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.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Through‐Space Conjugated Molecular Wire Comprising Three π‐Electron Systems

A [2.2]paracyclophane‐based through‐space conjugated oligomer comprising three π‐electron systems was designed and synthesized. The arrangement of three π‐conjugated systems in an appropriate order according to the energy band gap resulted in efficient unidirectional photoexcited energy transfer by the Förster mechanism. The energy transfer efficiency and rate constants were estimated to be >0.999 and >10¹² s^?1, respectively. The key point for the efficient energy transfer is the orientation of the transition dipole moments. The time‐dependent density functional theory (TD‐DFT) studies revealed the transition dipole moments of each stacked π‐electron system; each dipole moment was located on the long axis of each stacked π‐electron system. This alignment of the dipole moments is favorable for fluorescence resonance energy transfer (FRET).     

Toward the complete range separation of non‐hybrid exchange–correlation functional

In this study, we use a very simple scheme to achieve range separation of a total exchange–correlation functional. We have utilized this methodology to combine a short‐range pure density functional theory (DFT) functional with a corresponding long‐range pure DFT, leading to a “Range‐separated eXchange–Correlation” (RXC) scheme. By examining the performance of a range of standard exchange–correlation functionals for prototypical short‐ and long‐range properties, we have chosen B‐LYP as the short‐range functional and PBE‐B95 as the long‐range counterpart. The results of our testing using a more diverse range of data sets show that, for properties that we deem to be short‐range in nature, the performance of this prescribed RXC‐DFT protocol does resemble that of B‐LYP in most cases, and vice versa. Thus, this RXC‐DFT protocol already provides meaningful numerical results. Furthermore, we envisage that the general RXC scheme can be easily implemented in computational chemistry software packages. This study paves a way for further refinement of such a range‐separation technique for the development of better performing DFT procedures. © 2015 Wiley Periodicals, Inc.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

The role of errors related to DFT methods in calculations involving ion pairs of ionic liquids

Ionic liquids (ILs) play a key role in many chemical applications. As regards the theoretical approach, ILs show added difficulties in calculations due to the composition of the ion pair and to the fact that they are liquids. Although density functional theory (DFT) can treat this kind of systems to predict physico–chemical properties, common versions of these methods fail to perform accurate predictions of geometries, interaction energies, dipole moments, and other properties related to the molecular structure. In these cases, dispersion and self‐interaction error (SIE) corrections need to be introduced to improve DFT calculations involving ILs. We show that the inclusion of dispersion is needed to obtain good geometries and accurate interaction energies. SIE needs to be corrected to describe the charges and dipoles in the ion pair correctly. The use of range–separated functionals allows us to obtain interaction energies close to the CCSD(T) level. © 2017 Wiley Periodicals, Inc.     

Reaction energetics on long‐range corrected density functional theory: Diels–Alder reactions

The possibility of quantitative reaction analysis on the orbital energies of long‐range corrected density functional theory (LC‐DFT) is presented. First, we calculated the Diels–Alder reaction enthalpies that have been poorly given by conventional functionals including B3LYP functional. As a result, it is found that the long‐range correction drastically improves the reaction enthalpies. The barrier height energies were also computed for these reactions. Consequently, we found that dispersion correlation correction is also crucial to give accurate barrier height energies. It is, therefore, concluded that both long‐range exchange interactions and dispersion correlations are essentially required in conventional functionals to investigate Diels–Alder reactions quantitatively. After confirming that LC‐DFT accurately reproduces the orbital energies of the reactant and product molecules of the Diels–Alder reactions, the global hardness responses, the halves of highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) energy gaps, along the intrinsic reaction coordinates of two Diels–Alder reactions were computed. We noticed that LC‐DFT results satisfy the maximum hardness rule for overall reaction paths while conventional functionals violate this rule on the reaction pathways. Furthermore, our results also show that the HOMO‐LUMO gap variations are close to the reaction enthalpies for these Diels–Alder reactions. Based on these results, we foresee quantitative reaction analysis on the orbital energies. © 2012 Wiley Periodicals, Inc.     

Design of high‐performance chlorine type dyes for dye‐sensitized solar cells

Intrinsic defect of electronic structure for the chlorine‐type porphyrin 1, which was synthesized for use in dye‐sensitized solar cell (DSSC), is found by theoretical calculation including density functional method (DFT), time‐dependent DFT, and C+/C? function. It is believed that the limited cell performance obtained by using dye 1 as the sensitizer is due to the existence of this electronic defect. To avoid this defect, a series of novel molecules with electron deficient π bridge were designed. The subsequent theoretical calculation indicated that the electron deficient π bridge in the newly designed molecule is quite effective in offsetting the electronic defect observed for dye 1. The parameters for the designed molecules closely associated with open‐circuit voltage and short‐circuit current density including dipole moment of dye vertical to the surface of semiconductor and light‐harvesting efficiency were then evaluated. By comparing these parameters of designed dyes with those of dye 1, we can predict that the DSSC based on dye 4 (2, 6‐cyan benzoic acid as anchoring group) should possess enhanced performance, which would be a valuable theoretical guidance for the practical work. © 2013 Wiley Periodicals, Inc.     

A theoretical description of charge reorganization energies in molecular organic P‐type semiconductors

Charge transport properties of materials composed of small organic molecules are important for numerous optoelectronic applications. A material's ability to transport charges is considerably influenced by the charge reorganization energies of the composing molecules. Hence, predictions about charge‐transport properties of organic materials deserve reliable statements about these charge reorganization energies. However, using density functional theory which is mostly used for the predictions, the computed reorganization energies depend strongly on the chosen functional. To gain insight, a benchmark of various density functionals for the accurate calculation of charge reorganization energies is presented. A correlation between the charge reorganization energies and the ionization potentials is found which suggests applying IP‐tuning to obtain reliable values for charge reorganization energies. According to benchmark investigations with IP‐EOM‐CCSD single‐point calculations, the tuned functionals provide indeed more reliable charge reorganization energies. Among the standard functionals, ωB97X‐D and SOGGA11X yield accurate charge reorganization energies in comparison with IP‐EOM‐CCSD values. © 2016 Wiley Periodicals, Inc.     

Topological analysis of the molecular charge density and impact sensitivy models of energetic molecules

Important explosives of practical use are composed of nitroaromatic molecules. In this work, we optimized geometries and calculated the electron density of 17 nitroaromatic molecules using the Density Functional Theory (DFT) method. From the DFT one-electron density matrix, we computed the molecular charge densities, thus the electron densities, which were then decomposed into electric multipoles located at the atomic sites of the molecules using the distributed multipole analysis (DMA). The multipoles, which have a direct chemical interpretation, were then used to analyze in details the ground state charge structure of the molecules and to seek for correlations between charge properties and sensitivity of the corresponding energetic material. The DMA multipole moments do not present large variations when the size of the Gaussian basis set is changed; the largest variations occurred in the range 10-15% for the dipole and quadrupole moments of oxygen atoms. The charges on the carbon atoms of the aromatic ring of each molecule become more positive when the number of nitro groups increases and saturate when there are five and six nitro groups. The magnitude and the direction of the dipole moments of the carbon atoms, indicators of site polarization, also depend on the nature of adjacent groups, with the largest dipole value being for C-H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbon atoms indicates a decrease in the delocalized electron density due to an electron-withdrawing effect. Three models for sensitivity of the materials based on the DMA multipoles were proposed. Explosives with large delocalized electron densities in the aromatic ring of the component molecule, expressed by large quadrupole values on the ring carbon atoms, correspond to more insensitive materials. Furthermore, the charges on the nitro groups also influence the impact sensitivity.     

Static and Frequency‐Dependent Dipole–Dipole Polarizabilities of All Closed‐Shell Atoms up to Radium: A Four‐Component Relativistic DFT Study

We test the performance of four‐component relativistic density functional theory by calculating the static and frequency‐dependent electric dipole–dipole polarizabilities of all (ground‐state) closed‐shell atoms up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically shape‐corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient‐regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple‐zeta quality are used. The results are compared to experimental data or to accurate ab initio results. The reference static electric dipole polarizability of palladium has been obtained by finite‐field calculations using the coupled‐cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape‐corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare‐gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptotic correction is switched on in the core region.     

Wave‐function frozen‐density embedding: Approximate analytical nuclear ground‐state gradients

We report the derivation of approximate analytical nuclear ground‐state uncoupled frozen density embedding (FDEu) gradients for the resolution of identity (RI) variant of the second‐order approximate coupled cluster singles and doubles (RICC2) as well as density functional theory (DFT), and an efficient implementation thereof in the KOALA program. In order to guarantee a computationally efficient treatment, those gradient terms are neglected which would require the exchange of orbital information. This approach allows for geometry optimizations of single molecules surrounded by numerous molecules with fixed nuclei at RICC2‐in‐RICC2, RICC2‐in‐DFT, and DFT‐in‐DFT FDE level of theory using a dispersion correction, required due to the DFT‐based treatment of the interaction in FDE theory. Accuracy and applicability are assessed by the example of two case studies: (a) the Watson‐Crick pair adenine‐thymine, for which the optimized structures exhibit a maximum error of about 0.08 Å for our best scheme compared to supermolecular reference calculations, (b) carbon monoxide on a magnesium oxide surface model, for which the error amount up to 0.1 Å for our best scheme. Efficiency is demonstrated by successively including environment molecules and comparing to an optimized conventional supermolecular implementation, showing that the method is able to outperform conventional RICC2 schemes already with a rather small number of environment molecules, gaining significant speed up in computation time. © 2016 Wiley Periodicals, Inc.     

Application of potential constants: Charge transfer and electric dipole moment change in the formation of heteronuclear diatomic molecules—IV

The harmonic and anharmonic potential (force) constants of heteronuclear diatomic molecules, which are usually available from normal coordinate analyses, are applied to problems of determining the number of electrons transferred (charge transfer) and electric dipole moment functions of such molecules. The approach developed here is mainly based on Slater's orbital expansion method, that is, in a non-spin-polarized calculation atomic energies in a molecule are expanded with respect to the occupation number of electrons of atomic orbitals. To confirm the accuracy and the reliability of the approach, we have calculated the number of electrons transferred and electric dipole moments for alkali halides and other heteronuclear diatomic molecules. Specially, detailed analyses of electric dipole moment functions have been carried out on hydrogen fluoride (HF) and hydrogen oxide (OH) for which reliable experimental dipole moment functions are presently known over a wide range of internuclear distances. It is concluded from these analyses that the present approach is simple and useful in evaluating the charge transfer and the dipole moment change in the formation of heteronuclear diatomic molecules.     

On the negative dipole moment derivatives of HRgX (Rg=He, Ar, Kr; X=F, Cl) molecules

The large dipole moment and the negative dipole moment derivatives with respect to H–Rg displacement of the neutral HRgX (Rg=He, Ar, Kr; X=F, Cl) molecules have been rationalised by a charge/charge flux/dipole flux decomposition of the charge density using the ChelpG method. This approach was also applied to the hydrogen halides HF and HCl for the sake of comparison. It was found that the dipole moment of HRgX is dominated by the large positive charge contribution while the negative dipole moment derivative of HRgX is due to the dominance of the negative charge flux contribution.     

Order of stabilities in water nanoclusters: Insight from some recent double‐hybrid functionals

In the present work, the applicability of some of the recently proposed and modern double‐hybrid (DH) models and other density functional theory (DFT) approximations has been analyzed for a difficult test, the order of stability in low‐energy isomers of water nanoclusters. In particular, we aim to systematically investigate for these functionals the role played by several factors such as dispersion correction, integrand functions upon which the DHs are based, and different spin scaling for the perturbative term in DH calculations of the relative energies for various isomers of water nanoclusters (H₂O)₂₀. From the obtained results, the superior performance of DHs with respect to the functionals from previous rungs is confirmed. It is shown that the dispersion corrected DHs perform better than noncorrected counterparts. Plus, the DH models based on cubic integrand (CI) and quadratic integrand (QI) functions are nearly equivalent in performance. We also find that using only contributions of electron pairs with opposite spin for the perturbative correlation part through scaled opposite spin scheme does not represent a significant improvement on accuracy of the results. Putting all the results together, the dispersion corrected parameterized DHs and parameter‐free DH models involving CI and QI functions outperform other approximations for relative energies of water 20‐mers. Altogether, predicting the correct order of the stability in water nanoclusters may be considered as another Achilles' heel in DFT calculations, although more analyses in this context are still needed. © 2016 Wiley Periodicals, Inc.     

Assessing the performance of density functional theory for the dynamic polarizabilities of amino acids: Treatment of correlation and role of exact exchange

The theoretical determination of electric response properties of the biological systems is a field where the application of density functional theory (DFT) appears to be quite promising. In this work, the performance of 41 density functional methods is evaluated in predicting dynamic polarizabilities of an experimental benchmark set of 20 proteinogenic amino acids. The behavior of a large number of density functionals, including various types of the local spin density approximation (LSDA), generalized gradient approximation (GGA), meta‐GGA (m‐GGA), hybrid‐GGA (h‐GGA), hybrid meta‐GGA (hm‐GGA), and range‐separated hybrid‐GGA (rsh‐GGA), has been assessed for the purpose. Analyzing the results of our DFT benchmarking, we found that these computationally economical methods show very diverse predictive capability and a careful selection of DFT functionals is very important in the polarizability calculations. Considering the role of exchange, correlation, dispersion and long‐range corrections, it turned out that in the LSDA class, SVWN3 gives better results than SPL and SVWN5 toward the reference values. Of the GGA methods, OPBE outperforms all other functionals. The M06‐L is the best method of m‐GGA class. The B3LYP and TPSSh are the best functionals of h‐GGA and hm‐GGA lineages, respectively. Finally, CAM‐B3LYP is the best method of rsh‐GGA functionals that predicts the most accurate polarizability for amino acids by a large margin with respect to others. Overall, the best performing functionals turn out to be hm‐GGAs TPSSh, TPSS1KCIS, M05, tau‐HCTHhyb, and h‐GGA B3LYP. Hopefully, the results of this investigation might provide the useful guidance to propose a new exchange‐correlation functional for calculating the optical properties of biomolecular materials. © 2013 Wiley Periodicals, Inc.     

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.