Current‐density functional study of the HeH+ molecular ion under a strong ultrashort magnetic field

The HeH⁺ molecular ion under an ultrashort magnetic field on the order of 10⁹ G is investigated through quantum fluid dynamics and a current‐density functional theory (CDFT) based approach, employing a vector exchange–correlation (XC) potential which depends on the electronic charge‐density as well as on the current‐density. The behavior of the exchange and correlation energies of the HeH⁺ ion is analyzed and compared with those obtained using an approach based on the time‐dependent density functional theory (TD‐DFT) under similar computational constraints but employing a scalar XC potential dependent only on the electronic charge‐density. The CDFT‐based approach yields exchange and correlation energies as well as TD electronic charge‐densities drastically different from those obtained using the TD‐DFT‐based approach particularly, at typical TD magnetic field strengths. This is attributed to the nonadiabatic effects induced by the vector XC potential of the CDFT in the oscillating charge‐density of the HeH⁺ ion, which are further explained in the terminology of quantum fluid dynamics. The vector XC potential of the CDFT‐based approach is observed to augment the magnetic interactions in the H₂ molecule and in the He ion, whereas it opposes the magnetic interactions in the HeH⁺ ion particularly, at the intermediate magnetic field strengths. © 2012 Wiley Periodicals, Inc.     

A semiempirical long-range corrected exchange correlation functional including a short-range Gaussian attenuation (LCgau-B97)

We applied an improved long‐range correction scheme including a short‐range Gaussian attenuation (LCgau) to the Becke97 (B97) exchange correlation functional. In the optimization of LCgau‐B97 functional, the linear parameters are determined by least squares fitting. Optimizing μ parameter (0.2) that controls long‐range portion of Hartree‐Fock (HF) exchange to excitation energies of large molecules (Chai and Head‐Gordon, J Chem Phys 2008, 128, 084106) and additional short‐range Gaussian parameters (a = 0.15 and k = 0.9) that controls HF exchange inclusion ranging from short‐range to mid‐range (0.5–3 Å) to ground state properties achieved high performances of LCgau‐B97 simultaneously on both ground state and excited state properties, which is better than other tested semiempirical density functional theory (DFT) functionals, such as ωB97, ωB97X, BMK, and M0x‐family. We also found that while a small μ value (～0.2) in LC‐DFT is appropriate to the local excitation and intramolecular charge‐transfer excitation energies, a larger μ value (0.42) is desirable in the Rydberg excitation‐energy calculations. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Assessment of dispersion‐improved exchange‐correlation functionals for the simulation of CO2 binding by alcoholamines

In this study, 12 bound complexes were selected to construct a database for testing 15 dispersion‐improved exchange‐correlation (XC) functionals, including hybrid generalized gradient approximation (GGA), modified using the Grimme's pairwise strategy, and double hybrid XC functionals, for specifically characterizing the CO₂ binding by alcoholamines. Bound complexes were selected based on the characteristics of their hydrogen bonds, dispersion, and electrostatic (particularly between the positive charge of CO₂ and the lone pair of N of alcoholamines) interactions. The extrapolated binding energy from the aug‐cc‐pVTZ (ATZ) to aug‐cc‐pVQZ (AQZ) basis set at the CCSD(T)/CBS(MP2+DZ) level was used as the reference for the XC functional comparison. M06‐2X produced the optimal agreement if the optimized geometries at MP2/ATZ level were chosen for all the test bound complexes. However, M06‐L, ωB97X, and ωB97, and were preferred if the corresponding density functional theory (DFT) optimized geometries were adapted for the benchmark. Simple bimolecular reaction between CO₂ and monoethanolamine simulated using polarizable continuum solvation model confirmed that ωB97, ωB97X, and ωB97XD qualitatively reproduced the energetics of MP2 level. The inconsistent performance of the tested XC functionals, observed when using MP2 or DFT optimized geometries, raised concerns regarding using the single‐point ab initio correction combined with DFT optimized geometry, particularly for determining the nucleophilic attack by alcoholamines to CO₂. © 2014 Wiley Periodicals, Inc.     

Ab initio description of photoabsorption and electron transfer in a doubly-linked porphyrin-fullerene dyad

Structure, photoabsorption and excited states of two representative conformations obtained from molecular dynamics (MD) simulations of a doubly-linked porphyrin-fullerene dyad DHD6ee are studied by using both DFT and wavefunction based methods. Charge transfer from the donor (porphyrin) to the acceptor (fullerene) and the relaxation of the excited state are of special interest. The results obtained with LDA, GGA, and hybrid functionals (SVWN, PBE, and B3LYP, respectively) are analyzed with emphasis on the performance of used functionals as well as from the point of view of their comparison with wavefunction based methods (CCS, CIS(D), and CC2). Characteristics of the MD structures are retained in DFT optimization. The relative orientation of porphyrin and fullerene is significantly influencing the MO energies, the charge transfer (CT) in the ground state of the dyad and the excitation of ground state CT complex (g-CTC). At the same time, the excitation to the locally excited state of porphyrin is only little influenced by the orientation or cc distance. TD-DFT underestimates the excitation energy of the CT state, however for some cases (with relatively short donor-acceptor separations), the use of a hybrid functional like B3LYP alleviates the problem. Wavefunction based methods and CC2 in particular appear to overestimate the CT excitation energies but the inclusion of proper solvation models can significantly improve the results.     

Parallel implementation of γ‐point pseudopotential plane‐wave DFT with exact exchange

Semi‐local functionals commonly used in density functional theory (DFT) studies of solids usually fail to reproduce localized states such as trapped holes, polarons, excitons, and solitons. This failure is ascribed to self‐interaction which creates a Coulomb barrier to localization. Pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange (hybrid‐DFT, e.g., B3LYP and PBE0) have shown to promise in rectifying this type of failure, as well as producing more accurate band gaps and reaction barriers. The evaluation of exact exchange is challenging for large, solid state systems with periodic boundary conditions, especially when plane‐wave basis sets are used. We have developed parallel algorithms for implementing exact exchange into pseudopotential plane‐wave DFT program and we have implemented them in the NWChem program package. The technique developed can readily be employed in Γ‐point plane‐wave DFT programs. Furthermore, atomic forces and stresses are straightforward to implement, making it applicable to both confined and extended systems, as well as to Car‐Parrinello ab initio molecular dynamic simulations. This method has been applied to several systems for which conventional DFT methods do not work well, including calculations for band gaps in oxides and the electronic structure of a charge trapped state in the Fe(II) containing mica, annite. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Intramolecular electronic communication in a dimethylaminoazobenzene–fullerene C60 dyad: An experimental and TD‐DFT study

An electronically push–pull type dimethylaminoazobenzene–fullerene C₆₀ hybrid was designed and synthesized by tailoring N,N‐dimethylaniline as an electron donating auxochrome that intensified charge density on the β‐azonitrogen, and on N‐methylfulleropyrrolidine (NMFP) as an electron acceptor at the 4 and 4′ positions of the azobenzene moiety, respectively. The absorption and charge transfer behavior of the hybrid donor‐bridge‐acceptor dyad were studied experimentally and by performing TD‐DFT calculations. The TD‐DFT predicted charge transfer interactions of the dyad ranging from 747 to 601 nm were experimentally observed in the UV‐vis spectra at 721 nm in toluene and dichloromethane. A 149 mV anodic shift in the first reduction potential of the N?N group of the dyad in comparison with the model aminoazobenzene derivative further supported the phenomenon. Analysis of the charge transfer band through the orbital picture revealed charge displacement from the n_(N?N) (nonbonding) and π _(N?N) type orbitals centered on the donor part to the purely fullerene centered LUMOs and LUMO+n orbitals, delocalized over the entire molecule. The imposed electronic perturbations on the aminoazobenzene moiety upon coupling it with C₆₀ were analyzed by comparing the TD‐DFT predicted and experimentally observed electronic transition energies of the dyad with the model compounds, NMFP and (E)‐N,N‐dimethyl‐4‐(p‐tolyldiazenyl)aniline (AZNME). The n_(N?N) → π*_(N?N) and π_(N?N) → π*_(N?N) transitions of the dyad were bathochromically shifted with a significant charge transfer character. The shifting of π_(N?N) → π*_(N?N) excitation energy closer to the n → π*_(N?N) in comparison with the model aminoazobenzene emphasized the predominant existence of charge separated quinonoid‐like ground state electronic structure. Increasing solvent polarity introduced hyperchromic effect in the π_(N?N) → π*_(N?N) electronic transition at the expense of transitions involved with benzenic states, and the extent of intensity borrowing was quantified adopting the Gaussian deconvolution method. On a comparative scale, the predicted excitation energies were in reasonable agreement with the observed values, demonstrating the efficiency of TD‐DFT in predicting the localized and the charge transfer nature of transitions involved with large electronically asymmetric molecules with HOMO and LUMO centered on different parts of the molecular framework. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Simultaneous benchmarking of ground- and excited-state properties with long-range-corrected density functional theory

We present benchmark calculations using several long-range-corrected (LRC) density functionals, in which Hartree-Fock exchange is incorporated asymptotically using a range-separated Coulomb operator, while local exchange is attenuated using an ansatz introduced by Iikura et al. [J. Chem. Phys. 115, 3540 (2001)]. We calculate ground-state atomization energies, reaction barriers, ionization energies, and electron affinities, each as a function of the range-separation parameter mu. In addition, we calculate excitation energies of small- and medium-sized molecules, again as a function of mu, by applying the LRC to time-dependent density functional theory. Representative examples of both pure and hybrid density functionals are tested. On the basis of these results, there does not appear to be a single range-separation parameter that is reasonable for both ground-state properties and vertical excitation energies. Reasonable errors in atomization energies and barrier heights are achieved only at the expense of excessively high excitation energies, at least for the medium-sized molecules, whereas values of mu that afford reasonable excitation energies yield some of the largest errors for ground-state atomization energies and barrier heights in small molecules. Notably, this conclusion is obscured if the database of excitation energies includes only small molecules, as has been the case in previous benchmark studies of LRC functionals.     

Theoretical study of excited states of DNA base dimers and tetramers using optimally tuned range‐separated density functional theory

Excited states of various DNA base dimers and tetramers including Watson‐Crick H‐bonding and stacking interactions have been investigated by time‐dependent density functional theory using nonempirically tuned range‐separated exchange (RSE) functionals. Significant improvements are found in the prediction of excitation energies and oscillator strengths, with results comparable to those of high‐level coupled‐cluster (CC) models (RI‐CC2 and EOM‐CCSD(T)). The optimally‐tuned RSE functional significantly outperforms its non‐tuned (default) version and widely‐used B3LYP functional. Compared to those high‐level CC benchmarks, the large mean absolute deviations of conventional functionals can be attributed to their inappropriate amount of exact exchange and large delocalization errors which can be greatly eliminated by tuning approach. Furthermore, the impacts of H‐bonding and π‐stacking interactions in various DNA dimers and tetramers are analyzed through peak shift of simulated absorption spectra as well as corresponding change of absorption intensity. The result indicates the stacking interaction in DNA tetramers mainly contributes to the hypochromicity effect. The present work provides an efficient theoretical tool for accurate prediction of optical properties and excited states of nucleobase and other biological systems. © 2015 Wiley Periodicals, Inc.     

TD‐DFT benchmarks: A review

Time‐Dependent Density Functional Theory (TD‐DFT) has become the most widely‐used theoretical approach to simulate the optical properties of both organic and inorganic molecules. In this contribution, we review TD‐DFT benchmarks that have been performed during the last decade. The aim is often to pinpoint the most accurate or adequate exchange‐correlation functional(s). We present both the different strategies used to assess the functionals and the main results obtained in terms of accuracy. In particular, we discuss both vertical and adiabatic benchmarks and comparisons with both experimental and theoretical reference transition energies. More specific benchmarks (oscillator strengths, excited‐state geometries, dipole moments, vibronic shapes, etc.) are summarized as well. © 2013 Wiley Periodicals, Inc.     

Subsystem‐Based Theoretical Spectroscopy of Biomolecules and Biomolecular Assemblies

The absorption properties of chromophores in biomolecular systems are subject to several fine‐tuning mechanisms. Specific interactions with the surrounding protein environment often lead to significant changes in the excitation energies, but bulk dielectric effects can also play an important role. Moreover, strong excitonic interactions can occur in systems with several chromophores at close distances. For interpretation purposes, it is often desirable to distinguish different types of environmental effects, such as geometrical, electrostatic, polarization, and response (or differential polarization) effects. Methods that can be applied for theoretical analyses of such effects are reviewed herein, ranging from continuum and point‐charge models to explicit quantum chemical subsystem methods for environmental effects. Connections to physical model theories are also outlined. Prototypical applications to optical spectra and excited states of fluorescent proteins, biomolecular photoreceptors, and photosynthetic protein complexes are discussed.     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

Strongly Absorbing π–π* States in Heteroleptic Dipyrrin/2,2′‐Bipyridine Ruthenium Complexes: Excited‐State Dynamics from Resonance Raman Spectroscopy

A recently reported new class of ruthenium complexes containing 2,2′‐bipyridine and a dipyrrin ligand in the coordination sphere exhibit both strong metal‐to‐ligand charge‐transfer (MLCT) and π–π* transitions. Quantitative analysis of the resonance Raman scattering intensities and absorption spectra reveals only weak electronic interactions between these states despite direct coordination of the bipyridyl and dipyrrin ligands to the central ruthenium atom. On the basis of DFT calculations and time‐dependent DFT (TD‐DFT), we propose that the electronic excited states closely resemble “pure” MLCT and π–π* states. Resonance Raman intensity analysis demonstrates that a large amplitude transannular torsional motion provides a mechanism for relaxation on the π–π* excited‐state surface. We assert that this result is generally applicable to a range of dipyrrin complexes such as boron–dipyrrin and metallodipyrrin systems. Despite the large torsional distortion between the phenyl ring and the dipyrromethene plane, π–π* excitation extends out onto the phenyl ring which may have important consequences in solar‐energy‐conversion applications of ruthenium–dipyrrin complexes.     

The Excitation Spectra of Naphthalene Dimers: Frenkel and Charge‐transfer Excitons

Vertical electronic excitation energies have been calculated at the second‐order approximate coupled‐cluster (CC2) level for a series of dimeric naphthalene systems. The calculated excitation energies are compared with values obtained for a single naphthalene molecule and provide information about the coupling between the naphthalene moieties in the dimers. The calculations show that the coupling between the naphthalenes depends on the distance and the energy of the exciton. At long distances and high energies the excitons on the two naphthalenes are strongly coupled, whereas the excitation energies of the few lowest states are almost unaffected by the presence of the neighboring molecules. We have also analyzed the composition of the dimeric states that consist of the individual monomer states, to investigate the charge‐transfer (CT) and the Frenkel character of the excitons. Our results indicate that the CT exciton exists at short distances, and that its population drops as the distance between the two naphthalene increases.     

Quantum chemical comparison of vertical,adiabatic, and 0‐0 excitation energies: The PYP and GFP chromophores

A number of benchmark studies investigating the performance of quantum chemical methods for calculating vertical excitation energies are today available in the literature. However, less established is the variation between methods in their estimates of the differences between vertical, adiabatic, and 0‐0 excitation energies. To this end, such excitation energies are here calculated for the bright S₁ states of the anionic chromophores of the photoactive yellow protein (PYP) and the green fluorescent protein (GFP) in the gas phase using configuration interaction singles, complete active space self‐consistent field, coupled‐cluster singles and doubles, and time‐dependent density functional theory methods. Although the estimates of the excitation energies vary by more than 1 eV between the methods, the differences between the different types of excitation energies are found to be relatively method‐insensitive, varying by ～0.1 eV only for these particular chromophores. Specifically, the adiabatic energies are uniformly 0.10–0.17 (PYP) and 0.06–0.17 eV (GFP) lower than the vertical energies, and the 0‐0 energies are similarly 0.09–0.14 (PYP) and 0.07–0.17 eV (GFP) lower than the adiabatic energies. © 2012 Wiley Periodicals, Inc.     

DFT performance for the hole transfer parameters in DNA π stacks

Recently, we showed that unoccupied Kohn‐Sham (KS) orbitals stemming from DFT calculations of a neutral system can be used to derive accurate estimates of the free energy and electronic couplings for excess electron transfer in DNA (Félix and Voityuk, J Phys Chem A 2008, 112, 9043). In this article, we consider the propagation of radical cation states (hole transfer) through DNA π‐stacks and compare the performance of different exchange‐correlation functionals to estimate the hole transfer (HT) parameters. Two different approaches are used: (1) calculations that use occupied KS orbitals of neutral π stacks of nucleobases, and (2) the time‐dependent DFT method which is applied to the radical cation states of these stacks. Comparison of the calculated parameters with the reference data suggests that the best results are provided by the KS scheme with hybrid functionals (B3LYP, PBE0, and BH&HLYP). The TD DFT approach gives significantly less accurate values of the HT parameters. In agreement with high‐level ab initio results, the KS scheme predicts that the hole in π stacks is confined to a single nucleobase; in contrast, the spin‐unrestricted DFT method considerably overestimates the hole delocalization in the radical cations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011