Recent performance improvements to the DFT and TDDFT in GAMESS

The general atomic and molecular electronic structure system (GAMESS) is a quantum chemistry package used in the first-principles modeling of complex molecular systems using density functional theory (DFT) as well as a number of other post-Hartree-Fock methods. Both DFT and time-dependent DFT (TDDFT) are of particular interest to the materials modeling community. Millions of CPU hours per year are expended by GAMESS calculations on high-performance computing systems; any substantial reduction in the time-to-solution for these calculations represents a significant saving in CPU hours. As part of this work, three areas for improvement were identified: (1) the exchange-correlation (XC) integration grid, (2) profiling and optimization of the DFT code, and (3) TDDFT parallelization. We summarize the work performed in these task areas and present the resulting performance improvement. These software enhancements are available in 12JAN2009R3 or later versions of GAMESS.     

Time-dependent density-functional theory for open electronic systems

Time-dependent density-functional theory(TDDFT)has been successfully applied to predict excited-state properties of isolated and periodic systems.However,it cannot address a system coupled to an environment or whose number of electrons is not conserved.To tackle these problems,TDDFT needs to be extended to accommodate open systems.This paper provides a comprehensive account of the recent developments of TDDFT for open systems(TDDFT-OS),including both theoretical and practical aspects.The practicality and accuracy of a latest TDDFT-OS method is demonstrated with two numerical examples:the time-dependent electron transport through a series of quasi-one-dimensional atomic chains,and the real-time electronic dynamics on a two-dimensional graphene surface.The advancement of TDDFT-OS may lead to promising applications in various fields of chemistry,including energy conversion and heterogeneous catalysis.     

Pigment Yellow 101: A showcase for photo-initiated processes in medium-sized molecules

Pigment Yellow 101 (P.Y.101) is a fluorescent yellow pigment which exhibits a surprisingly rich photochemistry of several competing reaction pathways as revealed by recent time-resolved femtosecond experiments. Our elaborate quantum chemical investigations employing density functional theory (DFT) and time-dependent DFT (TDDFT) show that the observed fluorescence competes with excited state intramolecular proton transfer and trans–cis isomerization processes. Moreover, the experimentally observed spectral features of the complicated excited state dynamics can be assigned to stable trans-diol, trans-keto and cis-diol, cis-keto isomers on the ground and excited state surfaces. Still, due to its molecular size P.Y.101 poses a challenge to electronic structure theory and many problems occur in particular with respect to the excited state calculations. Thus, P.Y.101 serves also as an educative example for which TDDFT yields a reasonable vertical electronic spectrum, but fails in the prediction of excited state structures, when standard GGA or hybrid functionals with low fractions of Hartree–Fock exchange are employed. This failure is attributed to the charge-transfer failure of TDDFT.     

Failure of time-dependent density functional theory for long-range charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and bacteriochlorophyll-spheroidene complexes

It is well-known that time-dependent density functional theory (TDDFT) yields substantial errors for the excitation energies of charge-transfer (CT) excited states, when approximate standard exchange-correlation (xc) functionals are used, for example, SVWN, BLYP, or B3LYP. Also, the correct 1/R asymptotic behavior of CT states with respect to a distance coordinate R between the separated charges of the CT state is not reproduced by TDDFT employing these xc-functionals. Here, we demonstrate by analysis of the TDDFT equations that the first failure is due to the self-interaction error in the orbital energies from the ground-state DFT calculation, while the latter is a similar self-interaction error in TDDFT arising through the electron transfer in the CT state. Possible correction schemes, such as inclusion of exact Hartree-Fock or exact Kohn-Sham exchange, as well as aspects of the exact xc-functional are discussed in this context. Furthermore, a practical approach is proposed which combines the benefits of TDDFT and configuration interaction singles (CIS) and which does not suffer from electron-transfer self-interaction. The latter approach is applied to a (1,4)-phenylene-linked zincbacteriochlorin-bacteriochlorin complex and to a bacteriochlorophyll-spheroidene complex, in which CT states may play important roles in energy and electron-transfer processes. The errors of TDDFT alone for the CT states are demonstrated, and reasonable estimates for the true excitation energies of these states are given.     

Geometry,Electronic Structure,and Related Properties of Dye Sensitizer： 3,4-bis[1- （carboxymethyl）-3-indolyl]- 1 H-pyrrole-2,5-dione

The geometry, electronic structure, polarizability and hyperpolarizability of dye sensitizer 3,4-bis[1-（carboxymethyl）-3-indolyl]-1H-pyrrole-2,5-dione （BIMCOOH） were studied using density functional theory （DFT） with hybrid functional B3LYP, and the electronic absorption spectra were investigated using semi-empirical quantum chemical method ZINDO-1 and time-dependent DFT （TDDFT）. The results of natural bond orbital suggest that the natural charges of the dione, indole, and acetic groups are about 0.15e, -0.29e, and 0.44e, respectively. The calculated isotropic polarizability, polarizability anisotropy invariant and hyperpolarizability are 305.4, 188.3, and 1155.4 a.u., respectively. The electronic absorption spectral features in visible and near-UV region were assigned to the π→π^＊ transition due to the qualitative agreement between the experiment and the TDDFT calculations, and the transitions of the excited states 9-11 related to photoinduced intramolecular charge transfer processes. The analysis of electronic structure and UV-Vis absorption indicates that the indole groups primarily contributed sensitization of photo-to-currency conversion processes, and the interracial electron transfer between semiconductor TiO2 electrode and dye sensitizer BIMCOOH are electron injection processes from excited states of the dyes to the semiconductor conduction band.     

Comparison of time-dependent density-functional theory and coupled cluster theory for the calculation of the optical rotations of chiral molecules

A comparison of the abilities of time-dependent density-functional theory (TDDFT) and coupled cluster (CC) theory to reproduce experimental sodium D-line specific rotations for 13 conformationally rigid organic molecules is reported. The test set includes alkanes, alkenes, and ketones with known absolute configurations. TDDFT calculations make use of gauge-including atomic orbitals and give origin-independent specific rotations. CC rotations are computed using both the origin-independent dipole-velocity and origin-dependent dipole-length representations. The mean absolute deviations of calculated and experimental rotations are of comparable magnitudes for all three methods. The origin-independent DFT and CC methods give the same sign of [alpha]D for every molecule except norbornanone. For every large-rotation ketone and alkene for which DFT and CC yield the incorrect sign as compared to liquid-phase experimental data, the corresponding optical rotatory dispersion (ORD) curve is bisignate, suggesting that the two models cannot reliably reproduce the relative excitation energies and antagonistic rotational strengths of multiple competing electronic states that contribute to the total long-wavelength rotation. Several potential sources of error in the theoretical treatments are considered, including basis set incompleteness, vibrational and temperature effects, electron correlation, and solvent effects.     

A discrete time-dependent method for metastable atoms and molecules in intense fields

The full-dimensional time-dependent Schr?dinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments.     

Existence of time-dependent density-functional theory for open electronic systems: time-dependent holographic electron density theorem

We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.     

Theoretical studies on electronic spectroscopy and dynamics with the real-time time-dependent density functional theory

Time-dependent density functional theory (TDDFT) has evolved into a general routine to extract the energies of low-lying excited states over the last decades. Driven by the remarkable progress of laser technology, the study of the interaction between matter and intense laser fields with ultrashort pulse duration develops rapidly. A great number of new strong field phenomena emerge. The requirement of a theoretical tool to study the intense field phenomena and dynamical processes of polyatomic systems is urgent. To extend the power of the TDDFT beyond the linear responses, an alternative scheme has been developed by numerically solving the time-dependent Kohn-Sham equations directly in real-time domain. In this article, we summarize the algorithms and capabilities of the real-time TDDFTon studying electron spectroscopy and dynamics of polyatomic systems. The failure of TDDFT with the adiabatic localdensity approximation on some dynamical processes and the possible solutions are synopsized as well. The numerical implementation of algorithms and applications of RT-TDDFT on the linear and nonlinear spectroscopies and electronic dynamics of nano-size nonmetal clusters are displayed.     

Theoretical study on the second-order nonlinear optical properties of asymmetric spirosilabifluorene derivatives

The equilibrium geometries of four asymmetric spirosilabifluorene derivatives are optimized by means of the DFT/B3LYP method with the 6-31G* basis sets in this paper. On the basis of the optimized structures, the electronic structure and second-order nonlinear optical properties are calculated by using time-dependent density-functional theory (TDDFT) based on the 6-31G* level combined with the sum-over-states (SOS) method. The results show that these compounds possess remarkably larger molecular second-order polarizabilities than typical organometallic and organic compounds, and replacement of a carbon atom with nitrogen within the conjugated substituent has a great influence on the second-order nonlinear optical properties. Analysis of the main contributions to the second-order polarizability suggests that charge transfer from the z-axis directions plays a key role in the nonlinear optical response. These compounds have a possibility to be excellent second-order nonlinear optical (NLO) materials from the standpoint of large beta values, small dipole moment, high transparency, and small dispersion behaviors.     

Time-dependent density functional theory for calculating origin-independent optical rotation and rotatory strength tensors

An approach to calculate origin-independent electronic chiroptical property tensors using time-dependent density functional theory (TDDFT) and gauge-including atomic orbital (GIAO) basis sets is evaluated. Computations of origin-dependent optical rotation tensors and of rotatory strengths needed to simulate circular dichroism spectra are presented. The optical rotation tensor computations employ solutions of coupled perturbed Kohn-Sham equations for a dynamic electric field and a static magnetic field. Because the magnetic field is time independent, the GIAO treatment is somewhat simplified compared to a previously reported method, at some added computational cost if hybrid functionals are employed. GIAO rotatory strengths are also calculated, using transition density matrices from a standard TDDFT excitation energy module. A new implementation in the NWChem quantum chemistry package is employed for representative computations of origin-invariant chiroptical response tensors for methyloxirane, norbornenone, and the ketosteroid androstadienone. For the steroid molecule the vibrational structure of the CD spectrum is modeled explicitly by using calculated Franck-Condon factors. The agreement with experiment is favorable.     

Exact-exchange density functional theory for hyperpolarizabilities

Time-dependent density functional theory (TDDFT) employing the exact-exchange functional (TDDFTx) has been formulated using the optimized effective potential method for the beta static hyperpolarizabilities, where it reduces to coupled-perturbed Kohn-Sham theory. A diagrammatic technique is used to take the functional derivatives for the derivation of the adiabatic second kernel, which is required for the analytical calculation of the beta static hyperpolarizabilities with DFT. The derived formulas have been implemented using Gaussian basis sets. The structure of the adiabatic exact-exchange second kernel is described and numerical examples are presented. It is shown that no current DFT functional satisfies the correct properties of the second kernel. Not surprisingly, TDDFTx, which corrects the self-interaction error in standard DFT methods and has the correct long-range behavior, provides results close to those of time-dependent Hartree-Fock in the static limit.     

Excited States of Xanthene Analogues: Photofragmentation and Calculations by CC2 and Time‐Dependent Density Functional Theory

Action spectroscopy has emerged as an analytical tool to probe excited states in the gas phase. Although comparison of gas‐phase absorption properties with quantum‐chemical calculations is, in principle, straightforward, popular methods often fail to describe many molecules of interest—such as xanthene analogues. We, therefore, face their nano‐ and picosecond laser‐induced photofragmentation with excited‐state computations by using the CC2 method and time‐dependent density functional theory (TDDFT). Whereas the extracted absorption maxima agree with CC2 predictions, the TDDFT excitation energies are blueshifted. Lowering the amount of Hartree–Fock exchange in the DFT functional can reduce this shift but at the cost of changing the nature of the excited state. Additional bandwidth observed in the photofragmentation spectra is rationalized in terms of multiphoton processes. Observed fragmentation from higher‐lying excited states conforms to intense excited‐to‐excited state transitions calculated with CC2. The CC2 method is thus suitable for the comparison with photofragmentation in xanthene analogues.     

A theoretical, spectroscopic, and photophysical study of 2,7-carbazolenevinylene-based conjugated derivatives

A combined theoretical and experimental study of the structure, optical, and photophysical properties of four 2,7-carbazolenevinylene-based derivatives in solution is presented. Geometry optimizations of the ground states of PCP, PCP-CN, TCT, and TCT-CN were carried out using the density functional theory (DFT/B3LYP/6-31G*). It is found that PCP and TCT are nearly planar in their ground electronic states (S0), whereas the cyano derivatives are more twisted. The nature and the energy of the first singlet-singlet electronic transitions have been obtained from time-dependent density functional theory (TDDFT) calculations performed on the optimized geometries. For all the compounds, excitation to the S1 state corresponds mainly to the promotion of one electron from the highest-occupied molecular orbital to the lowest-unoccupied molecular orbital, and the S1 <-- S0 electronic transition is strongly allowed and polarized along the long axis of the molecular frame. The optimization (relaxation) of the first singlet excited electronic state (S1) has been done using the restricted configuration interaction (singles) (RCIS/6-31G*) approach. It is observed that all four investigated compounds become more planar in their S1 relaxed excited state. Electronic transition energies from the relaxed excited states have been obtained from TDDFT calculations performed on the S1-optimized geometries. The absorption and fluorescence spectra of the carbazolenevinylenes have been recorded in chloroform. A good agreement is obtained between TDDFT vertical transitions energies and the (0,0) absorption and fluorescence bands. The change from phenylene to thiophene rings as well as the incorporation of cyano substituents induce bathochromic shifts in the absorption and fluorescence spectra. From the analysis of the energy of the frontier molecular orbitals, it is believed that thiophene rings and CN substituents induce some charge-transfer character to the first electronic transition, which is responsible for the red shifts observed. Finally, the fluorescence quantum yield and the lifetime of the compounds in chloroform have been obtained. In sharp contrast with many oligothiophenes, it is observed that TCT possesses a high fluorescence quantum yield. On the other hand, the CN-containing derivatives exhibit much lower fluorescence quantum yields, probably due to the combined influence of steric effects and charge-transfer interactions caused by the cyano groups.     

Geometries, electronic structures, and excited states of UN2, NUO+, and UO 2 2+ : a combined CCSD(T), RAS/CASPT2 and TDDFT study

The ground- and excited-state geometries and electronic structures of the isoelectronic series of molecules UN₂, NUO⁺, and UO ₂ ²⁺ are investigated by using relativistic density functional theory (DFT) and ab initio wavefunction theory (WFT). Scalar relativistic and spin?Corbit-coupled quantum chemical methods at the CASPT2, RASPT2, CCSD(T), DFT and TDDFT levels are applied. Relativistic effects as elucidated by Pekka Pyykk? play an important role in these uranium compounds, in particular for the excited states. The three molecular species exhibit significantly different spectroscopic properties, concerning their excitation energies, bond lengths and vibrations. Density functional approaches yield qualitatively correct results for the ground states and the valence????U.7s,6d excited states. However, the performance of TDDFT for valence????U.5f type excitations (in particular of UN₂ and NUO⁺) is less satisfactory, indicating the importance of the self-interaction correction for such excitations.     

A comparative study on the photochemistry of two bipyridyl derivatives: [2,2'-bipyridyl]-3,3'-diamine and [2,2'-bipyridyl]-3,3'-diol.

The two isoelectronic bipyridyl derivatives, [2,2'-bipyridyl]-3,3'-diamine and [2,2'-bipyridyl]-3,3'-diol, are experimentally known to undergo very different excited-state double-proton-transfer processes, which result in fluorescence quantum yields that differ by four orders of magnitude. Herein, density functional theory (DFT), time-dependent DFT (TDDFT), and complete active space self-consistent field (CASSCF) calculations are used to study the double-proton-transfer processes in the ground and first singlet pi-->pi* excited state. The quantum-chemistry calculations indicate 1) the existence of only one energy minimum in the ground electronic state corresponding to reactants (thus avoiding the possibility of a fast fluorescent relaxation process from the photoproducts region), 2) an endoergic process of the complete double proton transfer, and 3) the presence of a conical intersection in the excited intermediate region of [2,2'-bipyridyl]-3,3'-diamine. These facts explain the very low fluorescence quantum yield in [2,2'-bipyridyl]-3,3'-diamine compared to [2,2'-bipyridyl]-3,3'-diol.     

A bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles

We describe a bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles. In this method, we apply a many-body scaling function (in similar manner as in the environment-modified total energy based tight-binding method) to the DFT-derived diatomic AO interaction potentials (like in the conventional orbital-based density-functional tight binding approach) strictly according to atomic valences acquired naturally in a bulk structure. This modification, (a) facilitates all atom orbital-based electronic structure calculations of charge carrier dynamics in nanoscale structures with a molecular acceptor, and (b) allows to closely match high-level density functional calculation data (previously adjusted to the available experimental findings) for bulk structures. To advance practical application of the BA-LCAO approach we parameterize the Hamiltonian of wurtzite CdSe by fitting its band structure to a high-level DFT reference, corrected for experimentally measured band edges. Here, unlike in conventional DFTB approach, we: (1) use hydrogen-like AOs for the basis as exact atomic eigenfunctions, while orbital energies of which are taken from experimentally measured ionization potentials, and (2) parameterize the many-body scaling functions rather than the atomic wavefunctions. Development of this approach and parameters is guided by our goals to devise a method capable of simultaneously treating the problems of (i) interfacial electron/hole transfer between finite, variable size nanoparticles and electron scavenging molecules, and (ii) high-energy electronic transitions (Auger transitions) that mediate multi-exciton decay in quantum dots. Electronic structure results are described for CdSe quantum dots of various sizes. © 2018 Wiley Periodicals, Inc.     

Push-pull bithienyl chromophore with an unusual transverse path of conjugation

The synthesis, structure, and electronic properties of a novel cross-conjugated 10H-bisthienodithiocin-10-dicyanoethylene are reported. The X-ray single-crystal structure of the compound reveals a nonplanar conformation. The FT-IR and FT-Raman spectra of the compound show a great resemblance, which is a spectroscopic observation common to many push-pull systems. The UV-vis spectrum in CHCl3 displays a strong absorption at 370 nm accompanied by a shoulder at 430 nm so that the optical gap is 2.88 eV. On the other hand, the electrochemical gap amounts to 2.38 V. DFT and TDDFT quantum chemical calculations, at the B3LYP/6-31G** level, have been also performed to (i) determine the minimum-energy molecular structure, (ii) gain knowledge about the equilibrium atomic charges distribution, the topologies, and absolute energies of the frontier molecular orbitals around the gap and about the molecular vibrations which give rise to the most outstanding Raman bands experimentally evidenced, and (iii) to analyze the nature of the vertical one-electron excitations associated to the strongest UV-vis absorptions.