Long-range Correction Scheme Research Articles

Exploring the Limits of the XYG3-Type Doubly Hybrid Approximations for the Main-Group Chemistry: The xDH@B3LYP Model.

Despite being the most accurate class of density functional approximations for the main-group chemistry, doubly hybrid approximations (DHAs) are generally considered to be incomplete in describing the medium- to long-range dispersive interactions. The existing DHAs are often supplemented with empirical long-range dispersion corrections. By using the extensive and chemically diverse GMTKN55 database, we explore the limits of the XYG3-type DHAs using the B3LYP reference orbitals, namely, xDH@B3LYP, with a gradually relaxed constraint on the mixing parameters of DHAs. Our results demonstrate that the xDH@B3LYP model can provide a balanced description of both covalent and noncovalent interactions with the accuracy and robustness comparable to or even better than the very expensive composite methods in wave function theory. Such an accuracy can be achieved without resorting to the use of any long-range correction scheme, shedding new light on the development of DHAs.

Comprehensive evaluation of the effect of various exchange correlation functionals on the optical properties of oligothiophenes

Time-dependent density functional theory (TD-DFT) calculations are performed to systematically investigate the absorption and emission properties of α-oligothiophenes taking into account of various functionals, basis sets and bulk solvent effects. The effects of different functionals on the optical properties are investigated employing global and meta hybrid functionals B3LYP, M06 and also with range separated hybrid functionals like ωB97XD and CAM-B3LYP. The results are further assessed to test their validity against the available experimental data. The bulk solvent effects are introduced by the linear response (LR) and the state specific (SS) models in the framework of the polarizable continuum model (PCM). Pople type of basis sets has been employed and the role of inclusion of polarized and diffused functions in the basis sets in determining the optical properties is investigated. The long-range correction scheme in CAM-B3LYP is found to produce accurate results for the excitation energies very much in agreement with the experimental data.

ωB2PLYP and ωB2GPPLYP: The First Two Double-Hybrid Density Functionals with Long-Range Correction Optimized for Excitation Energies.

Double-hybrid density functionals are currently the most accurate density functionals for ground-state properties and electronic excitations. Nevertheless, the lack of a long-range correction scheme makes them unreliable when it comes to long-range excitations. For this reason, we propose the first two time-dependent double-hybrid functionals with correct asymptotic long-range behavior named ωB2PLYP and ωB2GPPLYP. Herein, we demonstrate their excellent performance and show that they are the most accurate and robust time-dependent density functional theory methods for electronic excitation energies. They provide a balanced description of local-valence, Rydberg, and charge-transfer states. They are also able to tackle the difficult first two transitions in polycyclic aromatic hydrocarbons and show very promising results in a preliminary study on transition-metal compounds, exemplified for titanium dioxide clusters. This work shows that double hybrids can be systematically improved also for excitation energies, and further work in this field is warranted.

Long Range Corrections for Inhomogeneous Simulations of Mie n-m Potential.

The long-range correction scheme for dispersion interactions in inhomogeneous simulations is generalized to Mie n-m potential. The influence of the cutoff distance and lateral dimensions of the simulation box are studied for 8-6, 12-6, and 20-6 Mie fluids at two different temperatures (close and far from the critical point). For sufficiently large systems (2400 particles, Rc = 3.5σ) equilibrium properties are simulated over the whole vapor-liquid coexistence using the inhomogeneous Monte Carlo simulations, and the results are compared with the Gibbs Ensemble technique and with the square gradient theory combined with the SAFT Mie equation of state.

Assessment of various density functionals for intermolecular N → Sn interactions: The test case of trimethyltin cyanide dimer

An assessment of the performance of various density functionals for describing structural and energetic properties of a model system exhibiting the intermolecular N→Sn interaction has been presented. A set of 20 density functionals belonging to several density functional theory (DFT) classes was used to predict the geometry and the interaction energy in the trimethyltin cyanide dimer, (Me3SnCN)2. The assessment of the density functionals was carried out by comparing the DFT results with the corresponding wave function theory (WFT) results. The combinations of the 20 density functionals with a few basis sets, as well as the dispersion-corrected variants of selected density functionals were included in the assessment. The representatives of modern DFT classess, such as those utilizing the long-range correction scheme and the range-separated hybrids, reproduce the reference results with great accuracy. A comparison of the DFT results for the dimer with the experimental data for crystalline trimethyltin cyanide was also made to evaluate the usefulness of the density functionals working with such a model system for reproducing the crystal structure of Me3SnCN and, generally, for the investigations of N→Sn contacts in crystals. A survey of the Cambridge Structural Database (CSD) was conducted to provide additional structural information for such contacts.

Electronic excitations from a linear-response range-separated hybrid scheme

We study linear-response time-dependent density-functional theory (DFT) based on the single-determinant range-separated hybrid (RSH) scheme, i.e. combining a long-range Hartree–Fock exchange kernel with a short-range DFT exchange-correlation kernel, for calculating electronic excitation energies of molecular systems. It is an alternative to the more common long-range correction (LC) scheme which combines a long-range Hartree–Fock exchange kernel with a short-range DFT exchange kernel and a standard full-range DFT correlation kernel. We discuss the local-density approximation (LDA) to the short-range exchange and correlation kernels, and assess the performance of the linear-response RSH scheme for singlet → singlet and singlet → triplet valence and Rydberg excitations in the N2, CO, H2CO, C2H4 and C6H6 molecules, and for the first charge-transfer excitation in the C2H4–C2F4 dimer. For these systems, the presence of long-range LDA correlation in the ground-state calculation and in the linear-response kernel has only a small impact on the excitation energies and oscillator strengths, so that the RSH method gives results very similar to the ones given by the LC scheme. Like in the LC scheme, the introduction of long-range HF exchange in the present method corrects the underestimation of charge-transfer and high-lying Rydberg excitation energies obtained with standard (semi)local density-functional approximations, but also leads to underestimated excitation energies to low-lying spin-triplet valence states. This latter problem is largely cured by the Tamm–Dancoff approximation which leads to a relatively uniform accuracy for all excitation energies. This work thus suggests that the present linear-response RSH scheme is a reasonable starting approximation for describing electronic excitation energies, even before adding an explicit treatment of long-range correlation.

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.

Toward spectroscopic studies of biologically relevant systems: Vibrational spectrum of adenine as a test case for performances of long-range/dispersion corrected density functionals

Several recently introduced models rooted into the density functional theory and designed for the study of weakly bound molecular systems, with particular reference to the role of dispersion interactions, have been tested for their performances in prediction of vibrational properties for adenine molecule. Results obtained by semi-empirical correction for dispersion (DFT-D), semi-local density-functionals (M05-2X, M06-2X), and long-range correction scheme (LC- ωPBE, CAM-B3LYP) have been compared to the PT2 anharmonic frequencies computed by B3LYP functional and to the experimental results. From the tested computational models only the B3LYP-D/DM scheme provided quantitative agreement with the reference data and at the same time correctly described binding of adenine dimer.

Core-excitation energy calculations with a long-range corrected hybrid exchange-correlation functional including a short-range Gaussian attenuation (LCgau-BOP)

We report the calculations of core-excitation energies of first-row atoms using the time-dependent density functional theory (DFT) and the long-range correction (LC) scheme for exchange-correlation functionals, including LC-BOP, Coulomb-attenuated method BLYP, and our recently developed LCgau-BOP method, which includes a flexible portion of short-range Hartree-Fock (HF) exchange through the inclusion of a Gaussian function in the LC scheme. We show that the LC scheme completely fails to improve the poor accuracy of conventional generalized gradient approximation functionals, while the LCgau scheme gives an accuracy which is an order of magnitude better than BLYP and significantly better than B3LYP. A reoptimization of the two parameters controlling the inclusion of short-range HF exchange in the LCgau method enables the errors to be reduced to the order of 0.1 eV which is competitive with the best DFT methods we are aware of. This reparametrization does not affect the LC scheme and therefore maintains the high accuracy of predicted reaction barrier heights. Moreover, while there is some loss in accuracy in thermochemical predictions compared to the previously optimized LCgau-BOP, rms errors in the atomization energies over the G2 test set are found to be comparable to B3LYP. Finally, we attempt to rationalize the success of the LC and LCgau schemes in terms of the well-known self-interaction error (SIE) of conventional functionals. To estimate the role of the SIE, we examine the total energy calculations for systems with a fractional number of electrons, not only in the highest occupied molecular orbital but also in the 1s-characterized core orbital. Our conclusion is that the inclusion of short-range HF exchange in LC-type functionals can significantly alleviate the problems of the SIE in the core region. In particular, we confirm that the absence of the SIE diagnostics in the core orbital energies correlates with the accurate prediction of core-excitation energies using the newly optimized LCgau approach.

The role of dispersion correction to DFT for modelling weakly bound molecular complexes in the ground and excited electronic states

Several computational methodologies rooted into density-functional theory (DFT) or Møller–Plesset second order perturbation theory (MP2) have been applied to study the anisole–ammonia and anisole–water 1:1 molecular complexes in the ground and first excited electronic states, with special reference to the role of dispersion interactions. Semi-empirical correction to account for dispersion (DFT-D), a recently parameterized semi-local density functional (M05-2X), and long-range correction scheme (LC-ωPBE and LC-PBE-TPSS) have been tested. The results are compared with Coupled-Cluster calculations and with state-of-the-art experimental spectroscopic data. Regarding the ground electronic state, the best description of structures and energies has been achieved by MP2 computations, including a counterpoise correction for the basis-set superposition error. Besides, the density functionals corrected for dispersion have provided qualitative and in some cases also quantitative agreement with the experimental and reference data at a much lower computational cost.

An improved long-range corrected hybrid exchange-correlation functional including a short-range Gaussian attenuation (LCgau-BOP)

A new hybrid exchange-correlation functional is presented based on the long-range correction (LC) scheme [H. Iikura et al., J. Chem. Phys. 115, 3540 (2001); Tawada et al., J. Chem. Phys. 120, 8425 (2004)], named LCgau-BOP. The key feature is the use of a two-parameter Gaussian correction to the Coulomb attenuation, which allows a more flexible description of exact exchange at short-range interelectronic separations. The new partitioning preserves 100% exact exchange in the long range, which is known to be important for the success of the LC scheme, with an asymptotic attenuation described by a standard error function with a parameter of 0.42. The LCgau partitioning was optimized for the reproduction of atomization energies over the G2 set and reaction barrier heights over Database/3, and produced results which are superior to B3LYP, CAM-BLYP, and the best LC functionals we are aware of. The results highlight the importance of including a substantial portion of exact exchange in the short range. Using the same parameters, the new functional was tested for the reproduction of geometries, as well as valence, Rydberg and charge-transfer excitations which are known challenges for conventional density functional theory. Our conclusion is that LCgau-BOP can provide a consistently more accurate description of thermochemistries, chemical reactions, and excitation energies than other existing long-range corrected functionals.

Long-range corrected density functional study on weakly bound systems: Balanced descriptions of various types of molecular interactions

The long-range correction scheme for the density functional theory, combined with a van der Waals functional, is examined for its applicability to a wide variety of weakly bonded complexes including dispersion, dipole-induced dipole, dipole-dipole, and hydrogen-bonded complexes. The present method is able to describe geometries and binding energies of all these complexes accurately. Explicit inclusion of the long-range exchange and dispersion interactions is found to be important for the balanced description of various kinds of weak interactions. The present method is a promising alternative for high-level ab initio methods in calculations of large and complex systems, because it gives equally correct descriptions for various types of molecular interactions with much less computational cost.

Long-range corrected density functional calculations of chemical reactions: Redetermination of parameter

Chemical reaction calculations were carried out using the long-range correction (LC) scheme, which improves long-range exchange effects in density functional theory (DFT) [J. Chem. Phys. 115, 3540 (2001); 120, 8425 (2004)]. A new determination of the LC scheme parameter mu was made by a root mean square fit of the percent error in calculated atomization energies. As a result, the parameter mu was optimized as 0.47, which is higher than the previous one (mu=0.33). Using this new parameter mu, LC-DFT was firstly applied to geometry optimizations of the G2 benchmark set molecules. Consequently, this new LC-DFT gave more accurate bond lengths and bond angles than previous LC-DFT and hybrid B3LYP results. Following this result, the authors calculated reaction barrier height energies of benchmark reaction sets, which have been underestimated in conventional DFT calculations. Calculated results showed that LC-DFT provided much more accurate barrier height energies with errors less than half those of previous LC-DFT and B3LYP studies. To test the general validity of the new LC-DFT, the authors finally calculated reaction enthalpies. As a result, they found that the LC scheme using the new mu clearly improved the accuracy of calculated enthalpies. The authors therefore conclude that the insufficient inclusion of long-range exchange effects is responsible for the underestimation of reaction barriers in DFT calculations and that LC-DFT using the new parameter is a powerful tool for theoretically investigating chemical reactions.

A density-functional study on π-aromatic interaction: Benzene dimer and naphthalene dimer

The long-range correction (LC) scheme of density-functional theory (DFT) was applied to the calculation of the pi-aromatic interaction of the benzene dimer and naphthalene dimer. In previous calculations, it was confirmed that the LC scheme [Iikura et al., J. Chem. Phys. 115, 3540 (2001)] gives very accurate potential- energy surfaces (PESs) of small van der Waals (vdW) complexes by combining with the Anderson-Langreth-Lundqvist (ALL) vdW correlation functional [Andersson et al., Phys. Rev. Lett. 76, 102 (1996)] (LC-DFT + ALL). In this study, LC-DFT+ALL method was examined by calculating a wide range of PES of the benzene dimer including parallel, T-shaped, and parallel-displaced configurations. As a result, we succeeded in reproducing very accurate PES within the energy deviance of less than 1 kcalmol in comparison with the results of high-level ab initio molecular-orbital methods at all reference points on the PES. It was also found that LC-DFT + ALL gave accurate results independent of exchange-correlation functional used, in contrast with the strong functional dependencies of conventional pure functionals. This indicates that both exchange repulsion and van der Waals attractive interactions should be correctly incorporated in conventional pure functionals in order to calculate accurate pi-aromatic interactions. We also found that LC-DFT + ALL method has a low basis-set dependency in the calculations of pi-aromatic interactions. The present scheme was also successfully applied to the pi,[ellipsis (horizontal)],pi stacking interactions of naphthalene dimer. This may suggest that LC-DFT + ALL method would be a powerful tool in the calculations of large molecules such as biomolecules.

Nonlinear optical property calculations by the long-range-corrected coupled-perturbed Kohn–Sham method

The long-range correction (LC) scheme for the exchange functional of density-functional theory (DFT) was combined with the coupled-perturbed Kohn-Sham (CPKS) method to calculate nonlinear optical response properties. By using this LC-CPKS method, we calculated the hyperpolarizabilities of typical molecules and the dipole moments, polarizabilities, and hyperpolarizabilities of push-pull pi-conjugated systems: p-nitroaniline, 4-amino-4'-nitrostilbene, and alpha,omega-nitroaminopolyenes. It was found that the LC scheme clearly improved the calculation of these optical properties for all of these systems, which have been significantly overestimated by conventional DFTs. We therefore concluded that the long-range exchange interaction played an important role in calculating the optical properties using the DFT formalism.

A long-range correction scheme for generalized-gradient-approximation exchange functionals

We propose a new long-range correction scheme that combines generalized-gradient-approximation (GGA) exchange functionals in density-functional theory (DFT) with the ab initio Hartree–Fock exchange integral by using the standard error function. To develop this scheme, we suggest a new technique that constructs an approximate first-order density matrix that corresponds to a GGA exchange functional. The calculated results of the long-range correction scheme are found to support a previous argument that the lack of the long-range interactions in conventional exchange functionals may be responsible for the underestimation of 4s−3d interconfigurational energies of the first-row transition metals and for the overestimation of the longitudinal polarizabilities of π-conjugated polyenes in DFT calculations.