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.     

Electronic optical response of molecules in intense fields: comparison of TD-HF, TD-CIS, and TD-CIS(D) approaches

Time-dependent Hartree-Fock (TD-HF) and time-dependent configuration interaction (TD-CI) methods with Gaussian basis sets have been compared in modeling the response of hydrogen molecule, butadiene, and hexatriene exposed to very short, intense laser pulses (760 nm, 3 cycles). After the electric field of the pulse returns to zero, the molecular dipole continues to oscillate due to the coherent superposition of excited states resulting from the nonadiabatic excitation caused by the pulse. The Fourier transform of this residual dipole gives a measure of the nonadiabatic excitation. For low fields, only the lowest excited states are populated, and TD-CI simulations using singly excited states with and without perturbative corrections for double excitations [TD-CIS(D) and TD-CIS, respectively] are generally in good agreement with the TD-HF simulations. At higher field strengths, higher states are populated and the methods begin to differ significantly if the coefficients of the excited states become larger than approximately 0.1. The response of individual excited states does not grow linearly with intensity because of excited state to excited state transitions. Beyond a threshold in the field strength, there is a rapid increase in the population of many higher excited states, possibly signaling an approach to ionization. However, without continuum functions, the present TD-HF and TD-CI calculations cannot model ionization directly. The TD-HF and TD-CIS simulations are in good accord because the excitation energies obtained by linear response TD-HF [also known as random phase approximation (RPA)] agree very well with those obtained from singly excited configuration interaction (CIS) calculations. Because CIS excitation energies with the perturbative doubles corrections [CIS(D)] are on average lower than the CIS excitation energies, the TD-CIS(D) response is generally stronger than TD-CIS.     

TD-CI simulation of the electronic optical response of molecules in intense fields: comparison of RPA, CIS, CIS(D), and EOM-CCSD

A number of different levels of theory have been tested in TD-CI simulations of the response of butadiene interacting with very short, intense laser pulses. Excitation energies and transition dipoles were calculated with linear-response time-dependent Hartree-Fock (also known as the random phase approximation, RPA), configuration interaction in the space of single excitations (CIS), perturbative corrections to CIS involving double excitations [CIS(D)], and the equation-of-motion coupled-cluster (EOM-CC) method using the 6-31G(d,p) basis set augmented with n = 0-3 sets of diffuse sp functions on all carbons and only on the end carbons [6-31 n+ G(d,p) and 6-31(n+)G(d,p), respectively]. Diffuse functions are particularly important for transitions between the pseudocontinuum states above the ionization threshold. 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. Depending on the basis set, up to 500 excited states were needed for the simulations. Under the conditions selected, the response was too weak with the 6-31G(d,p) basis set, and the difference between levels of theory was more pronounced. When two or three set of diffuse functions were included on all of the carbons, the RPA, CIS, and EOM-CC results were comparable, but the CIS(D) response was too large compared to the more accurate EOM-CC calculations. Even though the frequency of the pulse is not resonant with any of the ground-to-excited transitions, excitations to valence and pseudocontinuum states occur readily above a threshold in the intensity.     

Computational studies on ethylene addition to nickel bis(dithiolene)

The density functionals B3LYP, B3PW91, BMK, HSE06, LC-ωPBE, M05, M06, O3LYP, TPSS, ω-B97X, and ω-B97XD are used to optimize key transition states and intermediates for ethylene addition to Ni(edt)(2) (edt = S(2)C(2)H(2)). The efficacy of the basis sets 6-31G**, 6-31++G**, cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ is also examined. The geometric parameters optimized with different basis sets and density functionals are similar and agree well with experimental values. The ω-B97XD functional gives relative energies closest to those from CCSD, while M06 and HSE06 yield results close to those from CCSD(T). CASSCF and CASSCF-PT2 calculation results are also given. Variation of the relative energies from different density functionals appears to arise, in part, from the multireference character of this system, as confirmed by the T1 diagnostic and CASSCF calculations.     

Optical rotation calculated with time-dependent density functional theory: the OR45 benchmark

Time-dependent density functional theory (TDDFT) computations are performed for 42 organic molecules and three transition metal complexes, with experimental molar optical rotations ranging from 2 to 2 × 10(4) deg cm(2) dmol(-1). The performances of the global hybrid functionals B3LYP, PBE0, and BHLYP, and of the range-separated functionals CAM-B3LYP and LC-PBE0 (the latter being fully long-range corrected), are investigated. The performance of different basis sets is studied. When compared to liquid-phase experimental data, the range-separated functionals do, on average, not perform better than B3LYP and PBE0. Median relative deviations between calculations and experiment range from 25 to 29%. A basis set recently proposed for optical rotation calculations (LPol-ds) on average does not give improved results compared to aug-cc-pVDZ in TDDFT calculations with B3LYP. Individual cases are discussed in some detail, among them norbornenone for which the LC-PBE0 functional produced an optical rotation that is close to available data from coupled-cluster calculations, but significantly smaller in magnitude than the liquid-phase experimental value. Range-separated functionals and BHLYP perform well for helicenes and helicene derivatives. Metal complexes pose a challenge to first-principles calculations of optical rotation.     

Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: a comparison between wave-function theory and density functional theory

In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO2(2+) molecule excitation energies and geometries of states originating from excitation from the sigma(u), sigma(g), pi(u), and pi(g) orbitals to the nonbonding 5f(delta) and 5f(phi) have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCFCASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFTMRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFTMRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied sigma(u) orbital are symmetric while that arising from excitations out of the pi(u) orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.     

The performance and relationship among range-separated schemes for density functional theory

The performance and relationship among different range-separated (RS) hybrid functional schemes are examined using the Coulomb-attenuating method (CAM) with different values for the fractions of exact Hartree-Fock (HF) exchange (α), long-range HF (β), and a range-separation parameter (μ), where the cases of α + β = 1 and α + β = 0 were designated as CA and CA0, respectively. Attenuated PBE exchange-correlation functionals with α = 0.20 and μ = 0.20 (CA-PBE) and α = 0.25 and μ = 0.11 (CA0-PBE) are closely related to the LRC-ωPBEh and HSE functionals, respectively. Time-dependent density functional theory calculations were carried out for a number of classes of molecules with varying degrees of charge-transfer (CT) character to provide an assessment of the accuracy of excitation energies from the CA functionals and a number of other functionals with different exchange hole models. Functionals that provided reasonable estimates for local and short-range CT transitions were found to give large errors for long-range CT excitations. In contrast, functionals that afforded accurate long-range CT excitation energies significantly overestimated energies for short-range CT and local transitions. The effects of exchange hole models and parameters developed for RS functionals for CT excitations were analyzed in detail. The comparative analysis across compound classes provides a useful benchmark for CT excitations.     

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.     

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.     

Accurate evaluation of valence and low-lying Rydberg states with standard time-dependent density functional theory

Using a standard exchange-correlation functional, namely, PBE0, the basis set dependence of time-dependent density functional theory (TD-DFT) calculations has been explored using 33 different bases and five organic molecules as test cases. The results obtained show that this functional can provide accurate (i.e., at convergence) results for both valence and low-lying Rydberg excitations if at least one diffuse function for the heavy atoms is included in the basis set. Furthermore, these results are in fairly good agreement with the experimental data and with those delivered by other functionals specifically designed to yield correct asymptotic/long-range behavior. More generally, the PBE0 calculations show that a greater accuracy can be obtained for both Rydberg and valence excitations if they occur at energies below the epsilonHOMO + 1 eV threshold. This latter value is proposed as a thumb rule to verify the accuracy of TD-DFT/PBE0 applications.     

Theoretical study of singlet and triplet excitation energies in oligothiophenes

We have analyzed singlet and triplet excitation energies in oligothiophenes (up to five rings) using time-dependent density-functional theory (TD-DFT) with different exchange-correlation functionals and compared them with results from the approximate coupled-cluster singles and doubles model (CC2) and experimental data. The excitation energies have been calculated in geometries obtained by TD-DFT optimization of the lowest excited singlet state and in the ground-state geometries of the neutral and anionic systems. TD-DFT methods underestimate photoluminescence energies but the energy difference between singlet and triplet states shows trends with the chain-length similar to CC2. We find that the second triplet excited state is below the first singlet excited state for long oligomers in contrast with the previous assignment of Rentsch et al. (Phys.Chem. Chem. Phys. 1999, 1, 1707). Their photodetachment photoelectron spectroscopy measurements are better described by considering higher triplet excited states.     

间位取代卟啉及其锌卟啉的电子吸收光谱

取代的卟啉类衍生物在气敏传感器方面具有广泛的应用前景.本文采用了密度泛函理论(DFT)和含时密度泛函理论(TD-DFT)研究了四种不同取代基的卟啉衍生物(meso位四硝基苯基/四氨基苯基卟啉(NO2PP,NH2PP)及其相应的锌金属卟啉衍生物(NO2ZnPP,NH2ZnPP))的紫外和近紫外光谱特征.利用两种不同的交换相关泛函(广义梯度近似泛函(PBE)和杂化密度泛函(B3LYP))优化了上述四种物质的结构,并应用TD-DFT计算了相应的电子激发能量和振动强度.结果表明,取代卟啉的吸收光谱与大量的电子跃迁有关;与B3LYP泛函预测的光谱相比,PBE泛函所得B带以及Q带的波长位置与实验值更为接近.另外,计算所得硝基取代基卟啉的B带相对于氨基取代基卟啉的B带发生了红移,这与实验现象也保持一致.由于卟啉衍生物的三重激发态在电子转移中有很重要的应用,因此在PBE/6-31G(d)水平上计算了四种物质的最低三重激发态能量,分别为1.426、1.469、1.608和1.581eV.     

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.     

Charge-transfer excited states in a pi-stacked adenine dimer, as predicted using long-range-corrected time-dependent density functional theory

The lowest few electronic excitations of a pi-stacked adenine dimer in its B-DNA geometry are investigated, in the gas phase and in a water cluster, using a long-range-corrected version of time-dependent density functional theory (TD-DFT) that asymptotically incorporates Hartree-Fock exchange. Long-range correction is shown to eliminate the catastrophic underestimation of charge-transfer (CT) excitation energies that plagues conventional TD-DFT, at the expense of introducing one adjustable parameter, mu, that determines the length scale on which Hartree-Fock exchange is turned on. This parameter allows us to interpolate smoothly between hybrid density functionals and time-dependent Hartree-Fock theory. Excitation energies for CT states (in which an electron is transferred from one adenine molecule to the other) are found to increase dramatically as a function of mu. Uncorrected hybrid functionals underestimate the CT excitation energies, placing them well below the valence excitations, while time-dependent Hartree-Fock calculations place these states well above the valence states. Values for mu determined from certain benchmark calculations place the CT states well above the valence pipi* and npi* states at the Franck-Condon point.     

Predictive power of long-range corrected functionals on the spectroscopic properties of tetrapyrrole derivatives for photodynamic therapy

Porphyrin and chlorin based compounds possess promising properties to be utilized as photosensitizers in photodynamic therapy (PDT). However, the photosensitizers available on the market today are not ideal for use in PDT, which has emphasized the need for new photosensitizers with improved photodynamic properties to be developed. Computational drug-design can be utilized in the search for improved pharmaceutical compounds, provided that the methods used are able to reproduce experimental data. In the present study we investigated, by the use of time-dependent density functional theory (TD-DFT), the performance of the long-range corrected functionals ωB97, ωB97X and ωB97XD on their ability to predict low-lying singlet excitations (>600 nm) of a set of well-known photosensitizing compounds. It was found that ωB97X reproduced the experimental red-most absorption band most satisfactorily. The use of either B3LYP, ωB97XD or M06 in geometry optimizations has a minor effect on the spectra in most cases. Calculated energy differences between the optimized singlet ground states and optimized first excited triplet states show consistent and overall higher triplet state energies for B3LYP, M06, and PBE0 compared with ωB97, ωB97X, and ωB97XD. The calculated triplet state energies are, however, sufficient to generate singlet oxygen in most cases.