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We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and co-workers [Flick et al., ACS Photonics 6, 2757-2778 (2019)], we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron–photon eigenstates. This leads to a Hermitian QED-TDDFT coupling matrix that is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating-wave approximation, and the Tamm–Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energies and compositions of polaritons associated with lower-energy electronic states.

Density functional theory and time-dependent (TDDFT) calculations were carried out for recently reported bisarylselanylbenzo-2,1,3-selenadiazoles derivatives capable of producing singlet oxygen (1O2) under UV–Vis irradiation. Conformational behaviors, excitation energies, singlet–triplet energy gaps, and spin–orbit coupling constants were evaluated. The conformational analysis evidences that two different conformers have to be taken into consideration to completely describe the photophysical properties of this class of molecules. TDDFT results show that these compounds, though possessing absorption wavelengths that fall in the violet region, are characterized by singlet–triplet energy gaps greater than the energy required to excite the molecular oxygen, thus being able to produce the cytotoxic species, spin-orbit coupling constants large enough to ensure efficient singlet–triplet intersystem spin crossing, and even the highly reactive superoxide anion O2•(−) by autoionization and subsequent electron transfer to molecular oxygen in its ground state.

In this study, the working mechanism of the first light-driven rotary molecular motors used to control an eight-base-pair DNA hairpin has been investigated. In particular, this linker was reported to have promising photophysical properties under physiological conditions, which motivated our work at the quantum mechanical level. Cis-trans isomerization is triggered by photon absorption at wavelengths ranging 300 nm-400 nm, promoting the rotor to the first excited state, and it is mediated by an energy-accessible conical intersection from which the ground state is reached back. The interconversion between the resulting unstable isomer and its stable form occurs at physiological conditions in the ground state and is thermally activated. Here, we compare three theoretical frameworks, generally used in the quantum description of medium-size chemical systems: Linear-Response Time-Dependent Density Functional Theory (LR-TDDFT), Spin-Flip TDDFT (SF-TDDFT), and multistate complete active space second-order perturbation theory on state-averaged complete active space self consistent field wavefunctions (MS-CASPT2//SA-CASSCF). In particular, we show the importance of resorting to a multireference approach to study the rotational cycle of light-driven molecular motors due to the occurrence of geometries described by several configurations. We also assess the accuracy and computational cost of the SF-TDDFT method when compared to MS-CASPT2 and LR-TDDFT.

We expand the concept of natural transition orbitals in the context of real-time time-dependent density functional theory (RT-TDDFT) and show its application in practical calculations. Kohn–Sham single-particle wavefunctions are propagated in RT-TDDFT simulation, and physical properties remain invariant under their unitary transformation. In this work, we exploit this gauge freedom and expand the concept of natural transition orbitals, which is widely used in linear-response TDDFT, for obtaining a particle–hole description in RT-TDDFT simulation. While linear-response TDDFT is widely used to study electronic excitation, RT-TDDFT can be employed more generally to simulate non-equilibrium electron dynamics. Studying electron dynamics in terms of dynamic transitions of particle–hole pairs is, however, not straightforward in the RT-TDDFT simulation. By constructing natural transition orbitals through projecting time-dependent Kohn–Sham wave functions onto occupied/unoccupied eigenstate subspaces, we show that linear combinations of a pair of the resulting hole/particle orbitals form a new gauge, which we refer to as dynamical transition orbitals. We demonstrate the utility of this framework to analyze RT-TDDFT simulations of optical excitation and electronic stopping dynamics in the particle–hole description.

In this work, a Raman bond model that partitions the Raman intensity to interatomic charge flow modulations or Raman bonds is extended from the static limit to frequency dependent cases. This model is based on damped response theory and, thus, enables a consistent treatment of off-resonance and resonance cases. Model systems consisting of pyridines and silver clusters are studied using time dependent density functional theory to understand the enhancement mechanisms of surface-enhanced Raman scattering (SERS). The Raman bonds in the molecule, the inter-fragment bond, and the cluster are mapped to the enhancement contributions of the molecular resonance mechanism, the charge transfer mechanism, and the electromagnetic mechanism. The mapping quantifies the interference among the coupled mechanisms and interprets the electromagnetic mechanism as charge flow modulations in the metal. The dependence of the enhancement on the incident frequency, the molecule–metal bonding, and the applied electric field is interpreted and quantified. The Raman bond framework offers an intuitive and quantitative interpretation of SERS mechanisms.

It is now well established that the spin-adapted time-dependent density functional theory [X-TD-DFT; Li and Liu, J. Chem. Phys. 135, 194106 (2011)] for low-lying excited states of open-shell systems has very much the same accuracy as the conventional TD-DFT for low-lying excited states of closed-shell systems. In particular, this has been achieved without computational overhead over the unrestricted TD-DFT (U-TD-DFT) that usually produces heavily spin-contaminated excited states. It is shown here that the analytic energy gradients of X-TD-DFT can be obtained by just slight modifications of those of U-TD-DFT running with restricted open-shell Kohn–Sham orbitals. As such, X-TD-DFT also has no overhead over U-TD-DFT in the calculation of energy gradients of excited states of open-shell systems. Although only a few prototypical open-shell molecules are considered as showcases, it can definitely be said that X-TD-DFT can replace U-TD-DFT for geometry optimization and dynamics simulation of excited states of open-shell systems.

Theoretical methods able to screen large sets (e.g., conformers) of possibly large compounds are needed in many typical quantum chemistry applications. For this purpose, we here extend the well-established simplified time-dependent density functional theory (sTD-DFT) method for the calculation of optical rotation. This new scheme is benchmarked against 42 compounds of the OR45 set as well as thirteen helicene derivatives and one bio-molecular system. The sTD-DFT method yields optical rotations in good quantitative agreement with experiment for compounds with a valence-dominated response, e.g., conjugated π-systems, at a small fraction of the computational cost compared to TD-DFT (1–3 orders of magnitude speed-up). For smaller molecules with a Rydberg state dominated response, the agreement between TD-DFT and the simplified version using standard hybrid functionals is somewhat worse but still reasonable for typical applications. Our new implementation in the stda code enables computations for systems with up to 1000 atoms, e.g., for studying flexible bio-molecules.

The vacuum ultraviolet (VUV) spectrum for cyclohepta-1,3,5-triene up to 10.8 eV shows several broad bands, which are compared with electron impact spectra. Local curve fitting exposed groups of sharp vibrational peaks, which are assigned to Rydberg states. The vertical excitation profile of the VUV spectrum, reproduced by time dependent density functional theory (TDDFT), gives a good interpretation of the principal regions of absorption. Fourth order Möller–Plessett perturbation theory, including single, double, and quadruple excitations, showed that the lowest singlet and triplet states retain CS symmetry. This contrasts with TDDFT where several low-lying excited states are planar. Detailed vibrational analysis of the first UV band was performed by Franck–Condon, Herzberg–Teller, and their combined methods. These show the dominance of mid-range frequencies, while the lowest frequency (75 cm−1) has negligible importance. In contrast, the second excited (Rydberg) state shows a major progression with separations of 115 (6) cm−1. This is interpreted by re-analysis of the X2A′ ionic state at the anharmonic level. Extremely low exponent Gaussian functions enabled several low-lying Rydberg state energies to be determined theoretically; extrapolation of the 3s-, 4s-, and 5s-Rydberg state calculated energies gives the adiabatic ionization energy as 7.837 eV (4) with δ 0.964 (2). Similarly, extrapolation of the centroids of the observed Rydberg states gave the vertical ionization energy (VIE) as VIE1 = 8.675 ± 0.077, close to the photoelectron spectroscopy VIE value [8.55 (1) eV]. Postprint

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states-particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

Nonadiabatic trajectory surface hopping simulations are reported for trans-C5H6NH2+, a model of the rhodopsin chromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C5H6NH2+, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck–Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method’s incorrect topology around S1/S0 conical intersections is immaterial to the photodynamics.

We present an algorithm for efficient calculation of analytic nonadiabatic derivative couplings between spin-adiabatic, time-dependent density functional theory states within the Tamm-Dancoff approximation. Our derivation is based on the direct differentiation of the Kohn-Sham pseudowavefunction using the framework of Ou et al. Our implementation is limited to the case of a system with an even number of electrons in a closed shell ground state, and we validate our algorithm against finite difference at an S1/T2 crossing of benzaldehyde. Through the introduction of a magnetic field spin-coupling operator, we break time-reversal symmetry to generate complex valued nonadiabatic derivative couplings. Although the nonadiabatic derivative couplings are complex valued, we find that a phase rotation can generate an almost entirely real-valued derivative coupling vector for the case of benzaldehyde. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in N. Bellonzi et al., J. Chem. Phys. 152, 044112 (2020) and may be found at https://doi.org/10.1063/1.5126440.

We present a novel approach for the calculation of vibrational (resonance) Raman optical activity (ROA) spectra based on real time propagation. The ROA linear electronic response tensors are formulated in a propagator formalism in order to treat linear response (LR-) and real time time dependent density functional theory (RT-TDDFT) on equal footing. The length, mixed, and velocity representations of these tensors are discussed with respect to the potential origin dependence of the ROA invariants in the calculations. The propagator formalism allows a straight forward extension of the optical LR tensors in a mixed or velocity representation to a coupling with nonlocal potentials, where an extra term appears in the definition of the momentum operator, in order to maintain the gauge invariance. Using RT-TDDFT paves the way for an innovative, efficient calculation of both on- and off-resonance ROA spectra. Exemplary results are given for the off-resonance and (pre-)resonance spectra of (R)-methyloxirane, considering the resonance effects due to one or more electronically excited states. Moreover, the developed real time propagation approach allows us to obtain entire excitation profiles in a computationally efficient way.

A necessary first step in the development of technologies such as artificial photosynthesis is understanding the photoexcitation process within the basic building blocks of naturally occurring light harvesting complexes (LHCs). The most important of these building blocks in biological LHCs such as LHC II from green plants are the chlorophyll a (Chl a) and chlorophyll b (Chl b) chromophores dispersed throughout the protein matrix. However, efforts to describe such systems are still hampered by the lack of computationally efficient and accurate methods that are able to describe optical absorption in large biomolecules. In this work, we employ a highly efficient linear combination of atomic orbitals (LCAOs) to represent the Kohn–Sham (KS) wave functions at the density functional theory (DFT) level and perform time-dependent density functional theory (TDDFT) calculations in either the reciprocal space and frequency domain (LCAO-TDDFT-k-ω) or real space and time domain (LCAO-TDDFT-r-t) of the optical absorption spectra of Chl a and b monomers and dimers. We find that our LCAO-TDDFT-k-ω and LCAO-TDDFT-r-t calculations reproduce results obtained with a plane-wave (PW) representation of the KS wave functions (PW-TDDFT-k-ω) but with a significant reduction in computational effort. Moreover, by applying the Gritsenko, van Leeuwen, van Lenthe, and Baerends solid and correlation derivative discontinuity correction Δx to the KS eigenenergies, with both LCAO-TDDFT-k-ω and LCAO-TDDFT-r-t methods, we are able to semiquantitatively reproduce the experimentally measured photoinduced dissociation results. This work opens the path to first principles calculations of optical excitations in macromolecular systems.

This paper presents the nonadiabatic molecular dynamics simulation combined with the spin-flip time-dependent density functional theory (SF-TDDFT). In contrast to the conventional single-reference electronic structure methods, which have difficulty in describing the S0/S1 conical intersections, the SF-TDDFT can yield the correct topology of crossing points. Thus, one expects that the method can take naturally into account the S1 → S0 nonadiabatic transitions. We adopt Tully's fewest switch surface hopping algorithm by introducing the analytic SF-TDDFT nonadiabatic coupling vector. We apply the proposed method to the photoisomerization reactions of E-azomethane, methanimine, and ethene molecules and reproduce the results of previous studies based on the multireference methods. The proposed approach overcomes the ad hoc treatment of S1 → S0 transition at the single-reference calculation level and affords both the dynamics on the S1 state and the recovery of the S0 state with modest computational costs.

Analytic energy gradients of individual singlet and triplet states with respect to nuclear coordinates are derived and implemented for the collinear mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT), which eliminates the problematic spin-contamination of SF-TDDFT. Dimensional-transformation matrices for the singlet and triplet response spaces are introduced, simplifying the subsequent derivations. These matrices enable the general forms of MRSF-TDDFT equations to be similar to those of SF-TDDFT, suggesting that the computational overhead of singlet or triplet states for MRSF-TDDFT is nearly identical to that of SF-TDDFT. In test calculations, the new MRSF-TDDFT yields quite different optimized structures and energies as compared to SF-TDDFT. These differences turned out to mainly come from the spin-contamination of SF-TDDFT, which are largely cured by MRSF-TDDFT. In addition, it was demonstrated that the clear separation of singlet states from triplets dramatically simplifies the location of minimum energy conical intersection. As a result, it is clear that the MRSF-TDDFT has advantages over SF-TDDFT in terms of both accuracy and practicality. Therefore, it can be a preferred method, which is readily applied to other "black-box" type applications, such as the minimum-energy optimization, reaction path following, and molecular dynamics simulations.

The energy conversion efficiency of organic solar cells seems crucial for a clean future. The design of new light-harvesting devices needs an in-depth understanding of their optical properties, including the excited-state absorption (ESA). In biology, the optical characterization of photochemical/physical processes happening in photosynthetic pigments and proteins can be difficult to interpret due to their structural complexities. Experimentally, an ultrafast transient absorption experiment can probe the excited state interaction with light. Quantum chemistry could play an important role to model the transient absorption spectrum of excited states. However, systems that need to be investigated can be way too large for existent software implementations. In this contribution, we present the first sTDA/sTD-DFT (simplified time-dependent density functional theory with and without Tamm Dancoff approximation) implementation to evaluate the ESA of molecules. The ultrafast ESA evaluation presents a negligible extra cost with respect to sTDA/sTD-DFT original schemes for standard ground state absorption. The sTD-DFT method shows ability to assign ESA spectra to the correct excited state. We showed that in the literature, wrong assignments were proposed as for the L34/L44 mixture and N-methylfulleropyrrolidine. In addition, sTDA/sTD-DFT-xTB tight-binding variants are also available, allowing the evaluation of ESA for systems of a few thousands of atoms, e.g., the spectrum of the photoactive yellow protein composed of 1931 atoms.

The accuracy and efficiency of time-dependent density functional theory (TDDFT) excited state gradient calculations using the pseudospectral method are presented. TDDFT excited state geometry optimizations of the G2 test set molecules, the organic fluorophores with large Stokes shifts, and the Pt-complexes show that the pseudospectral method gives average errors of 0.01–0.1 kcal/mol for the TDDFT excited state energy, 0.02–0.06 pm for the bond length, and 0.02–0.12° for the bond angle when compared to the results from conventional TDDFT. TDDFT gradient calculations of fullerenes (Cn, n up to 540) with the B3LYP functional and 6-31G** basis set show that the pseudospectral method provides 8- to 14-fold speedups in the total wall clock time over the conventional methods. The pseudospectral TDDFT gradient calculations with a diffuse basis set give higher speedups than the calculations for the same basis set without diffuse functions included.

The theory of solvation structure in an electronically polarizable solvent recently proposed by us, referred to as the "solvent-polarizable three-dimensional reference interaction-site model theory," is extended to dynamics in this study through the combination with time-dependent density functional theory. Test calculations are performed on model charge-transfer systems in water, and the effects of electronic polarizability on solvation dynamics are examined. The electronic polarizability slightly retards the solvation dynamics. This is ascribed to the decrease in the curvature of the nonequilibrium free energy profile along the solvation coordinate. The solvent relaxation is bimodal, and the faster and the slower modes are assigned to the reorientational and the translational modes, respectively, as was already reported by the surrogate theory combined with the site-site Smoluchowski-Vlasov equation. The relaxation path along the solvation coordinate is a little higher than the minimum free energy path because the translational mode is fixed in the time scale of the reorientational relaxation.

Tip-enhanced Raman spectroscopy in combination with scanning tunneling microscopy could produce ultrahigh-resolution Raman spectra and images for single-molecule vibrations. Furthermore, a recent experimental study successfully decoupled the interaction between the molecule and the substrate/tip to investigate the intrinsic properties of molecules and their near-field interactions by Raman spectroscopy. In such a circumstance, more explicit treatments of the near field and molecular interactions beyond the dipole approximation would be desirable. Here, we propose a theoretical method based on the multipolar Hamiltonian that considers full spatial distribution of the electric field under the framework of real-time time-dependent density functional theory. This approach allows us to treat the on- and off-resonance Raman phenomena on the same footing. For demonstration, a model for the on- and off-resonance tip-enhanced Raman process in benzene was constructed. The obtained Raman spectra are well understood by considering both the spatial structure of the near field and the molecular vibration in the off-resonance condition. For the on-resonance condition, the Raman spectra are governed by the transition moment, in addition to the selection rule of off-resonance Raman. Interestingly, on-resonance Raman can be activated even when the near field forbids the pi-pi (*) transition at equilibrium geometry due to vibronic couplings originating from structural distortions.

Remarkable interest is associated with the interpretation of the Prodan fluorescent spectrum. A sequential hybrid Quantum Mechanics/Molecular Mechanics method was used to establish that the fluorescent emission occurs from two different excited states, resulting in a broad asymmetric emission spectrum. The absorption spectra in several solvents were measured and calculated using different theoretical models presenting excellent agreement. All theoretical models [semiempirical, time dependent density functional theory and and second-order multiconfigurational perturbation theory] agree that the first observed band at the absorption spectrum in solution is composed of three electronic excitations very close in energy. Then, the electronic excitation around 340 nm-360 nm may populate the first three excited states (π-π*Lb, n-π*, and π-π*La). The ground state S0 and the first three excited states were analyzed using multi-configurational calculations. The corresponding equilibrium geometries are all planar in vacuum. Considering the solvent effects in the electronic structure of the solute and in the solvent relaxation around the solute, it was identified that these three excited states can change the relative order depending on the solvent polarity, and following the minimum path energy, internal conversions may occur. A consistent explanation of the experimental data is obtained with the conclusive interpretation that the two bands observed in the fluorescent spectrum of Prodan, in several solvents, are due to the emission from two independent states. Our results indicate that these are the n-π* S2 state with a small dipole moment at a lower emission energy and the π-π*Lb S1 state with large dipole moment at a higher emission energy.

First-principles calculations offer the chance to obtain a microscopic understanding of light-harvesting processes. Time-dependent density functional theory can have the computational efficiency to allow for such calculations. However, the (semi-)local exchange-correlation approximations that are computationally most efficient fail to describe charge-transfer excitations reliably. We here investigate whether the inexpensive average density self-interaction correction (ADSIC) remedies the problem. For the systems that we study, ADSIC is even more prone to the charge-transfer problem than the local density approximation. We further explore the recently reported finding that the electrostatic potential associated with the chromophores' protein environment in the light-harvesting complex 2 beneficially shifts spurious excitations. We find a great sensitivity on the chromophores' atomistic structure in this problem. Geometries obtained from classical molecular dynamics are more strongly affected by the spurious charge-transfer problem than the ones obtained from crystallography or density functional theory. For crystal structure geometries and density-functional theory optimized ones, our calculations confirm that the electrostatic potential shifts the spurious excitations out of the energetic range that is most relevant for electronic coupling.

The enhancement mechanism due to the molecule-surface chemical interaction in surface-enhanced Raman scattering (SERS) has been characterized using a theoretical approach based on time dependent density functional theory. This includes a systematic study of the chemical mechanism (CM) to the SERS enhancement for halogen substituted benzenethiols interacting with a silver cluster. Changing the halogen on benzenethiol enables us to systematically modulate interactions between the benzenethiol ring and the metal cluster. We observe a decrease in the CM enhancement factor with an increase in the atomic number of the halogen for para-substitutions. For meta-substitutions, there is no such trend. However, the results scale linearly with the Hammett parameters for both meta and para halogens, which provides an important predictive tool for interpreting chemical enhancements. We also study the effect of solvation on the CM, showing that there is a systematic increase in enhancement with the increasing solvent dielectric constant. The correlation of CM with other properties, such as the amount of charge transfer between adsorbate and metal and the excitation energies of charge transfer states, is much less predictive than the Hammett parameter correlation.

The time-dependent density functional theory (TDDFT) has been broadly used to investigate the excited-state properties of various molecular systems. However, the current TDDFT heavily relies on outcomes from the corresponding ground-state density functional theory (DFT) calculations which may be prone to errors due to the lack of proper treatment in the non-dynamical correlation effects. Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, \textit{J. Chem. Phys.} \textbf{136}, 154104 (2012)], a DFT with fractional orbital occupations, was proposed, explicitly incorporating the non-dynamical correlation effects in the ground-state calculations with low computational complexity. In this work, we develop time-dependent (TD) TAO-DFT, which is a time-dependent, linear-response theory for excited states within the framework of TAO-DFT. With tests on the excited states of H$_{2}$, the first triplet excited state ($1^3\Sigma_u^+$) was described well, with non-imaginary excitation energies. TDTAO-DFT also yields zero singlet-triplet gap in the dissociation limit, for the ground singlet ($1^1\Sigma_g^+$) and the first triplet state ($1^3\Sigma_u^+$). In addition, as compared to traditional TDDFT, the overall excited-state potential energy surfaces obtained from TDTAO-DFT are generally improved and better agree with results from the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD).

In this study, we developed a time-dependent density-functional theory (TDDFT) with a finite-temperature (FT) scheme, denoted as FT-TDDFT. We introduced the concept of fractional occupation numbers for random phase approximation equation and evaluated the excited-state electronic entropy terms with excited-state occupation number. The orbital occupation numbers for the excited state were evaluated from the change in the ground-state electron configuration with excitation and deexcitation coefficients. Furthermore, we extended the FT formulation to the time-dependent density-functional tight-binding (TDDFTB) method for larger systems, denoted as FT-TDDFTB. Numerical assessment for the FT-(TD)DFT method showed smooth potential curves for double-bond rotation of ethylene in both ground and excited states. Excited-state calculations based on the FT-TDDFTB method were applied to the uniform π-stacking columns composed of trioxotriangulene, possessing neutral radicals in strong correlation systems.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac–Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin–spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program’s website http://www.respectprogram.org.

Integration schemes are implemented with a plane-wave basis in the context of real-time time-dependent density functional theory. Crank-Nicolson methods and three classes of explicit integration schemes are explored and assessed in terms of their accuracy and stability properties. Within the framework of plane-wave density functional theory, a graphene monolayer system is used to investigate the error, stability, and serial computational cost of these methods. The results indicate that Adams-Bashforth and Adams-Bashforth-Moulton methods of orders 4 and 5 outperform commonly used methods, including Crank-Nicolson and Runge-Kutta methods, in simulations where a relatively low error is desired. Parallel runtime scaling of the most competitive serial methods is presented, further demonstrating that the Adams-Bashforth and Adams-Bashforth-Moulton methods are efficient methods for propagating the time-dependent Kohn-Sham equations. Our integration schemes are implemented as an extension to the Quantum ESPRESSO code.

We propose an ab initio formulation that enables a rigorous calculation of the first-order nonadiabatic couplings (NAC) between electronic states based on time-dependent density functional theory in conjunction with planewave bases, projector augmented-wave pseudopotentials, and hybrid exchange-correlation functionals. The linear and quadratic time-dependent response theory is used to derive analytic expressions for the NAC matrix elements. In contrast to the previous formulation in atomic basis sets, the present formulation eliminates explicit references to Kohn-Sham virtual orbitals. With the introduction of Lagrangian functionals, the present formulation circumvents expensive derivative calculations of Kohn-Sham orbitals with respect to ionic coordinates. As a validation of the formulation, the NAC matrix elements of small molecules LiH and HeH+ are calculated and compared to previous results with the atomic orbital basis. This development paves the way for accurate ab initio nonadiabatic molecular dynamics in extended systems.

In this paper, real-time time-dependent density functional theory (RT-TDDFT) calculations of realistically sized nanodevices are presented. These microcanonical simulations rely on a closed boundary approach based on recent advances in the software package CP2K. The obtained results are compared to those derived from the open-boundary Non-equilibrium Green's Function (NEGF) formalism. A good agreement between the "current vs. voltage" characteristics produced by both methods is demonstrated for three representative device structures, a carbon nanotube field-effect transistor, a GeSe selector for crossbar arrays, and a conductive bridging random-access memory cell. Different approaches to extract the electrostatic contribution from the RT-TDDFT Hamiltonian and to incorporate the result into the NEGF calculations are presented.

A hybrid Bethe–Salpeter/time-dependent density-functional-theory method is described that aims at improving the performance of the GW/Bethe–Salpeter-equation (GW/BSE) method in general and for excited triplet states in particular. The static screened exchange W used in the BSE is combined with the correlation kernel of the underlying density functional in a manner that retains a proven feature of the BSE, that is, the correct description of charge–transfer excitations. The performance of the new method, labeled cBSE, is assessed using G0W0 or evGW quasiparticle energies, and an improved performance is observed. The cBSE approach shows nearly equal performance for excited singlet and triplet states, rivaling coupled-cluster theory (in the CC2 approximation) in accuracy at a computational cost that is at least one order of magnitude smaller.

Frozen-density-embedding (FDE) linear response time-dependent density functional theory (TDDFT) is generalized to the case of spin-unrestricted reference orbitals. FDE-TDDFT in the uncoupled approximation is applied to calculate vertical excitation energies of diatomic radicals interacting with closed-shell atoms (helium) or molecules like water. Unrestricted FDE-TDDFT can reproduce the vertical valence excitation energies obtained from conventional supermolecular TDDFT with good accuracy, provided that a good embedding potential is available. To investigate the influence of approximate embedding potentials, we also combine the unrestricted FDE-TDDFT formalism with projection-operator and potential reconstruction techniques, thus enabling calculations with accurate ("exact") embedding potentials.

In the present work, we model artificial neural network (ANN) potentials for Au n (SH) m nanoclusters in the range of n = 10 to n = 38. The accuracy of ANN potentials is tested by comparing the global minimum (GM) structures of Au n (SH) m nanoclusters, at saturated amount of SH, with the earlier reported structures. The GM structures are reported for the first time for nanoclusters with compositions lower than the saturated SH composition. We calculate the probability of low energy isomers to explain the fluxional behaviour of Au n (SH) m nanoclusters at lower SH compositions. Furthermore, we try to correlate the structures of Au n (SH) m nanoclusters with UV-visible spectra based on Time-dependent density functional theory (TDDFT) calculations. The UV-visible spectral analysis reveals that significant spectroscopic variations are observed at different SH compositions. This study provides a fundamental understanding of structural changes with decreasing SH compositions and with increasing the size of the nanocluster.

The vacuum ultraviolet (VUV) spectrum for CH2F2 from a new synchrotron study has been combined with earlier data and subjected to detailed scrutiny. The onset of absorption, band I and also band IV, is resolved into broad vibrational peaks, which contrast with the continuous absorption previously claimed. A new theoretical analysis, using a combination of time dependent density functional theory (TDDFT) calculations and complete active space self-consistent field, leads to a major new interpretation. Adiabatic excitation energies (AEEs) and vertical excitation energies, evaluated by these methods, are used to interpret the spectra in unprecedented detail using theoretical vibronic analysis. This includes both Franck-Condon (FC) and Herzberg-Teller (HT) effects on cold and hot bands. These results lead to the re-assignment of several known excited states and the identification of new ones. The lowest calculated AEE sequence for singlet states is 11B1 ~ 11A2 < 21B1 < 11A1 < 21A1 < 11B2 < 31A1 < 31B1. These, together with calculated higher energy states, give a satisfactory account of the principal maxima observed in the VUV spectrum. Basis sets up to quadruple zeta valence with extensive polarization are used. The diffuse functions within this type of basis generate both valence and low-lying Rydberg excited states. The optimum position for the site of further diffuse functions in the calculations of Rydberg states is shown to lie on the H-atoms. The routine choice on the F-atoms is shown to be inadequate for both CHF3 and CH2F2. The lowest excitation energy region has mixed valence and Rydberg character. TDDFT calculations show that the unusual structure of the onset arises from the near degeneracy of 11B1 and 11A2 valence states, which mix in symmetric and antisymmetric combinations. The absence of fluorescence in the 10.8-11 eV region contrasts with strong absorption. This is interpreted by the 21B1 and 11A1 states where no fluorescence is calculated for these two states, which are only active in absorption. The nature of the two states, 11B1 and 21B1, is fundamentally different, but both are complex owing to the presence of FC and HT effects occurring in different ways. The two most intense bands, close to 12.5 and 15.5 eV, contain valence states as expected; the onset of the 15.5 eV band shows a set of vibrational peaks, but the vibration frequency does not correspond to any of the photoelectron spectral (PES) structure and is clearly valence in nature. The routine use of PES footprints to detect Rydberg states in VUV spectra is shown to be inadequate. The combined effects of FC and HT in the VUV spectral bands lead to additional vibrations when compared with the PES.

Exploiting the machinery of Constrained Density Functional Theory (CDFT), we propose a variational method for calculating low-lying excited states of molecular systems. We dub this method eXcited CDFT (XCDFT). Excited states are obtained by self-consistently constraining a user-defined population of electrons, Nc, in the virtual space of a reference set of occupied orbitals. By imposing this population to be Nc = 1.0, we computed the first excited state of 15 molecules from a test set. Our results show that XCDFT achieves an accuracy in the predicted excitation energy only slightly worse than linear-response time-dependent DFT (TDDFT), but without incurring into problems of variational collapse typical of the more commonly adopted ΔSCF method. In addition, we selected a few challenging processes to test the limits of applicability of XCDFT. We find that in contrast to TDDFT, XCDFT is capable of reproducing energy surfaces featuring conical intersections (azobenzene and H3) with correct topology and correct overall energetics also away from the intersection. Venturing to condensed-phase systems, XCDFT reproduces the TDDFT solvatochromic shift of benzaldehyde when it is embedded by a cluster of water molecules. Thus, we find XCDFT to be a competitive method among single-reference methods for computations of excited states in terms of time to solution, rate of convergence, and accuracy of the result.

In this work, we examine the importance of nuclear quantum effects on capturing the line broadening and vibronic structure of optical spectra. We determine the absorption spectra of three aromatic molecules indole, pyridine, and benzene using time dependent density functional theory with several molecular dynamics sampling protocols: force-field based empirical potentials, ab initio simulations, and finally path-integrals for the inclusion of nuclear quantum effects. We show that the absorption spectrum for all these chromophores are similarly broadened in the presence of nuclear quantum effects regardless of the presence of hydrogen bond donor or acceptor groups. We also show that simulations incorporating nuclear quantum effects are able to reproduce the heterogeneous broadening of the absorption spectra even with empirical force fields. The spectral broadening associated with nuclear quantum effects can be accounted for by the broadened distribution of chromophore size as revealed by a particle in the box model. We also highlight the role that nuclear quantum effects have on the underlying electronic structure of aromatic molecules as probed by various electrostatic properties.

The Near-Edge X-ray-Absorption Fine-Structure (NEXAFS) and X-ray Photoemission Spectroscopy (XPS) of short-chain oligothiophenes (thiophene, 2,2'-bithiophene, and 2,2':5',2 ''-terthiophene) in the gas phase have been measured in the sulfur L-2,L-3-edge region. The assignment of the spectral features is based on the relativistic two-component zeroth-order regular approximation time dependent density functional theory approach. The calculations allow us to estimate both the contribution of the spin-orbit splitting and of the molecular-field splitting to the sulfur binding energies and give results in good agreement with the experimental measurements. The deconvolution of the calculated S2p NEXAFS spectra into the two manifolds of excited states converging to the L-III and L-II edges facilitates the attribution of the spectral structures. The main S2p NEXAFS features are preserved along the series both as concerns the energy positions and the nature of the transitions. This behaviour suggests that the electronic and geometrical environment of the sulfur atom in the three oligomers is relatively unaffected by the increasing chain length. This trend is also observed in the XPS spectra. The relatively simple structure of S2p NEXAFS spectra along the series reflects the localized nature of the virtual states involved in the core excitation process. Published by AIP Publishing.

In order to inquire the microscopic origin of observed multiple time scales in solvation dynamics, we carry out several computer experiments. We perform atomistic molecular dynamics simulations on three protein-water systems, namely, lysozyme, myoglobin, and sweet protein monellin. In these experiments, we mutate the charges of the neighbouring amino acid side chains of certain natural probes (tryptophan) and also freeze the side chain motions. In order to distinguish between different contributions, we decompose the total solvation energy response in terms of various components present in the system. This allows us to capture the interplay among different self- and cross-energy correlation terms. Freezing the protein motions removes the slowest component that results from side chain fluctuations, but a part of slowness remains. This leads to the conclusion that the slow component approximately in the 20-80 ps range arises from slow water molecules present in the hydration layer. While the more than 100 ps component has multiple origins, namely, adjacent charges in amino acid side chains, hydrogen bonded water molecules and a dynamically coupled motion between side chain and water. In addition, the charges enforce a structural ordering of nearby water molecules and helps to form a local long-lived hydrogen bonded network. Further separation of the spatial and temporal responses in solvation dynamics reveals different roles of hydration and bulk water. We find that the hydration layer water molecules are largely responsible for the slow component, whereas the initial ultrafast decay arises predominantly (approximately 80%) due to the bulk. This agrees with earlier theoretical observations. We also attempt to rationalise our results with the help of a molecular hydrodynamic theory that was developed using classical time dependent density functional theory in a semi-quantitative manner.

Plasmon properties are of significant interest in pure and applied nanoscience. While time-dependent density functional theory (TDDFT) can be used to study plasmons, it becomes impractical for elucidating the effect of size, geometric arrangement, and dimensionality in complex nanosystems. In this study, a new multiscale formalism that addresses this challenge is proposed. This formalism is based on Trotter factorization and the explicit introduction of a coarse-grained (CG) structure function constructed as the Weierstrass transform of the electron wavefunction. This CG structure function is shown to vary on a time scale much longer than that of the latter. A multiscale propagator that coevolves both the CG structure function and the electron wavefunction is shown to bring substantial efficiency over classical propagators used in TDDFT. This efficiency follows from the enhanced numerical stability of the multiscale method and the consequence of larger time steps that can be used in a discrete time evolution. The multiscale algorithm is demonstrated for plasmons in a group of interacting sodium nanoparticles (15-240 atoms), and it achieves improved efficiency over TDDFT without significant loss of accuracy or space-time resolution.

This paper presents the nonadiabatic molecular dynamics simulation in the solution phase using the spin-flip time-dependent density functional theory (SF-TDDFT). Despite the single-reference level of theory, the SF-TDDFT method can generate the correct topology of S0/S1 crossing points, thus providing a natural S1 → S0 nonadiabatic transition. We extend the gas-phase trajectory surface hopping simulation with the SF-TDDFT [N. Minezawa and T. Nakajima, J. Chem. Phys. 150, 204120 (2019)] to the hybrid quantum mechanical/molecular mechanics (QM/MM) scheme. To this end, we modify the code to evaluate the electrostatic interaction between the QM and MM atoms and to extract the classical MM energy and forces from the MM program package. We apply the proposed method to the photoisomerization reaction of aqueous E-azomethane and anionic green fluorescent protein chromophore in water and compare the results with those of the previous simulation studies based on the multireference methods.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in The Journal of Chemical Physics, 151(18), 184111 and may be found at https://doi.org/10.1063/1.5121713. We present a formulation of relativistic linear response time-dependent density functional theory for the calculation of electronic excitation energies in the framework of the four-component Dirac-Coulomb Hamiltonian. This approach is based on the noncollinear ansatz originally developed by Scalmani and Frisch [J. Chem. Theory Comput. 8, 2193 (2012)] and improves upon the past treatment of the limit cases in which the spin density approaches zero. As a result of these improvements, the presented approach is capable of treating both closed- and open-shell reference states. Robust convergence of the Davidson-Olsen eigenproblem algorithm for open-shell reference states was achieved through the use of a solver which considers both left and right eigenvectors. The applicability of the present methodology on both closed- and open-shell reference states is demonstrated on calculations of low-lying excitation energies for Group 3 atomic systems (Sc3+–Ac3+) with nondegenerate ground states, as well as for Group 11 atomic systems (Cu–Rg) and octahedral actinide complexes (PaCl2−6, UCl−6, and NpF6) with effective doublet ground states.

X-ray absorption spectroscopy (XAS) is a powerful tool that can provide physical insights into element-specific chemical processes and reactivities. Although relativistic time-dependent density functional theory (TDDFT) has been previously applied to model the L-edge region in XAS, there has not been a more comprehensive study of the choices of basis sets and density functional kernels available for variational relativistic excited state methods. In this work, we introduce the implementation of the generalized preconditioned locally harmonic residual algorithm to solve the complex-valued relativistic TDDFT for modeling the L-edge X-ray absorption spectra. We investigate the L2,3-edge spectra of a series of molecular complexes using relativistic linear response TDDFT with a hybrid iterative diagonalization algorithm. A systematic error analysis was carried out with a focus on the energetics, intensities, and magnitude of L2-L3 splitting compared to experiments. Additionally, the results from relativistic TDDFT calculations are compared to those computed using other theoretical methods, and the multideterminantal effects on the L-edge XAS were investigated.

The multicomponent extension of time-dependent density functional theory (TDDFT) within the nuclear-electronic orbital (NEO) framework enables the calculation of both electronic and vibrational excitations simultaneously. In this NEO-TDDFT approach, all electrons and select nuclei, typically protons, are treated quantum mechanically on the same level. Herein, the dependence of the proton vibrational excitation energies on the nuclear and electronic basis sets is examined. Protonic basis sets that include f basis functions in conjunction with substantial electronic basis sets for the quantum hydrogen are found to produce accurate proton vibrational excitation energies that are mostly within ∼30 cm-1 of reference values for the molecules studied. The NEO-TDDFT approach is shown to be effective for open-shell as well as closed-shell systems. Additionally, an approach for computing and visualizing the nuclear transition densities associated with the proton vibrational excitations is implemented. These nuclear transition densities are important for characterizing the proton vibrational excitations and determining the spatial orientations of the corresponding vibrational modes. These capabilities are essential for a variety of applications, including the incorporation of anharmonic effects into molecular vibrational frequency calculations.

In this communication, we show that coupled subsystem time-dependent density functional theory (subsystem TDDFT) [J. Neugebauer, J. Chem. Phys. 126, 134116 (2007)] in combination with projection-based embedding (PbE) is an exact subsystem theory in the sense that supermolecular TDDFT excitation energies can exactly be restored. A correct handling of the kernel contribution due to the enforced orthogonality is crucial in this context, which leads to different PbE kernel contributions in the A and B matrices of the general TDDFT eigenvalue problem. Although this formalism has been proposed before [D. V. Chulhai and L. Jensen, Phys. Chem. Chem. Phys. 18, 21032 (2016)], the symmetric eigenvalue problem used in that work implicitly introduces an approximation concerning this kernel contribution. We show that our treatment numerically exactly reproduces supermolecular results for the previously investigated helium dimer and for the fluoroethane molecule as a more challenging case with a partitioning of a covalent bond. We also demonstrate that the symmetric approximation can lead to significant deviations, including a wrong ordering of electronic transitions.

Inner-shell absolute photoabsorption and photoionization cross sections of the formic acid, HCOOH, and its small hydrogen-bonded clusters, i.e., (HCOOH)2, HCOOH2+, HCOHOH+, and HCOOH·H3O+, were calculated at the time-dependent density functional theory (TDDFT) level, and the results were used to analyze the effect of the formic acid clustering on the carbon and oxygen K-edge photoionization cross sections. The discrete electronic pseudospectra obtained with square-integrable (L2) basis set calculations were used in an analytic continuation procedure based on continued fraction functions to obtain the photoabsorption cross sections. Symmetry adapted cluster configuration interaction calculations on the small formic acid clusters have also been performed at the oxygen K-edge to assign the discrete transitions and ionization potentials in support to the TDDFT results.

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an $N$-electron system from a ground state KS or generalized KS calculations of an $(N-1)$-electron system via its orbital energies. In present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations, due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependant DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as $\Delta$SCF, $G_0W_0$ with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction method like CC2. Our analysis show that the correct $1/R$ trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

In this study, density functional theory calculation on mono-cationic cation-π complexes of diborynes has been made to understand the interaction in cation-π complexes of diboryne. Results suggest that apart from the smaller cations Li+ and Na+, larger cation like K+ ion could also form complexes with diboryne compounds via cation-π interaction. From the calculated structural and spectroscopic analysis 11B, 13C NMR (Nuclear Magnetic Resonance), FTIR (Fourier Transform Infra red) (force constant, value), and UV-vis spectra, it is found that the interaction between the cations and π-electron cloud of the diboryne is purely electrostatic. It is also observed that smaller cation (Li+) with high electronegativity interacts more strongly compared to larger cation (K+). Calculated interaction energy advocates that the π-electron cloud of the B2 unit contributes more to the cation-π interaction than the two aromatic phenyl rings of the NHC (N-heterocyclic carbene) substituted with 2,6-diisopropylphenyl group. The aryl substituent at the NHC-ligands undergoes a change in spatial orientation with respect to the size of cations in order to provide suitable space to the cations for effective cation-π interaction. Quantum theory of atoms in molecules study clarifies further the nature and extent of B-B and B2-cation interactions.11B-NMR, 13C-NMR, and time dependent density functional theory analysis indicate that cation-π interaction annihilates the B → C (NHC) π-back donation and favours the B≡B bond formation.

Transition densities between excited states are key for nonlinear theoretical spectroscopy and multi-state non-adiabatic molecular dynamics (NAMD) simulations. In the framework of response theory, these transition densities are accessible from poles of the quadratic response function. It was shown recently that the thus obtained transition densities within time-dependent Hartree-Fock (TDHF) and adiabatic time-dependent density functional theory (TDDFT) exhibit unphysical divergences when the difference in excitation energy of the two states of interest matches another excitation energy. This unphysical behavior is a consequence of spurious poles in the quadratic response function. We show that the incorrect pole structure of the quadratic response is not limited to TDHF and adiabatic TDDFT, but is also present in many other approximate many-electron response functions, including those from coupled cluster and multiconfigurational self-consistent field response theory. The divergences appear in regions of the potential energy surface where the ground state is perfectly well behaved, and they are frequently encountered in NAMD simulations of photochemical reactions. The origin of the divergences is traced to an incorrect instantaneous time-dependence of the effective Hamiltonian. The implications for computations of frequency-dependent response properties are considerable and call into question the validity of conventional approximate many-electron response theories beyond linear response.

This manuscript presents the second, consistent density functional in the QTP (Quantum Theory Project) family, that is, the CAM-QTP(01). It is a new range-separated exchange-correlation functional in which the non-local exchange contribution is 100% at large separation. It follows the same basic principles of this family that the Kohn-Sham eigenvalues of the occupied orbitals approximately equal the vertical ionization energies, which is not fulfilled by most of the traditional density functional methods. This new CAM-QTP(01) functional significantly improves the accuracy of the vertical excitation energies especially for the Rydberg states in the test set. It also reproduces many other properties such as geometries, reaction barrier heights, and atomization energies.