Shaohong L. Li

Perspective: Kohn-Sham density functional theory descending a staircase

This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and-like Marcel Duchamp-we hope to convey progress in a stimulating way.

Configuration Interaction-Corrected Tamm-Dancoff Approximation: A Time-Dependent Density Functional Method with the Correct Dimensionality of Conical Intersections.

Linear response (LR) Kohn-Sham (KS) time-dependent density functional theory (TDDFT), or KS-LR, has been widely used to study electronically excited states of molecules and is the method of choice for large and complex systems. The Tamm-Dancoff approximation to TDDFT (TDDFT-TDA or KS-TDA) gives results similar to KS-LR and alleviates the instability problem of TDDFT near state intersections. However, KS-LR and KS-TDA share a debilitating feature; conical intersections of the reference state and a response state occur in F - 1 instead of the correct F - 2 dimensions, where F is the number of internal degrees of freedom. Here, we propose a new method, named the configuration interaction-corrected Tamm-Dancoff approximation (CIC-TDA), that eliminates this problem. It calculates the coupling between the reference state and an intersecting response state by interpreting the KS reference-state Slater determinant and linear response as if they were wave functions. Both formal analysis and test results show that CIC-TDA gives similar results to KS-TDA far from a conical intersection, but the intersection occurs with the correct dimensionality. We anticipate that this will allow more realistic application of TDDFT to photochemistry.

Model space diabatization for quantum photochemistry

Diabatization is a procedure that transforms multiple adiabatic electronic states to a new representation in which the potential energy surfaces and the couplings between states due to the electronic Hamiltonian operator are smooth, and the couplings due to nuclear momentum are negligible. In this work, we propose a simple and general diabatization strategy, called model space diabatization, that is applicable to multi-configuration quasidegenerate perturbation theory (MC-QDPT) or its extended version (XMC-QDPT). An advantage over previous diabatization schemes is that dynamical correlation calculations are based on standard post-multi-configurational self-consistent field (MCSCF) multi-state methods even though the diabatization is based on state-averaged MCSCF results. The strategy is illustrated here by applications to LiH, LiF, and thioanisole, with the fourfold-way diabatization and XMC-QDPT, and the results illustrate its validity.

Modeling the Partial Atomic Charges in Inorganometallic Molecules and Solids and Charge Redistribution in Lithium-Ion Cathodes

Partial atomic charges are widely used for the description of charge distributions of molecules and solids. These charges are useful to indicate the extent of charge transfer and charge flow during chemical reactions in batteries, fuel cells, and catalysts and to characterize charge distributions in capacitors, liquid-phase electrolytes, and solids and at electrochemical interfaces. However, partial atomic charges given by various charge models differ significantly, especially for systems containing metal atoms. In the present study, we have compared various charge models on both molecular systems and extended systems, including Hirshfeld, CM5, MK, ChElPG, Mulliken, MBS, NPA, DDEC, LoProp, and Bader charges. Their merits and drawbacks are compared. The CM5 charge model is found to perform well on the molecular systems, with a mean unsigned percentage deviation of only 9% for the dipole moments. We therefore formulated it for extended systems and applied it to study charge flow during the delithiation process in lithium-containing oxides used as cathodes. Our calculations show that the charges given by the CM5 charge model are reasonable and that during the delithiation process, the charge flow can occur not only on the transition metal but also on the anions. The oxygen atoms can lose a significant density of electrons, especially for deeply delithiated materials. We also discuss other methods in current use to analyze the charge transfer and charge flow in batteries, in particular the use of formal charge, spin density, and orbital occupancy. We conclude that CM5 charges provide useful information in describing charge distributions in various materials and are very promising for the study of charge transfer and charge flows in both molecules and solids.

Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme

Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations and atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.

Testing time-dependent density functional theory with depopulated molecular orbitals for predicting electronic excitation energies of valence, Rydberg, and charge-transfer states and potential energies near a conical intersection

Kohn-Sham (KS) time-dependent density functional theory (TDDFT) with most exchange-correlation functionals is well known to systematically underestimate the excitation energies of Rydberg and charge-transfer excited states of atomic and molecular systems. To improve the description of Rydberg states within the KS TDDFT framework, Gaiduk et al. [Phys. Rev. Lett. 108, 253005 (2012)] proposed a scheme that may be called HOMO depopulation. In this study, we tested this scheme on an extensive dataset of valence and Rydberg excitation energies of various atoms, ions, and molecules. It is also tested on a charge-transfer excitation of NH3-F2 and on the potential energy curves of NH3 near a conical intersection. We found that the method can indeed significantly improve the accuracy of predicted Rydberg excitation energies while preserving reasonable accuracy for valence excitation energies. However, it does not appear to improve the description of charge-transfer excitations that are severely underestimated by standard KS TDDFT with conventional exchange-correlation functionals, nor does it perform appreciably better than standard TDDFT for the calculation of potential energy surfaces.

Full-dimensional ground- and excited-state potential energy surfaces and state couplings for photodissociation of thioanisole

Analytic potential energy surfaces (PESs) and state couplings of the ground and two lowest singlet excited states of thioanisole (C6H5SCH3) are constructed in a diabatic representation based on electronic structure calculations including dynamic correlation. They cover all 42 internal degrees of freedom and a wide range of geometries including the Franck-Condon region and the reaction valley along the breaking S-CH3 bond with the full ranges of the torsion angles. The parameters in the PESs and couplings are fitted to the results of smooth diabatic electronic structure calculations including dynamic electron correlation by the extended multi-configurational quasi-degenerate perturbation theory method for the adiabatic state energies followed by diabatization by the fourfold way. The fit is accomplished by the anchor points reactive potential method with two reactive coordinates and 40 nonreactive degrees of freedom, where the anchor-point force fields are obtained with a locally modified version of the QuickFF package. The PESs and couplings are suitable for study of the topography of the trilayer potential energy landscape and for electronically nonadiabatic molecular dynamics simulations of the photodissociation of the S-CH3 bond.

Nonintuitive Diabatic Potential Energy Surfaces for Thioanisole.

Diabatization of potential energy surfaces is a technique that enables convenient molecular dynamics simulations of electronically nonadiabatic processes, but diabatization itself is nonunique and can be inconvenient; the best methods to achieve diabatization are still under study. Here, we present the diabatization of two electronic states of thioanisole in the S-CH3 bond stretching and C-C-S-C torsion two-dimensional nuclear coordinate space containing a conical intersection. We use two systematic methods: the (orbital-dependent) 4-fold way and the (orbital-free) Boys localization diabatization method. These very different methods yield strikingly similar diabatic potential energy surfaces that cross at geometries where the adiabatic surfaces are well separated and do not exhibit avoided crossings, and the contours of the diabatic gap and diabatic coupling are similar for the two methods. The validity of the diabatization is supported by comparing the nonadiabatic couplings calculated from the diabatic matrix elements to those calculated by direct differentiation of the adiabatic states.

Franck–Condon Models for Simulating the Band Shape of Electronic Absorption Spectra

Band shape is an essential ingredient in the simulation of electronic absorption spectra. The excitation of multiple series of vibrational levels during an electronic excitation is a main contributor to band shapes. Here we present two simple models based on the Franck-Condon displaced-harmonic-oscillator model. The models are both derived from the time-dependent formulation of electronic spectroscopy. They assume that the transition dipoles do not depend on geometry and that the potential energy surfaces are locally quadratic; one model is second order in time and is called LQ2, and the other is third order in time and is called LQ3. These models are suitable for simulating the unresolved vibronic band shapes of electronic spectra that involve many vibrational modes. The models are straightforward and can be easily applied to simulate absorption spectra that are composed of many electronic transitions. As compared to carrying out molecular dynamics simulations, they require relatively few electronic structure calculations, and the additional cost for constructing the spectra is negligible. Therefore, the models are suitable for simulating the spectra of complex systems such as transition-metal complexes.

Full-dimensional multi-state simulation of the photodissociation of thioanisole

The photodissociation of thioanisole is very interesting because the experiments of Lim and Kim provide evidence for mode-specific effects on the product distribution. They showed that, with a specific S-CH3 stretching mode being excited as the reagent is excited to the S1 electronic state, there is a sharp increase in the proportion of the ground-state product to the excited-state product. In the present work, we report 78 011 full-dimensional semiclassical multi-state trajectories of the photodissociation process using the coherent switching with decay of mixing dynamics method. The potential surfaces and couplings are based on electronic structure calculations that include dynamic correlation through second order perturbation theory. We report results for four sets of initial conditions, one corresponding roughly to 0-0 excitation and three corresponding to exciting one vibrational mode, to look for mode-specific effects. The simulations show no significant mode-specific effect on the product energy distributions, but they do show an effect on the distribution of minimum-energy gaps in the trajectories and on the lifetime for dissociation. In particular, excitation of the S-CH3 stretching mode leads to trajectories passing closer to the S1-S2 conical intersection and to shorter lifetimes. This provides a possible explanation of why experimental results are different for excitation of this vibration.