Excited-State Potential Energy Surfaces, Conical Intersections, and Analytical Gradients from Ground-State Density Functional Theory

Presenting a new fluorescent probe, methyl(10-phenylphenanthren-9-yl)sulfane sensitive to the polarity and rigidity of the microenvironment: applications toward microheterogeneous systems

A molecule, methyl(10-phenylphenanthren-9-yl)sulfane (MPPS), with a straightforward structure, has been synthesized, characterized, and explored as a new fluorescent probe for microheterogeneous systems. The photophysical properties of MPPS have been studied through experimental and theoretical calculations using the range-separated hybrid functional CAM-B3LYP in conjunction with a 6-311++g(d,p) basis set. Theoretical calculations show that the freely rotating phenyl ring forms a 94° dihedral angle with the phenanthrene ring in the ground state. Experimentally found two absorption bands correspond to the n → π* and π → π* transitions supported by the frontier molecular orbital calculations. Two excited singlet states, E-1 and E-2 (the former being more stable than the latter in the gas phase), exist with dihedral angles between the phenyl and phenanthrene rings as 142° and 133°, respectively, in the gas phase. Two emitting states in a condensed medium of varying polarities are supported by the steady-state fluorescence and fluorescence intensity decay data. Emission energies, fluorescence intensities, and excited singlet state lifetimes change with the polarity of the solvents. To support that the free rotation in the molecule is responsible for these changes, the fluorescence properties of another molecule, methyl(10-(o-tolyl)phenanthren-9-yl)sulfane (MTPS), with restricted rotation of the substituted benzene, i.e., o-tolyl ring have been studied. The fast-intensity decay component of MPPS is ascribed to the conformer in the E-1 state. The molecule has proved to be an excellent polarity probe explored to determine the critical micelle concentrations (cmc) values of different surfactants, which agree well with the literature reports. Different regions of binding isotherm (specific, non-cooperative, cooperative, and massive binding) of a gemini surfactant, 12-6-12,2Br- with bovine serum albumin (BSA) have been successfully demonstrated by the steady-state and time-resolved fluorescence and fluorescence anisotropic properties of MPPS. Docking results show that MPPS resides in the hydrophobic pocket of BSA. The fluorescence quenching of BSA by MPPS reveals the location of Trp residues of BSA. Thus, a polarity and molecular rigidity-sensitive fluorescent molecule, MPPS has been presented here that can potentially be used to monitor the changes in the microenvironment of biomolecules in different processes.

Excited-State Charge Transfer Coupling from Quasiparticle Energy Density Functional Theory

The recently developed Quasiparticle Energy (QE) scheme, based on a DFT calculation with one more (or less) electron, offers a good description of excitation energies, even with charge transfer characters. In this work, QE is further extended to calculate electron transfer (ET) couplings involving two excited states. We tested it with a donor-acceptor complex, consisting of a furan and a 1,1-dicyanoethylene (DCNE), in which two low lying charge transfer and local excitation states are involved. With generalized Mülliken-Hush and fragment charge-difference schemes, couplings from the QE approach generally agree well with those obtained from TDDFT, except that QE couplings exhibit better exponential distance dependence. Couplings from half-energy gaps with an external field are also calculated and reported. Our results show that the QE scheme is robust in calculating ET couplings with greatly reduced computational time.

Intermolecular-Type Conical Intersections in Benzene Dimer

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

Analytical gradients and derivative couplings for the TDDFT-1D method

We derive and implement analytic gradients and derivative couplings for time-dependent density functional theory plus one double (TDDFT-1D) which is a semiempirical configuration interaction method whereby the Hamiltonian is diagonalized in a basis of all singly excited configurations and one doubly excited configuration as constructed from a set of reference Kohn-Sham orbitals. We validate the implementation by comparing against finite difference values. Furthermore, we show that our implementation can locate both optimized geometries and minimum-energy crossing points along conical seams of S₁/S₀ surfaces for a set of test cases.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Interplay of conformational relaxation and hydrogen bond dynamics in the excited states of fluorescent Schiff base anions

Time resolved fluorescence spectroscopic investigation of four Schiff base anions has established that their excited state dynamics is governed by several solvent properties: polarity, viscosity and hydrogen bond donating ability. With viscous protic solvents like glycerol, fluorescence lifetimes of anions have been found to be markedly longer than those in ethanol, implying that conformational relaxation of molecules plays a key role in their nonradiative relaxation. Surprisingly, the lifetimes in less viscous aprotic solvents, like acetonitrile, are found to be even longer. The only plausible rationalization of this observation is in the light of hydrogen bond-assisted nonradiative phenomena that are operative in protic solvents. This contention draws support from a time evolution of the emission in the red end of the spectrum in low to moderately hydrogen bond donating protic solvents, with regard to an absence of such a rise time in aprotic solvents and strongly hydrogen bond donating solvents, viz., 2,2,2-trifluoroethanol. Rudimentary quantum chemical calculations provide a preliminary idea about the nature of excited state hydrogen bond redistribution involved in the process.

Theoretical Study of Light-Induced Crosslinking Reaction Between Pyrimidine DNA Bases and Aromatic Amino Acids

Low-lying electronic excited states and their relaxation pathways as well as energetics of the crosslinking reaction between uracil as a model system for pyrimidine-type building blocks of DNA and RNA and benzene as a model system for aromatic groups of tyrosine (Tyr) and phenylalanine (Phe) amino acids have been studied in the framework of density functional theory. The equilibrium geometries of the ground and electronic excited states as well as the crossing points between the potential energy surfaces of the uracil–benzene complex were computed. Based on these results, different relaxation pathways of the electronic excited states that lead to either back to the initial geometry configuration or the dimerization between the six-membered rings of the uracil–benzene complex have been identified, and the energetic conditions for their occurrence are discussed. It can be concluded that the DNA–protein crosslinking reaction can be induced by the external electromagnetic field via the dimerization reaction between the six-membered rings of the uracil–benzene pair at the electronic excited-state level of the complex. In the case of the uracil–phenol complex, the configuration of the cyclic adduct (dimerized) conformation is less likely to be formed.

On the inclusion of one double within CIS and TDDFT

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.

Exact Second-Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory

We develop a second-order correction to commonly used density functional approximations (DFAs) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are a highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum, and photoexcitation energies beyond previous approximate second-order approaches, thus showing potential for broad applications in computational spectroscopy.

Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane-Wave Basis Set

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane-wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density-dependent (ODD) functionals including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate π* orbitals where the importance of complex orbitals is illustrated. The application of this method to several metal-to-ligand charge-transfer and metal-centered excited states of an Fe^II photosensitizer complex is described, and the results are compared to reported experimental estimates. This method is also used to study the effect of the Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.

Materials Design and Optimization for Next-Generation Solar Cell and Light-Emitting Technologies

We review some of the most potent directions in the design of materials for next-generation solar cell and light-emitting technologies that go beyond traditional solid-state inorganic semiconductor-based devices, from both the experimental and computational standpoints. We focus on selected recent conceptual advances in tackling issues which are expected to significantly impact applied literature in the coming years. Specifically, we consider solution processability, design of dopant-free charge transport materials, two-dimensional conjugated polymeric semiconductors, and colloidal quantum dot assemblies in the fields of experimental synthesis, characterization, and device fabrication. Key modeling issues that we consider are calculations of optical properties and of effects of aggregation, including recent advances in methods beyond linear-response time-dependent density functional theory and recent insights into the effects of correlation when going beyond the single-particle ansatz as well as in the context of modeling of thermally activated fluorescence.

Trajectory surface-hopping photoinduced dynamics from Rydberg states of trimethylamine

We present a computational study on nonadiabatic excited-state dynamics initiated from the 3p Rydberg states of trimethylamine (TMA). We utilise a methodology based on full-dimensional (39 D) trajectory surface-hopping (TSH) simulations, in which propagation is carried out on on-the-fly density functional theory (DFT)/time-dependent DFT (TD-DFT) potentials. Both our electronic structure benchmarks to high-level ab initio methods (EOM-CCSD, CASPT2) and TSH simulations demonstrate high-accuracy of the applied CAM-B3LYP functional for the description of Rydberg excited states. Based on our excited-state simulations, we construct the following mechanistic picture: when pumped resonantly to the 3p Rydberg manifold, TMA coherently vibrates along the planarisation mode with a period of 104 fs and an exponential coherence decay time constant of 240 fs. Nonadiabatic dynamics occur on a faster (∼1 ps) and a slower (∼3 ps) timescale, along the N-C stretching mode by mixing with a dissociative σN-C* state. As a minor relaxation channel, 3p → 3s internal conversion occurs via branching at the σN-C*/3s intersection. We find that photodissociaton is hardly observable within 3 ps (1%), which is a failure of the range-separated hybrid CAM-B3LYP functional, as a consequence of its static electron correlation deficiency at long range. In contrast, pure DFT (GGA-BLYP) provides an accurate long-range description (19% dissociation yield), also supported by comparison to recent ultrafast experiments, even if the Rydberg state energies are significantly underestimated (>1 eV). Finally, we reveal the crucial role of vibrational coherence and energy transfer from the planarisation mode for N-C bond activation and resulting nonadiabatic dynamics. The present work illustrates the importance of nuclear-electronic coupling for excited-state dynamics and branching at conical intersections.

Koopmans'-Type Theorem in Kohn-Sham Theory with Optimally Tuned Long-Range-Corrected (LC) Functionals

In the present study, we have investigated the applicability of long-range-corrected (LC) functionals to a Kohn-Sham (KS) Koopmans'-type theorem. Specifically, we have examined the performance of optimally tuned LCgau-core functionals (in combination with BOP and PW86-PW91 exchange-correlation functionals) by calculating the ionization potential (IP) within the context of Koopmans' prediction. In the LC scheme, the electron repulsion operator, 1/r₁₂, is divided into short-range and long-range components using a standard error function, with a range separation parameter μ determining the weight of the two ranges. For each system that we have examined (H₂O, CO, benzene, N₂, HF, H₂CO, C₂H₄, and five-membered ring compounds cyclo-C₄H₄X, with X = CH₂, NH, O, and S, and pyridine), the value of μ is optimized to minimize the deviation of the negative HOMO energy from the experimental IP. Our results demonstrate the utility of optimally tuned LC functionals in predicting the IP of outer valence levels. The accuracy is comparable to that of highly accurate ab initio theory. However, our Koopmans' method is less accurate for the inner valence and core levels. Overall, our results support the notion that orbitals in KS-DFT, when obtained with the LC functional, provide an accurate one-electron energy spectrum. This method represents a one-electron orbital theory that is attractive in its simple formulation and effective in its practical application.

Density Functional Prediction of Quasiparticle, Excitation, and Resonance Energies of Molecules With a Global Scaling Correction Approach

Molecular quasiparticle and excitation energies determine essentially the spectral characteristics measured in various spectroscopic experiments. Accurate prediction of these energies has been rather challenging for ground-state density functional methods, because the commonly adopted density function approximations suffer from delocalization error. In this work, by presuming a quantitative correspondence between the quasiparticle energies and the generalized Kohn–Sham orbital energies, and employing a previously developed global scaling correction approach, we achieve substantially improved prediction of molecular quasiparticle and excitation energies. In addition, we also extend our previous study on temporary anions in resonant states, which are associated with negative molecular electron affinities. The proposed approach does not require any explicit self-consistent field calculation on the excited-state species, and is thus highly efficient and convenient for practical purposes.

Self-Consistent Calculation of the Localized Orbital Scaling Correction for Correct Electron Densities and Energy-Level Alignments in Density Functional Theory

The recently developed localized orbital scaling correction (LOSC) method shows the ability to systematically and size-consistently reduce the delocalization error existing in conventional density functional approximations (DFAs). However, the application of LOSC to DFAs was mainly through a post self-consistent field (SCF) manner, and few results from applying LOSC to DFAs in an SCF manner have been reported. The reason is that the originally proposed SCF approach to SCF-LOSC calculation uses an approximate Hamiltonian and encounters convergence problems easily in practice. In this work, we develop a new SCF approach with a correct Hamiltonian and achieve reliable SCF-LOSC calculations. We demonstrate the capability of the new SCF approach for SCF-LOSC to correctly describe the electron densities, total energies, and energy-level alignment for the molecular dissociation process, while conventional DFAs or LOSC-DFAs with post-SCF calculations show large errors. This work demonstrates that the new SCF approach for SCF-LOSC would be a promising method for studying problems for correct electron densities and energy-level alignments in large systems.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.