Time-dependent Density Functional Theory Scheme Research Articles

Combining Graphics Processing Units, Simplified Time-Dependent Density Functional Theory, and Finite-Difference Couplings to Accelerate Nonadiabatic Molecular Dynamics.

Starting from our recently published implementation of nonadiabatic molecular dynamics (NAMD) on graphics processing units (GPUs), we explore further approaches to accelerate ab initio NAMD calculations at the time-dependent density functional theory (TDDFT) level of theory. We employ (1) the simplified TDDFT schemes of Grimme et al. and (2) the Hammes-Schiffer–Tully approach to obtain nonadiabatic couplings from finite-difference calculations. The resulting scheme delivers an accurate physical picture while virtually eliminating the two computationally most demanding steps of the algorithm. Combined with our GPU-based integral routines for SCF, TDDFT, and TDDFT derivative calculations, NAMD simulations of systems of a few hundreds of atoms at a reasonable time scale become accessible on a single compute node. To demonstrate this and to present a first, illustrative example, we perform TDDFT/MM-NAMD simulations of the rhodopsin protein.

Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments.

A composite of time-dependent density functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calculation of spectral properties of molecules. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approximation for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-reduction approach is also presented, which further speeds up the calculations. Our benchmark calculations show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.

Assessment of charge-transfer excitations with time-dependent, range-separated density functional theory based on long-range MP2 and multiconfigurational self-consistent field wave functions

Charge transfer excitations can be described within Time-Dependent Density Functional Theory (TD-DFT), not only by means of the Coulomb Attenuated Method (CAM) but also with a combination of wave function theory and TD-DFT based on range separation. The latter approach enables a rigorous formulation of multi-determinantal TD-DFT schemes where excitation classes, which are absent in conventional TD-DFT spectra (like for example double excitations), can be addressed. This paper investigates the combination of both the long-range Multi-Configuration Self-Consistent Field (MCSCF) and Second Order Polarization Propagator Approximation (SOPPA) ansätze with a short-range DFT (srDFT) description. We find that the combinations of SOPPA or MCSCF with TD-DFT yield better results than could be expected from the pure wave function schemes. For the Time-Dependent MCSCF short-range DFT ansatz (TD-MC-srDFT) excitation energies calculated over a larger benchmark set of molecules with predominantly single reference character yield good agreement with their reference values, and are in general comparable to the CAM-B3LYP functional. The SOPPA-srDFT scheme is tested for a subset of molecules used for benchmarking TD-MC-srDFT and performs slightly better against the reference data for this small subset. Beyond the proof-of-principle calculations comprising the first part of this contribution, we additionally studied the low-lying singlet excited states (S1 and S2) of the retinal chromophore. The chromophore displays multireference character in the ground state and both excited states exhibit considerable double excitation character, which in turn cannot be described within standard TD-DFT, due to the adiabatic approximation. However, a TD-MC-srDFT approach can account for the multireference character, and excitation energies are obtained with accuracy comparable to CASPT2, although using a much smaller active space.

Tuned CAM-B3LYP functional in the time-dependent density functional theory scheme for excitation energies and properties of diarylethene derivatives

Abstract We present the CAM (Coulomb Attenuated Method)-B3LYP functional tuned for excitation energies and properties of diarylethene derivatives in the time-dependent density functional theory (TD-DFT) scheme. The CAM-B3LYP parameters are tuned so as to well reproduce the experimental excitation energies and properties of a prototypical diarylethene derivative. The TD-DFT method with the tuned CAM-B3LYP parameters ( μ = 0.150, α = 0.0799 and β = 0.9201) is found to semi-quantitatively reproduce several excitation energies obtained from the experimental UV–vis spectra of 15 closed forms of diarylethene derivatives. In contrast, it turns out that the use of default CAM-B3LYP parameters ( μ = 0.33, α = 0.19, and β = 0.46) fails to well reproduce these experimental UV–vis spectra. We also clarified that this difference does not originate from the functional dependence of the ground state optimized geometry, but from the CAM-B3LYP parameter dependences of excitation energies and properties in the TD-DFT scheme.

A sequential MC/TD-DFT study of the solvatochromic shift of the pyridinium-N-phenoxide betaine dye in water using standard and long-range corrected functionals

Solvatochromic shifts of the π–π∗ and n–π∗ transitions for the pyridinium-N-phenoxide [2-(pyridinium-1-yl)phenolate] betaine changing from vacuum to water, have been investigated using Monte Carlo simulations and time-dependent density functional theory schemes using standard and long-range corrected functionals. The classical Boltzmann distribution of the interring twist angle obtained from the calculated free energy agrees with a Car–Parrinello distribution. For the calculated spectral shifts BHandHLYP/6-311+G(2d,p) performs better than the CAM-B3LYP/6-311+G(2d,p) or LC-ωPBE/6-311+G(2d,p) model but the experimental shift is very well reproduced only after the inclusion of solute polarization and proper consideration of the twist geometry relaxation associated with the intramolecular charge transfer.

Optical absorption of small copper clusters in neon: Cun, (n = 1–9)

We present optical absorption spectra in the UV-visible range (1.6 eV < ℏω < 5.5 eV) of mass selected neutral copper clusters Cu(n)(n = 1-9) embedded in a solid neon matrix at 7 K. The atom and the dimer have already been measured in neon matrices, while the absorption spectra for sizes between Cu(3) and Cu(9) are entirely (n = 6-9) or in great part new. They show a higher complexity and a larger number of transitions distributed over the whole energy range compared to similar sizes of silver clusters. The experimental spectra are compared to the time dependent density functional theory (TD-DFT) implemented in the TURBOMOLE package. The analysis indicates that for energies larger than 3 eV the transitions are mainly issued from d-type states; however, the TD-DFT scheme does not reproduce well the detailed structure of the absorption spectra. Below 3 eV the agreement for transitions issued from s-type states is better.

All-electron calculation of nonadiabatic couplings from time-dependent density functional theory: Probing with the Hartree–Fock exact exchange

We present the all-electron scheme of calculating nonadiabatic couplings (NACs) from time-dependent density functional theory (TDDFT) using atomic orbital basis. The formal expression for calculating NAC from linear response TDDFT [Hu et al., J. Chem. Phys. 127, 064103 (2007)] can be straightforwardly adapted to the all-electron TDDFT scheme. However, in contrast to the planewave basis, the nuclear coordinate dependence of atomic orbital basis needs to be considered when constructing the matrix elements of the nuclear derivative of Hamiltonian. Practical calculations show that the contribution of atomic orbital basis ("Pulay term") is significant and comparable to that of the Hellmann-Feynman term. In particular, we probe the all-electron formalism of NAC with the Hartree-Fock exact exchange, which serves as the prerequisite for hybrid functionals. It is validated that in the present framework the sum rule of NAC is rigorously satisfied, which has not been the case in the pseudopotential planewave calculations. Reasonably good results can be obtained in the vicinity of various Renner-Teller (and also Jahn-Teller) intersections when the intersection point is not too closely approached, while further tests show that correlation effects should be taken into account in general cases.

Testing the numerical stability of time-dependent density functional simulations using the Suzuki-Trotter formula

In this paper, the numerical stability of simulations of the real-time propagation of electron wave functions under dynamical external fields is shown within the framework of the time-dependent density functional theory (TDDFT) by using periodic boundary conditions. The plane-wave basis set is used to express valence wave functions and fast Fourier transformation is used to treat differential terms in the Schr\"odinger (Kohn-Sham) and Poisson equations. The Suzuki-Trotter formula is applied for expressing time propagation of electron wave functions. An energy conservation rule for conditions with ions in motion and with a time-varying external dielectric field is shown, and numerical stability that satisfies this conservation rule is demonstrated. This will be a benchmark in developing a simulation with the use of other TDDFT schemes different from the current one, such as the real-space method.

Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities

The authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency-dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a real-space (basis-set-free) code and applied it to benchmark molecules, namely, CO, H2O, and para-nitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.

Modified linear response for time-dependent density-functional theory: Application to Rydberg and charge-transfer excitations

We present an improved ab initio time-dependent density-functional theory (TDDFT) approach to electronic excitations. A conventional TDDFT scheme within the local-density approximation (LDA) inaccurately predicts Rydberg and charge-transfer excitation energies, mainly because the electron-hole $(e\text{\ensuremath{-}}h)$ interaction is inappropriately described in these excitations, as can be found by analyzing the linear response formula [M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996)]. When the formula is averaged over the electron occupation, the inappropriate $e\text{\ensuremath{-}}h$ interaction within LDA is corrected to become explicitly similar to that of the exact exchange system. As anticipated from the similarity, our proposed scheme of modified linear response greatly improves the prediction of the problematic excitations, which are exemplified for typical molecules.

An ab initio scheme for quantitative predictions of the visible spectra of diarylethenes

A fully ab intio approach is shown to provide the visible absorption spectra of diarylethene derivatives with a quantitative accuracy. Indeed, a fitted-parameter-free time-dependent density functional theory scheme, combined to the modelling of the surrounding effects, leads to an excellent agreement with the available experimental data. For the λ max ⁡ of 17 closed-ring structures, the mean absolute error (MAE) is limited to 9.4 nm (0.036 eV), although no statistical correction has been performed. The present ab intio scheme is compared to other theoretical schemes previously proposed for diarylethenes.

Time Dependent Density Functional Theory of X-ray Absorption Spectroscopy of Alkaline-Earth Oxides

The time dependent density functional theory (TDDFT) has been employed to calculate the X-ray absorption spectra of the alkaline-earth oxides at the metal K and L and oxygen K edges. Cluster models to mimic the bulk are considered, embedded within an array of point charges to simulate the Madelung potential. Comparison with experimental data allows a precise assessment of the performances of the method, which appears competitive and suitable to reproduce the measurements. The configuration mixing explicitly included in the TDDFT scheme appears mandatory for a correct reproduction of the oscillator strength distribution in the metal 2p spectra. The origin of the theoretical spectral features is investigated with the help of the partial density of the virtual states (PDOS) calculated for each core hole considered. The trends of the spectral features along the series are discussed in terms of the nature of the virtual final states and related to the presence of the empty nd orbitals of the metal cations. The trend of the below-edge features in the O1s excitation spectra is discussed in terms of the metal-oxygen bonding interaction.