investigated sputtered films, could be modified by spin density wave antiferromagnetism in Cr.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0103664
