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.     

The role of range-separated Hartree-Fock exchange in the calculation of magnetic exchange couplings in transition metal complexes

We assess the dependence of magnetic exchange couplings on the variation of Hartree-Fock exchange (HFX) admixture in global hybrid functionals and the range-separation parameter ω in range-separated hybrid functionals in a set of 12 spin-1/2 binuclear transition metal complexes. The global hybrid PBEh (hybrid Perdew-Burke-Ernzerhof) and range-separated hybrids HSE (Heyd-Scuseria-Ernzerhof) and LC-ωPBE (long-range corrected hybrid PBE) are employed for this assessment, and exchange couplings are calculated from energy differences within the framework of the spin-projected approach. It is found that these functionals perform optimally for magnetic exchange couplings with 35% HFX admixture for PBEh, ω = 0.50 a.u.(-1) for LC-ωPBE, and ω at or near 0.0 a.u.(-1) for HSE (which corresponds to PBEh). We find that in their standard respective forms, LC-ωPBE slightly outperforms PBEh, while PBEh with 35% HFX yields exchange couplings closer to experiment than those of LC-ωPBE with ω = 0.50 a.u.(-1). Additionally, we show that the profile of exchange couplings with respect to ω in HSE is appreciably flat from 0 to 0.2 a.u.(-1). This combined with the fact that HSE is computationally more tractable than global hybrids makes HSE an attractive alternative for the evaluation of exchange couplings in extended systems. These results are rationalized with respect to how varying the parameters within these functionals affects the delocalization of the magnetic orbitals, and conclusions are made regarding the relative importance of range separation versus global mixing of HFX for the calculation of exchange couplings.     

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.     

Characterizing the potential energy surface of the water dimer with DFT: failures of some popular functionals for hydrogen bonding

Ten stationary points on the water dimer potential energy surface have been examined with ten density functional methods (X3LYP, B3LYP, B971, B98, MPWLYP, PBE1PBE, PBE, MPW1K, B3P86, and BHandHLYP). Geometry optimizations and vibrational frequency calculations were carried out with the TZ2P(f,d)+dif basis set. All ten of the density functionals correctly describe the relative energies of the ten stationary points. However, correctly describing the curvature of the potential energy surface is far more difficult. Only one functional (BHandHLYP) reproduces the number of imaginary frequencies from CCSD(T) calculations. The other nine density functionals fail to correctly characterize the nature of at least one of the ten (H(2)O)(2) stationary points studied here.     

Density functional analysis of geometries and electronic structures of gold-phosphine clusters. The case of Au4(PR3)42+ and A(u4μ2-I)2(PR3)4

Geometries, ligand binding energies, electronic structure, and excitation spectra are determined for Au(4)(PR(3))(4)(2+) and Au(4)(μ(2)-I)(2)(PR(3))(4) clusters (R = PH(3), PMe(3), and PPh(3)). Density functionals including SVWN5, Xα, OPBE, LC-ωPBE, TPSS, PBE0, CAM-B3LYP, and SAOP are employed with basis sets ranging from LANL2DZ to SDD to TZVP. Metal--metal and metal--ligand bond distances are calculated and compared with experiment. The effect of changing the phosphine ligands is assessed for geometries and excitation spectra. Standard DFT and hybrid ONIOM calculations are employed for geometry optimizations with PPh(3) groups. The electronic structure of the gold--phosphine clusters examined in this work is analyzed in terms of cluster ("superatom") orbitals and d-band orbitals. Transitions out of the d band are significant in the excitation spectra. The use of different basis sets and DFT functionals leads to noticeable variations in the relative intensities of strong transitions, although the overall spectral profile remains qualitatively unchanged. The replacement of PMe(3) with PPh(3) changes the nature of the electronic transitions in the cluster due to low-lying π*-orbitals. To reproduce the experimental geometries of clusters with PPh(3) ligands, computationally less expensive PH(3) or PMe(3) ligands are sufficient for geometry optimizations. However, to predict cluster excitation spectra, the full PPh(3) ligand must be considered.     

A DFT conformational analysis and VCD study on methyl tetrahydrofuran-2-carboxylate

DFT calculations were performed on (S)-methyl tetrahydrofuran-2-carboxylate to facilitate the interpretation of IR and VCD spectra. The potential energy surface could not be described unambiguously using the 6-31G* basis set in combination with different density functionals including B1LYP, B3LYP, B3P86, B3PW91, B98, BHandH, BHandHLYP, MPW1PW91 and PBE1PBE. In contrast, a uniform conformational picture could be found using the cc-pVTZ basis set. Using this large basis set and the collection of nine functionals from above, the dipole and rotational strengths were calculated, and compared to experimental values which were extracted from the experimental IR and VCD spectra for (+)-(S)-methyl tetrahydrofuran-2-carboxylate. A detailed analysis on the agreement between experiment and simulated spectra was performed by assigning the experimental bands based on the harmonic fundamentals obtained for all functionals except BHandH, which performs badly over the whole line. Assessing the dipole strengths, all tested functionals perform equally well. For the rotational strengths, differences can be observed: B3LYP, B1LYP and B98 give the highest correlation with experiment, while PBE1PBE gives the lowest correlation. Comparable conclusions are obtained using a neighborhood similarity measure.     

Simulations of photoemission and equilibrium redox processes of ionic liquids: the role of ion pairing and long-range polarization

We have studied oxidation and reduction of ionic liquids using methods of theoretical chemistry. In particular, we have modeled photoelectron spectra of 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([emim][Tf(2)N]) and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([bmim][Tf(2)N]) ionic liquids and their components. We have considered ion pairs in the gas phase and solvated in the water represented by a dielectric continuum. We have also characterized the isolated cation and anion of the ionic liquids. The calculated quantities have been compared with available experiments. The photoelectron spectra were modeled within linearized reflection approximation, using a composite ab initio approach based on combination of the MP2 method for the ground state, the PMP2 method for the first ionized electronic state and the TDDFT method to estimate the higher ionization energies. We have also briefly explored energetics of processes following the vertical electron attachment/detachment. Our calculations were able to reproduce the measured photoelectron spectra. We have shown that the valence photoelectron spectrum results from simultaneous ionization from many molecular orbitals. In the threshold region, the electron is ejected from the anion in the gas phase ion pair while the cationic moiety is ionized when the ion pair is solvated. We have investigated the effect of both short-range and long-range interactions on the ionization characteristics, showing that the long-range polarization of the solvent effectively screens the specific short-range interactions. The large difference between the HOMO-LUMO gap and the electrochemical window has been rationalized in terms of relaxation following the redox processes, i.e. solute and solvent geometric relaxation and reactions, e.g. dimerization of the imidazolium radical formed during the reduction.     

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.     

Ab initio investigation of the n --> pi* transitions in thiocarbonyl dyes

The n --> pi* transitions in more than 100 thiocarbonyl dyes have been calculated with an ab initio procedure relying on the combination of time-dependent density functional theory (TD-DFT) for evaluating excited states and the polarizable continuum model (PCM) for modeling the bulk solvent effects on both the geometrical and electronic structures. Two hybrid functionals (B3LYP and PBE0) and several basis sets, some including f polarization functions, have been used. B3LYP provides the most accurate raw estimates, but once simple linear regression is performed, both functionals give similar results with a small advantage for PBE0. By use of the latter, the mean absolute deviation with respect to experiment is limited to 0.06 eV whereas less than 20% of the estimates differ from absorption data by more than 0.10 eV. To assess the validity limits of our model, compounds containing multiple C=S chromophores have also been considered.     

Ab initio, density functional theory, and continuum solvation model prediction of the product ratio in the S(N)2 reaction of NO2(-) with CH3CH2Cl and CH3CH2Br in DMSO solution

The reaction pathways for the interaction of the nitrite ion with ethyl chloride and ethyl bromide in DMSO solution were investigated at the ab initio level of theory, and the solvent effect was included through the polarizable continuum model. The performance of BLYP, GLYP, XLYP, OLYP, PBE0, B3PW91, B3LYP, and X3LYP density functionals has been tested. For the ethyl bromide case, our best ab initio calculations at the CCSD(T)/aug-cc-pVTZ level predicts product ratio of 73% and 27% for nitroethane and ethyl nitrite, respectively, which can be compared with the experimental values of 67% and 33%. This translates to an error in the relative DeltaG* of only 0.17 kcal mol(-1). No functional is accurate (deviation <0.5 kcal mol(-1)) for predicting relative DeltaG*. The hybrid X3LYP functional presents the best performance with deviation 0.82 kcal mol(-1). The present problem should be included in the test set used for the evaluation of new functionals.     

Ab initio calculation of bowl, cage, and ring isomers of C20 and C20-

High-level ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of C(20) and C(20)(-). The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid density-functional (DF) methods B3LYP, B3PW91, PBE1PBE, and a new hybrid-meta-DF method TPSSKCIS, only the PBE1PBE method (with cc-pVTZ basis set) gives qualitatively correct energy ordering as that predicted from ab initio CCSD(T)/cc-pVDZ [CCSD(T)-coupled-cluster method including singles, doubles, and noniterative perturbative triples; cc-pVDZ-correlation consistent polarized valence double zeta] as well as from MP4(SDQ)/cc-pVTZ [MP4-fourth-order Moller-Plesset; cc-pVTZ-correlation consistent polarized valence triple zeta] calculations. Both CCSD(T) and MP4 calculations indicate that the bowl is most likely the global minimum of neutral C(20) isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/cc-pVTZ calculation, both predicting that the bowl is still the lowest-energy structure of C(20)(-) at T=0 K, followed by the ring and the cage. In contrast, both B3LYP/cc-pVTZ and B3PW91/cc-pVTZ calculations predict that the ring is the lowest-energy structure of C(20)(-). Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among large-sized carbon clusters and other carbon nanostructures (e.g., finite-size carbon nanotubes, nano-onions, or nanohorns). The relative stabilities derived from total energy with Gibbs free-energy corrections demonstrate a changing ordering in which ring becomes more favorable for both C(20) and C(20)(-) at high temperatures. Finally, photoelectron spectra (PES) for the anionic C(20)(-) isomers have been computed. With binding energies up to 7 eV, the simulated PES show ample spectral features to distinguish the three competitive C(20)(-) isomers.     

Doping-enhanced hyperpolarizabilities of silicon clusters: a global ab initio and density functional theory study of Si10 (Li, Na, K)n (n=1, 2) clusters

A global theoretical study of the (hyper)polarizabilities of alkali doped Si(10) is presented and discussed. First, a detailed picture about the low lying isomers of Si(10)Li, Si(10)Na, Si(10)K, Si(10)Li(2), Si(10)Na(2), and Si(10)K(2) has been obtained in a global manner. Then, the microscopic first (hyper)polarizabilities of the most stable configurations have been determined by means of ab initio methods of high predictive capability such as those based on the M?ller-Plesset perturbation and coupled cluster theory, paying extra attention to the (hyper)polarizabilities of the open shell mono-doped systems Si(10)Li, Si(10)Na, Si(10)K, and the influence of spin contamination. These results were used to assess the performance of methods of low computational cost based on density functional theory (DFT) in the reliable computation of these properties in order to proceed with an in-depth study of their evolution as a function of the alkali metal, the cluster composition, and the cluster structure. The most interesting outcomes of the performed (hyper)polarizability study indicate that while alkali doping leaves the per atom polarizability practically unaffected, influences dramatically the hyperpolarizabilities of Si(10). The lowest energy structures of the mono-doped clusters are characterized by significantly enhanced hyperpolarizabilities as compared to the analogue neutral or charged bare silicon clusters Si(10) and Si(11), while, certain patterns governed by the type and the number of the doping agents are followed. The observed hyperpolarizability increase is found to be in close connection with specific cluster to alkali metal charge transfer excited states and to the cluster structures. Moreover, an interesting correlation between the anisotropy of the electron density, and the hyperpolarizabilities of these systems has been observed. Finally, it is important to note that the presented method assessment points out that among the various DFT functionals used in this work, (B3LYP, B3PW91, BhandHLYP, PBE0, CAM-B3LYP, LC-BLYP, LC-BPW91) only B3PW91 and PBE0 out of the seven provided a consistent quantitative performance for both polarizabilities and hyperpolarizabilities with respect to the ab initio methods utilized here. On the other hand, the long range corrected functionals LC-(U)BLYP and LC-(U)BPW91 (μ = 0.47) failed to supply quantitatively accurate hyperpolarizability results in all the studied clusters while the CAM-(U)B3LYP functional performs satisfactory only in the case of the Na and K doped systems.     

Photoelectron spectra of molecules. II. Carboxylic acids and their esters

He I photoelectron (PE) spectra of four carboxylic acids and five esters are measured. Semiempirical and ab initio quantum chemical calculations are used for the interpretation of the spectra. The complex approach which uses empirically established relationships (the dependence of valence electron ionization energies on proton affinities in the gas phase, on the core level ionization energies, and on the structure) was developed. © 1997 John Wiley & Sons, Inc.     

Theoretical investigation of the EPR hyperfine coupling constants in amino derivatives

The HFCCs of the radical cations of a series of amines have been determined at different levels of approximation including the CISD, QCISD, and CCSD ab initio correlated methods and density functional theory approaches employing the B3LYP, PBE0, BHandHLYP, TPSS, and BLYP exchange-correlation functionals. Although quantitative differences with respect to experimental data have been noticed, these are mostly systematic within a given class of N and H atoms. As a consequence, these different levels of theory are reliable in most cases to account for the substituent and structure effects on the HFCCs of amines. Linear regression fits have then been performed to reach quantitative agreement between the theoretical and experimental values. This has finally been substantiated by considering the EPR signal of the recently synthesized radical cations of two derivatives of [10-(4-aminophenyl)-9-anthryl]aniline as well as in confirming a recent assignment of the EPR signal of n-propylamine.     

The excited states of adenine and thymine nucleoside and nucleotide in aqueous solution: a comparative study by time-dependent DFT calculations

The effect substitutions at nitrogen atom 1 of thymine and nitrogen atom 9 of adenine have on lowest energy excited electronic states has been studied by means of time-dependent PBE0 calculations in aqueous solution. In agreement with the experimental indications, the vertical excitation energy of the bright state of 1,methyl-thymine, thymine nucleoside and thymine nucleotide is red-shifted with respect to that of thymine. Deoxyribose and deoxyribose-phosphate substituents affect mainly the lowest energy dark state of adenine and thymine, slightly increasing their oscillator strength. The excited states of 9, methyl-adenine and 1, methyl-thymine have also been studied by using the recently developed M052X, CAM-B3LYP and LC-ωPBE density functionals. The computed VEE are in good agreement with those obtained by using PBE0, which, however, provides values closer to the experimental band maximum.     

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.