TD-CI simulation of the electronic optical response of molecules in intense fields II: comparison of DFT functionals and EOM-CCSD

Time-dependent configuration interaction (TD-CI) simulations can be used to simulate molecules in intense laser fields. TD-CI calculations use the excitation energies and transition dipoles calculated in the absence of a field. The EOM-CCSD method provides a good estimate of the field-free excited states but is rather expensive. Linear-response time-dependent density functional theory (TD-DFT) is an inexpensive alternative for computing the field-free excitation energies and transition dipoles needed for TD-CI simulations. Linear-response TD-DFT calculations were carried out with standard functionals (B3LYP, BH&HLYP, HSE2PBE (HSE03), BLYP, PBE, PW91, and TPSS) and long-range corrected functionals (LC-ωPBE, ωB97XD, CAM-B3LYP, LC-BLYP, LC-PBE, LC-PW91, and LC-TPSS). These calculations used the 6-31G(d,p) basis set augmented with three sets of diffuse sp functions on each heavy atom. Butadiene was employed as a test case, and 500 excited states were calculated with each functional. Standard functionals yield average excitation energies that are significantly lower than the EOM-CC, while long-range corrected functionals tend to produce average excitation energies slightly higher. Long-range corrected functionals also yield transition dipoles that are somewhat larger than EOM-CC on average. The TD-CI simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. The nonlinear response as indicated by the residual populations of the excited states after the pulse is far too large with standard functionals, primarily because the excitation energies are too low. The LC-ωPBE, LC-PBE, LC-PW91, and LC-TPSS long-range corrected functionals produce responses comparable to EOM-CC.     

Performance of recently developed kinetic energy density functionals for the calculation of hydrogen binding strengths and hydrogen-bonded structures

 The accuracy of predicted hydrogen binding energies and equilibrium structures for a benchmark set of molecules is compared for some recently developed density functionals, Becke's three parameter hybrid method with the Lee, Yang, and Parr (LYP) correlation functional (B3LYP), Becke's half and half functional combined with the LYP correlation functional (BHLYP), Perdew, Burke and Ernzerhof functional (PBE), Van Voorhis, Scuseria exchange correlation functional (VSXC), the hybrid Perdew, Burke and Ernzerhof functional (PBE1PBE), and meta-generalized gradient approximation (meta-GGA). Overall, the hybrid functionals which contain a portion of Hartree–Fock exchange (B3LYP, BHLYP, and PBE1PBE) yield the most accurate results. The kinetic-energy-density-dependent functionals, VSXC and meta-GGA, are significantly less accurate. Received: 10 December 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

Performance of conventional and range-separated hybrid density functionals in calculations of electronic circular dichroism spectra of transition metal complexes

A number of density functionals, including 'pure' (nonhybrid) functionals, global hybrids, and range-separated hybrids, were used to calculate the electronic circular dichroism (CD) spectra of 10 tris-bidentate transition metal complexes. The results are compared to one another and to experimental CD spectra, in an effort to illustrate the shortcomings of particular approximations in time-dependent density functional theory (TDDFT). The use of an origin invariant formalism to calculate magnetic transition dipole moments with the help of gauge-including atomic orbitals (GIAOs) is also investigated. With valence basis sets of moderate flexibility, good agreement between GIAO results and rotatory strengths calculated from the dipole-velocity representation is obtained for selected test cases. Empirically broadened vertical CD spectra calculated with the global hybrid functionals B3LYP and PBE0 are found to agree overall the best with experimental CD spectra.     

DFT and TDDFT study related to electron transfer in nonbonded porphine...C60 complexes

Spectroscopic properties of a ground state nonbonded porphine-buckminsterfullerene (H2P...C60) complex are studied in several different relative orientations of C60 with respect to the porphine plane by using the density functional (DFT) and time-dependent density functional (TDDFT) theories. The geometries and electronic structures of the ground states are optimized with the B3LYP and PBE functionals and a SVP basis set. Excitation energies and oscillator strengths are obtained from the TDDFT calculations. The relative orientation of C60 is found to affect the equilibrium distance between H2P and C60 especially in the case of the PBE functional. The excitation energies of different H2P...C60 complexes are found to be practically the same for the same excitations when the B3LYP functional is used but to differ notably when PBE is used in calculations. Existence of the states related to a photoinduced electron transfer within a porphyrin-fullerene dyad is also studied. All calculations predict a formation of an excited charge-transfer complex state, a locally excited donor (porphine) state, as well as a locally excited acceptor (fullerene) state in the investigated H2P...C60 complexes.     

一些密度泛函方法预测电子亲和势

选取了杂化泛函B3LYP, B3PW91, O3LYP, PBE0, 以及与之相对应的GGA泛函BLYP, BPW91, OLYP和PBE, 还选取了能更好地兼顾强相互作用和弱相互作用的X3LYP泛函和在预测NMR的化学位移有较好表现的OPBE泛函, 以及两种meta-GGA泛函VSXC和TPSS, 共12种泛函, 详细地考察了这些泛函在预测EA方面的准确性.     

A Density Functional Theory Study of Optical Rotation in Some Aziridine and Oxirane Derivatives

We present time-dependent density functional theory (TDDFT) calculations of the electronic optical rotation (ORP) for seven oxirane and two aziridine derivatives in the gas phase and in solution and compare the results with the available experimental values. For seven of the studied molecules it is the first time that their optical rotation was studied theoretically and we have therefore investigated the influence of several settings in the TDDFT calculations on the results. This includes the choice of the one-electron basis set, the exchange-correlation functional or the particular polarizable continuum model (PCM). We can confirm that polarized quadruple zeta basis sets augmented with diffuse functions are necessary for converged results and find that the aug-pc-3 basis set is a viable alternative to the frequently employed aug-cc-pVQZ basis set. Based on our study, we cannot recommend the generalized gradient functional KT3 for calculations of the ORP in these compounds, whereas the hybrid functional PBE0 gives results quite similar to the long-range correct CAM−B3LYP functional. Finally, we observe large differences in the solvent effects predicted by the integral equation formalism of PCM and the SMD variant of PCM. For the majority of solute/solvent combinations in this study, we find that the SMD model in combination with the PBE0 functional and the aug-pc-3 basis set gives the best agreement with the experimental values.     

General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: theory, implementation, and benchmarks

We report an implementation of the spin-flip (SF) variant of time-dependent density functional theory (TD-DFT) within the Tamm-Dancoff approximation and non-collinear (NC) formalism for local, generalized gradient approximation, hybrid, and range-separated functionals. The performance of different functionals is evaluated by extensive benchmark calculations of energy gaps in a variety of diradicals and open-shell atoms. The benchmark set consists of 41 energy gaps. A consistently good performance is observed for the Perdew-Burke-Ernzerhof (PBE) family, in particular PBE0 and PBE50, which yield mean average deviations of 0.126 and 0.090 eV, respectively. In most cases, the performance of original (collinear) SF-TDDFT with 50-50 functional is also satisfactory (as compared to non-collinear variants), except for the same-center diradicals where both collinear and non-collinear SF variants that use LYP or B97 exhibit large errors. The accuracy of NC-SF-TDDFT and collinear SF-TDDFT with 50-50 and BHHLYP is very similar. Using PBE50 within collinear formalism does not improve the accuracy.     

Is the spin‐orbit coupling important in the prediction of the 51V hyperfine coupling constants of VIVO2+ species? ORCA versus Gaussian performance and biological applications

Density functional theory calculations of the (51)V hyperfine coupling (HFC) tensor A, have been completed for eighteen V(IV)O(2+) complexes with different donor set, electric charge and coordination geometry. A tensor was calculated with ORCA software with several functionals and basis sets taking into account the spin-orbit coupling contribution. The results were compared with those obtained with Gaussian 03 software using the half-and-half functional BHandHLYP and 6-311g(d,p) basis set. The order of accuracy of the functionals in the prediction of A(iso), A(z) and dipolar term A(z,anis) is BHandHLYP > PBE0 > B3PW > TPSSh > B3LYP > BP86 > VWN5 (for A(iso)), BHandHLYP > PBE0 > B3PW > TPSSh > B3LYP > BP86 > VWN5 (for A(z)), B3LYP > PBE0 ～ B3PW ～ BHandHLYP > TPSSh > BP86 ～ VWN5 (for A(z,anis)). The good agreement in the prediction of A(z) with BHandHLYP is due to a compensation between the overestimation of A(iso) and underestimation of A(z,anis) (A(z) = A(iso) + A(z,anis)), whereas among the hybrid functionals PBE0 performs better than the other ones. BHandHLYP functional and Gaussian software are recommended when the V(IV)O(2+) species contains only V-O and/or V-N bonds, whereas PBE0 functional and ORCA software for V(IV)O(2+) complexes with one or more V-S bonds. Finally, the application of these methods to the coordination environment of V(IV)O(2+) ion in V-proteins, like vanadyl-substituted insulin, carbonic anhydrase, collagen and S-adenosylmethionine synthetase, was discussed.     

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.     

Assessing alkyl-, silyl-, and halo-substituent effects on the electron affinities of silyl radicals

Neutral anion energy differences for a large class of alpha-substituted silyl radicals have been computed to determine the effect of alkyl, silyl, and halo substituents on their electron affinities. In particular, we report theoretical predictions of the adiabatic electron affinities (AEAs), vertical electron affinities (VEAs), and vertical detachment energies (VDEs) for a series of methyl-, silyl-, and halo-substituted silyl radical compounds. This work utilizes the carefully calibrated DZP++ basis set, in conjunction with the pure BLYP and OLYP functionals, as well as with the hybrid B3LYP, BHLYP, PBE1PBE, MPW1K, and O3LYP functionals. Bromine has the largest effect in stabilizing the anions, and the BLYP/DZP++ AEA for SiBr(3) is 3.29 eV. The other predicted electron affinities are for SiH(3) (1.37 eV), SiH(2)CH(3) (1.09 eV), SiH(2)F (1.54 eV), SiH(2)Cl (1.94 eV), SiH(2)Br (2.05 eV), SiH(2)(SiH(3)) (1.77 eV), SiH(CH(3))(2) (0.92 eV), SiHF(2) (1.86 eV), SiHCl(2) (2.53 eV), SiHBr(2) (2.67 eV), Si(CH(3))(3) (0.86 eV), SiF(3) (2.66 eV), SiCl(3) (3.21 eV), Si(SiH(3))(3) (2.25 eV), and SiFClBr (3.13 eV). For the five silyl radicals where experimental data are available, the BLYP functional gives the most accurate determination of AEAs; the average absolute error is 0.04(1) eV, whereas the corresponding errors for the O3LYP, MPW1K, PBE1PBE, B3LYP, OLYP, and BHLYP functionals are 0.05(8), 0.06(0), 0.06(3), 0.08(5), 0.11(5), and 0.15(3) eV, respectively.     

Combined quantum mechanical/molecular mechanical study on the pentacoordinated ferric and ferrous cytochrome P450cam complexes

The pentacoordinated ferric and ferrous cytochrome P450(cam) complexes have been investigated by combined quantum mechanical/molecular mechanical (QM/MM) calculations in the presence of a protein/solvent environment and by QM calculations on the isolated QM regions with use of density functional theory. The B3LYP functional has been found more reliable than the BLYP and BHLYP functionals for estimating the relative state energies. The B3LYP/CHARMM calculations with an all-electron basis set for iron give high-spin ground states for the title complexes, in agreement with experiment. The comparison of the B3LYP/CHARMM results of the entire protein system with the B3LYP calculations on the naked QM regions shows that the amount of stabilization by the protein environment is largest for the intermediate-spin states, followed by the high-spin states of the complexes. The calculation of M?ssbauer parameters in the presence of the enzyme environment confirms the double occupation of the d(xz) orbital in the quintet spin state of the ferrous complex, consistent with the computed QM/MM energies in the enzyme environment, while the d(x)2(-)(y)2 orbital is doubly occupied in the gas-phase quintet state.     

Computational study of static first hyperpolarizability of donor-acceptor substituted (E)-benzaldehyde phenylhydrazone

Various hybrid functionals (B3LYP, B97-2, PBE0, BMK, BH&HLYP, CAM-B3LYP, and LC-ωPBE) implemented in density functional theory were applied to give estimate of static first hyperpolarizabilty (β(0)) of (E)-benzaldehyde phenylhydrazone designated as (E)-BPH. Against those of MP2 computations as a function of the underlying density functional, good agreement was obtained with the BH&HLYP and CAM-B3LYP functionals. The LC-ωPBE functional and the B3LYP, PBE0, B97-2, and BMK functionals underestimated and overestimated β(0), respectively. The basis set effect on the calculated β(0) was also investigated. It turned out that the 6-311+G(2d,p) basis set provided excellent converged value of β(0). On the basis of the calculated results, we investigated the substituent effect on β(0) of donor-acceptor (D-A) substituted (E)-BPH systematically by using the BH&HLYP and CAM-B3LYP computations with the 6-311+G(2d,p) basis set. We proposed a Zwitterion structure to explain the calculated trend in the substituent effect and the enhanced hyperpolarizability of type II compounds (A-(E)-BPH-D) than type I compounds (D-(E)-BPH-A). Natural bonding orbital analysis carried out at BH&HLYP/6-311+G(2d,p)//B3LYP/6-31G(2df,p) level of theory substantiated the claim.     

Electronic spectroscopy of UO2(2+), NUO(+) and NUN: an evaluation of time-dependent density functional theory for actinides

The performance of the time-dependent density functional theory (TDDFT) approach has been evaluated for the electronic spectrum of the UO(2)(2+), NUO(+) and NUN molecules. Different exchange-correlation functionals (LDA, PBE, BLYP, B3LYP, PBE0, M06, M06-L, M06-2X, CAM-B3LYP) and the SAOP model potential have been investigated, as has the relative importance of the adiabatic local density approximation (ALDA) to the exchange-correlation kernel. The vertical excitation energies have been compared with reference data obtained using accurate wave-function theory (WFT) methods.     

Density functional study of AuXq (X = O, S, Se, Te, q = +1, 0, -1) molecules

Bond distances, vibrational frequencies, electron affinity, ionization potential, and dissociation energies of the title molecules were studied by use of density functional methods B3LYP, B3P86, B3PW91, BHLYP, BLYP, BP86, mPW1PW91, and PBE1PBE. It was found that the ground electronic state is doublet for neutral species, singlet for the anion, and triplet for the cation, in agreement with experiments and previous theoretical studies. The calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy. The predicted bond distances and vibrational frequencies are in agreement with experiments and previous theoretical results. BP86 and BLYP have relatively good performance in reproducing the experimental results, while BHLYP is the worst functional method compared with the other density functional methods used for the title molecules.     

Effect of substituents on the absorption properties of three pyridylindolizine derivatives: A DFT and TDDFT study

Ground state properties and the UV–Vis absorption spectra of three recently synthesized pyridylindolizine derivatives have been studied by using density functional theory (DFT) and its time-dependent counterpart TDDFT. Performances of the two widely used hybrid functionals, B3LYP and PBE0, and of four different basis sets have been compared. The two functionals yield absorption spectra which have very similar shapes and characteristics but the excitations calculated with PBE0 are obtained at slightly shorter wavelengths. Basis sets affect the appearances of the calculated absorption spectra only little. Independent of the solvent polarity, simulation of the solvent effects by COSMO induces only slight changes into the ground state properties compared to those calculated in the gas-phase and into the absorption spectra.     

Theoretical Study on Resonance Raman Spectra of Tetraoxaporphyrin Dication by TDDFT Calculation

The B state excited resonance Raman scattering of tetraoxaporphyrin dication (TOP²⁺) was theoretically studied with DFT/TDDFT calculations and the sum-over-states approach of polarizability including both the A and B terms contributions. The resonance Raman spectra calculated with PBE1PBE, B3LYP, Cam-B3LYP, and B3LYP-D3 functionals are similar to each other in general, with PBE1PBE and B3LYP being better in reproducing resonance Raman intensities in comparison with the experiment. The calculated relative intensities of the totally symmetric modes are excellently consistent with the experiment. The TDDFT calculations manifested a considerable deformation of the B state along theυ2,υ6, υ7, and υ8 modes, which is responsible for the strong resonance Raman intensities of these modes. The resonance Raman intensities of non-totally symmetric modes were calculated to be weaker than the totally symmetric modes by one or two order of magnitude, whichqualitatively agrees with the experiment. However, the resonance Raman intensity of the υ10 mode (C_βC_β stretch, B_1g symmetry) predicted by TDDFT calculations is unexpectedly small whereas that of the υ11 mode (symmetric C_αC_m stretch, B_1g symmetry) is too large, which is assumed to be caused by the Jahn-Teller instability for the B state of TOP²⁺.     

Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite Mg2SiO4

The performance of six different density functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in describing the infrared spectrum of forsterite, a crystalline periodic system with orthorhombic unit cell (28 atoms in the primitive cell, Pbmn space group), is investigated by using the periodic ab initio CRYSTAL09 code and an all‐electron Gaussian‐type basis set. The transverse optical (TO) branches of the 35 IR active modes are evaluated at the equilibrium geometry together with the oscillator strengths and the high‐frequency dielectric tensor ?_∞. These quantities are essential to compute the dielectric function ?(ν), and then the reflectance spectrum R(ν), which is compared with experiment. It turns out that hybrid functionals perform better than LDA and GGA, in general; that B3LYP overperforms WC1LYP and, in turn, PBE0; that PBESOL is better than PBE; that LDA is the worst performing functional among the six under study. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Systematic investigation on the geometric dependence of the calculated nuclear magnetic shielding constants

We perform a systematic examination on the dependence of the calculated nuclear magnetic shielding constants on the chosen geometry for a selective set of density functional methods of B3LYP, PBE0, and OPBE. We find that the OPBE exchange-correlation functional performs remarkably well when either the optimized geometries or the experimental geometries are used. The popular B3LYP and PBE0 functionals have a clear tendency of deshielding, giving shieldings that are usually too low and shifts that are usually too high, at the experimental geometries. Combined with the Hartree-Fock geometries, however, much improved magnetic constants are obtained for B3LYP and PBE0, due to the compensation effect from the systematic underestimation of bond lengths by the Hartree-Fock method.