Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism: calculation of B terms

Magnetically perturbed time-dependent density functional theory is applied to the calculation of the magnetic circular dichroism (MCD) B terms of closed shell molecules. Two approaches to evaluating B term parameters are described: a sum-over-states-type approach and an approach based on the direct solution of the matrix equations. The advantages and disadvantages and technical challenges of each approach are described. The interpretation of the parameters in terms of ground and excited state perturbations are discussed. Several applications of the methodology are described. Calculations of the MCD of ethene are used to compare the sum-over-states and direct solution approaches and to illustrate the potential for analysis. The other applications involving azabenzes, sulfur-nitrogen heterocycles and quinone molecules are compared with experiment and other theoretical calculations. For the most part, all important features of the observed spectra are reproduced.     

Magnetic circular dichroism of porphyrins containing M = Ca, Ni, and Zn. A computational study based on time-dependent density functional theory

A theoretical study is presented on the magnetic circular dichroism (MCD) exhibited by the porphyrin complexes MP (M = Mg,Ni,Zn), MTPP (M = Mg,Ni,Zn), and NiOEP, where P = porphyrin, TPP = tetraphenylporphyrin, and OEP = octaethylporphyrin. The study makes use of a newly implemented method for the calculation of A and B terms from the theory of MCD and is based on time-dependent density functional theory (TD-DFT). It is shown that the MCD spectrum is dominated by a single positive A term in the Q-band region in agreement with experiment where available. The band can be fully explained as the first transition in Gouterman's four-orbital model for the type of porphyrins studied here. For the Soret band, the experimental MCD spectrum appears as a single positive A term. This is also what is found computationally for NiP and NiTPP, where the second transition in Gouterman's four-orbital model give rise to a positive A term. However, for the remaining systems, the simulated MCD spectrum is actually due to two B terms that have the appearance of one positive pseudo A term. The two B terms appear because the second Gouterman state is coupled strongly to a second excited state (b(2u) --> 2e(g)) of nearly the same energy by the external magnetic field.     

Magnetic circular dichroism of phthalocyanine (m=mg, zn) and tetraazaporphyrin (m=mg, zn, ni) metal complexes. A computational study based on time-dependent density functional theory

We present here simulated magnetic circular dichroism (MCD) spectra of MTAP (M=Mg, Ni, Zn) and MPc (M=Mg, Zn) where TAP=tetraazaporphyrin and Pc=phthalocyanine. The study is based on magnetically perturbed time-dependent density functional theory (MP-TDDFT) and a newly implemented method for the calculation of A and B terms from the theory of MCD. It follows from our investigation that the MCD spectrum for the MTAP and MPc systems in the Q-band region consists of a single positive A term augmented by a positive B term, in agreement with experiment where available. The Q band can be fully characterized in terms of the 2a1u-->2eg one-electron excitation. For the aza systems MgTAP and ZnTAP, the simulated MCD spectra in the Soret region are dominated by the two one-electron excitations 2a2u-->2eg and 1a2u-->2eg and has the appearance of a positive A term (with values between 1.33-1.55, depending on the MTAP system) made asymmetric by a negative B term, in good agreement with experiment. We find, in agreement with all available experimental findings on MPc (M=Mg, Zn) type systems, that the MCD spectra in the Soret region are dominated by two transitions with positive A/ D-term values and two negative B/ D-term values. The major contribution to the two transitions comes from the 2a2u-->2eg and 1a2u-->2eg one-electron excitations. It appears that the ratio of A/ B for the term parameters is underestimated by theory.     

Electronic transitions and magnetic circular dichroism of the naphthalene monogenegative ion

The optical absorption and magnetic circular dichroism (MCD) spectra of the mononegative ion of naphthalene in a solution of 2-methyltetrahydrofuran have been measured at room temperature over the 25000–41000 cm^?1 spectral region. Experimental values of the MCD parameter B/D are compared with theoretical data obtained by means of an LCAO SCF CI calculation according to Pariser, Parr and Pople. The agreement between theory and experiment is rather good.     

Magnetic circular dichroism in real-time time-dependent density functional theory

We apply the adiabatic time-dependent density functional theory to magnetic circular dichroism (MCD) spectra using the real-space, real-time computational method. The standard formulas for the MCD response and its A and B terms are derived from the observables in the time-dependent wave function. We find real-time method is well suited for calculating the overall spectrum, particularly at higher excitation energies where individual excited states are numerous and overlapping. The MCD sum rules are derived and intepreted in the real-time formalism; we find that they are very useful for normalization purposes and assessing the accuracy of the theory. The method is applied to MCD spectrum of C(60) using the adiabatic energy functional from the local density approximation. The theory correctly predicts the signs of the A and B terms for the lowest allowed excitations. However, the magnitudes of the terms only show qualitative agreement with experiment.     

Resolving Electronic Transitions in Synthetic Fluorescent Protein Chromophores by Magnetic Circular Dichroism

The detailed electronic structures of fluorescent chromophores are important for their use in imaging of living cells. A series of green fluorescent protein chromophore derivatives is examined by magnetic circular dichroism (MCD) spectroscopy, which allows the resolution of more bands than plain absorption and fluorescence. Observed spectral patterns are rationalized with the aid of time‐dependent density functional theory (TDDFT) computations and the sum‐over‐state (SOS) formalism, which also reveals a significant dependence of MCD intensities on chromophore conformation. The combination of organic and theoretical chemistry with spectroscopic techniques also appears useful in the rational design of fluorescence labels and understanding of the chromophore's properties. For example, the absorption threshold can be heavily affected by substitution on the phenyl ring but not much on the five‐member ring, and methoxy groups can be used to further tune the electronic levels.     

Porphyrin protonation studied by magnetic circular dichroism

Magnetic circular dichroism (MCD) spectroscopy provides valuable information about electronic excited states in molecules. The interpretation of spectra is however difficult, often requiring additional theoretical calculations to rationalize the observed signal. Recent developments in time-dependent density functional theory (TDDFT) bring hope that the applicability of MCD spectroscopy for chemical problems may be significantly extended. In this study, two modern analytical TDDFT implementations are compared and used to understand experimental MCD spectra of a model porphyrin system upon protonation. Changes in porphyrin geometry and electronic structure are related to MCD intensities by comparing the spectra of 5,10,15,20-tetraphenyl-21H,23H-porphyrintetrasulfonic acid (TPPS) measured at different pH values with the TDDFT calculations. Although the theoretical results slightly depended on the chosen exchange-correlation functional, the computations provided MCD curves that could well rationalize the experimental data. The protonation of the porphyrin core causes marked changes in the MCD spectrum, whereas the role of the substituents is limited. Also, different conformations of the porphyrin substituents cause relatively minor changes of the MCD pattern, mostly in the Soret region, where the porphine and phenyl electronic transitions start to mix. The solvent environment simulated by the dielectric model caused a shift (~20 nm) of the absorption bands but only minor variations in the absorption and MCD spectral shapes. The study thus demonstrates that the recently available first-principles interpretations of MCD spectra significantly enhance the applicability of the technique for molecular structural studies.     

Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism. II. Calculation of A terms

The magnetically perturbed time-dependent density functional theory is used to derive equations for the magnetic circular dichroism (MCD) of degenerate transitions of closed shell molecules. The MCD of this type of transition can be divided into two contributions. The dominant contribution is usually that from A terms that arise because of the breaking of the degeneracy of the excited state in the presence of the magnetic field. The second contribution comes from B terms that arise because of the perturbation of the transition dipole by the magnetic field. The formalism is applied to ten tetrahedral d(0) transition metal oxy- and thioanions. The MCD parameters of these systems are reproduced quite well by the calculations. Simulated spectra derived from the calculated parameters are in good agreement with the observed 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⁺.     

呋喃同系物C4H4X(X=O,S,Se,Te)非线性光学性质的TDDFT-SOS理论研究

用含时密度泛函理论(TD-DFT)组合态求和(SOS)方法计算了呋喃同系物[呋喃(C4H4O)、噻吩(C4H4S)、硒吩(C4H4Se)、碲吩(C4H4Te)]的非线性光学性质.计算结果表明,体系的三阶NLO系数(γ)随着杂原子被重原子的取代而逐步增大,B3LYP等4种势函数计算的NLO系数基本一致.计算的色散关系曲线表明,标题化合物在宽频区存在小的色散作用,是一类具有应用前景的NLO材料.     

Computation of magnetic circular dichroism by sum‐over‐states summations

Magnetic circular dichroism (MCD) spectroscopy has been established as a convenient method to study electronic structure, in particular for small symmetric organic molecules. Newer applications on more complex systems are additionally stimulated by the latest availability of precise quantum‐chemical techniques for the spectral simulations. In this work, a sum over states (SOS) summation is reexamined as an alternative to the derivative techniques for the MCD modeling. Unlike in previous works, the excited electronic states are calculated by the time‐dependent density functional theory (TDDFT). A gradient formulation of the MCD intensities is also proposed, less dependent on the origin choice than the standard expressions. The dependencies of the results on the basis set, number of electronic states, and coordinate origin are tested on model examples, including large symmetric molecules with degenerate electronic states. The results suggest that the SOS/TDDFT approach is a viable and accurate technique for spectral simulation. It may even considerably reduce the computational time, if compared with the traditional MCD computational procedures based on the response theory. © 2013 Wiley Periodicals, Inc.     

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.     

Theoretical study on the second-order nonlinear optical properties of asymmetric spirosilabifluorene derivatives

The equilibrium geometries of four asymmetric spirosilabifluorene derivatives are optimized by means of the DFT/B3LYP method with the 6-31G* basis sets in this paper. On the basis of the optimized structures, the electronic structure and second-order nonlinear optical properties are calculated by using time-dependent density-functional theory (TDDFT) based on the 6-31G* level combined with the sum-over-states (SOS) method. The results show that these compounds possess remarkably larger molecular second-order polarizabilities than typical organometallic and organic compounds, and replacement of a carbon atom with nitrogen within the conjugated substituent has a great influence on the second-order nonlinear optical properties. Analysis of the main contributions to the second-order polarizability suggests that charge transfer from the z-axis directions plays a key role in the nonlinear optical response. These compounds have a possibility to be excellent second-order nonlinear optical (NLO) materials from the standpoint of large beta values, small dipole moment, high transparency, and small dispersion behaviors.     

Theoretical evolution of the third-order molecular polarizabilities as a function of chain length in thiophene and pyrrole oligomers

On the basis of INDO (intermediate neglect of differential overlap)/MRD -CI (multireference determinant–configuration interaction) calculations, the SOS (sum-over-states) formalism is applied to calculate the third-order polarizabilities, γ, in thiophene and pyrrole oligomers. For both types of oligomers, the chain-length dependence of γ can be divided into three regimes: Describing γ as a power law of the number of rings (N), we observe that the power value first strongly increases with N, than reaches a nearly constant value (power regime), and, finally, decreases toward one, indicating the appearance of a saturation regime. Very good agreement with the experimental evolution has been found in the case of the oligothiophenes. The comparison of the results obtained for the two types of oligomers indicates a lower polarizability in the oligopyrroles. © 1994 John Wiley & Sons, Inc.     

First-principles calculations of magnetic circular dichroism spectra

An elaborate approach for the prediction of magnetic circular dichroism (MCD) spectra in the framework of highly correlated multiconfigurational ab initio methods is presented. The MCD transitions are computed by the explicit treatment of spin-orbit coupled (SOC) and spin-spin coupled (SSC) N-electron states. These states are obtained from the diagonalization of the SOC and SSC operators along with the spin and orbital Zeeman operators in the basis of a preselected number of roots of the spin-free Hamiltonian. Therefore, zero-field splittings due to the SOC and SSC interactions along with the magnetic field splittings are explicitly accounted for in the ground as well as the excited states. This makes it possible to calculate simultaneously all MCD A, B, and C terms even beyond the linear response limit. The SOC is computed using a multicenter mean-field approximation to the Breit-Pauli Hamiltonian. Two-electron SSC terms are included in the treatment without further approximations. The MCD transition intensities are subjected to numerical orientational averaging in order to treat the most commonly encountered case of randomly oriented molecules. The simulated MCD spectra for the OH, NH, and CH radicals as well as for [Fe(CN)(6)](3-) are in good agreement with the experimental spectra. In the former case, the significant effects of the inert gas matrices in which the experimental spectra were obtained were modeled in a phenomenological way.     

CNDO/S calculations of magnetic circular dichroism of some mono-substituted benzenes using the complete angular momentum operator

Magnetic Circular Dichroism (MCD) B term calculations are performed using the CNDO/S method on mono-substituted benzene derivatives. The influence of geometry, origin dependency, extent of Configuration Interaction (CI) and the choice of the basis set is investigated numerically.For the lowest-lying singlet transitions in these molecules excellent agreement with experiment is obtained.     

Spectroscopic and theoretical studies of optically active porphyrin dimers: a system uninterpretable by exciton coupling theory.

The electronic excited states of a meso-meso beta-beta doubly linked bis-porphyrin are comprehensively investigated by measuring its circular dichroism (CD) and magnetic circular dichroism (MCD) spectra. The observed spectroscopic properties are rationalized by DFT calculations. The frontier molecular orbitals (MOs) are constructed by the linear combinations of the constituent monomers' four MOs. Comparison of a theoretical CD spectrum based on time-dependent DFT (TDDFT) with the experimental spectra resulted in the assignment of the helical conformation of the dimer. This assignment is contrary to the previous assignment based on the point-dipole approximation (exciton coupling theory).     

Time-dependent density functional theory for calculating origin-independent optical rotation and rotatory strength tensors

An approach to calculate origin-independent electronic chiroptical property tensors using time-dependent density functional theory (TDDFT) and gauge-including atomic orbital (GIAO) basis sets is evaluated. Computations of origin-dependent optical rotation tensors and of rotatory strengths needed to simulate circular dichroism spectra are presented. The optical rotation tensor computations employ solutions of coupled perturbed Kohn-Sham equations for a dynamic electric field and a static magnetic field. Because the magnetic field is time independent, the GIAO treatment is somewhat simplified compared to a previously reported method, at some added computational cost if hybrid functionals are employed. GIAO rotatory strengths are also calculated, using transition density matrices from a standard TDDFT excitation energy module. A new implementation in the NWChem quantum chemistry package is employed for representative computations of origin-invariant chiroptical response tensors for methyloxirane, norbornenone, and the ketosteroid androstadienone. For the steroid molecule the vibrational structure of the CD spectrum is modeled explicitly by using calculated Franck-Condon factors. The agreement with experiment is favorable.