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.     

Absolute configuration of Buagafuran:An experimental and theoretical electronic circular dichroism study

Buagafuran is a novel drug candidate derived from natural product.Its absolute configuration has been confirmed by electronic circular dichroism combined with modern quantum-chemical calculation using time-dependent density functional theory.The predicted UV absorbance peak is underestimated by several nanometers compared with the experimental data.The applicability of empirical rule for the C=C-C-O system in Buagafuran has also been discussed.Our results show that electronic circular dichroism could be a useful tool for the absolute configuration assignment of chiral drugs,especially for the oily or semisolid substances,whose crystal structures are impossible to obtain.     

秋水仙碱立体异构体电子结构及圆二色谱性质的理论研究

采用量子化学密度泛函理论(DFT)在B3LYP/6-311++G二水平上对秋水仙碱四个立体异构体分子几何构型进行了优化,在优化的基础上进行了振动圆二色谱(VCD),紫外-可见光谱(UV-Vis)和电子圆二色谱(ECD)研究.为模拟真实条件,以水为溶剂,计算其对分子电子结构和光谱性质的影响.研究结果表明:秋水仙碱四个立体...     

Absolute configuration of conformationally flexible cis-dihydrodiol metabolites by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations

We have determined the absolute configurations of conformationally flexible cis-dihydrodiol metabolites (cis-1,2-dihydroxy-3,5-cyclohexadienes), bearing different substituents (e.g., Br, F, CF3, CN, Me) in 3- and 5-positions, by the method of confrontation of experimental and calculated electronic CD spectra and optical rotations. Convergent results were obtained by both methods in eight out of ten cases. For the difficult cases, where either conformer population and/or chiroptical properties (calculated rotational strengths of the long-wavelength Cotton effect or optical rotations) of contributing conformers remain inconclusive, the absolute configuration could still be correctly assigned based on one of the biased properties (either ECD or optical rotation). This approach appears well-suited for a broad spectrum of conformationally flexible chiral molecules.     

Frenkel‐exciton decomposition analysis of circular dichroism and circularly polarized luminescence for multichromophoric systems

Recently, a method to calculate the absorption and circular dichroism (CD) spectra based on the exciton coupling has been developed. In this work, the method was utilized for the decomposition of the CD and circularly polarized luminescence (CPL) spectra of a multichromophoric system into chromophore contributions for recently developed through‐space conjugated oligomers. The method which has been implemented using rotatory strength in the velocity form and therefore it is gauge‐invariant, enables us to evaluate the contribution from each chromophoric unit and locally excited state to the CD and CPL spectra of the total system. The excitonic calculations suitably reproduce the full calculations of the system, as well as the experimental results. We demonstrate that the interactions between electric transition dipole moments of adjacent chromophoric units are crucial in the CD and CPL spectra of the multichromophoric systems, while the interactions between electric and magnetic transition dipole moments are not negligible. © 2018 Wiley Periodicals, Inc.     

The structure and electronic property of the smallest C20‐glycine and Gd‐encapsulated C20‐glycine derivatives with potentially biological activity

Theoretical calculations on interaction of the C₂₀ fullerene (consists solely by pentagons) with the smallest amino acid (glycine) were carried out using density‐functional theory method. The glycine molecule energetically prefers to interact with the Top‐site on the C₂₀ cage via its amino nitrogen (N) active site. The stable ordering of three active sites on glycine molecule is NH₂‐site > O‐site > OH‐site. Moreover, when the Gd atom is encapsulated to the center of C₂₀‐glycine, the cage volume obviously increase ～24.8%; and the endohedral atom induces the generation of two strong bands in the partial density of states spectra, which could cause the effect on optical properties. Additionally, it is also found that the modified C₂₀‐glycine derivative by Gd atom can reduce the thermodynamic and kinetic stabilities. It could be expected that the study may provide a theoretical reference in exploring their intrinsic feature structurally to antitumor activity. © 2012 Wiley Periodicals, Inc.     

Theoretical studies on electronic structure and magnetic properties of mixed‐valence uteroferrin active site

The electronic structure and magnetic interaction of the active site of pig purple acid phosphatase (PAP, uteroferrin) were investigated using pure DFT (UBLYP) and hybrid DFT methods (UB3LYP and UB2LYP). Uteroferrin catalyzes the hydrolysis of a phosphate ester under acidic conditions and contains a binuclear iron center. The mammalian PAPs are expected to be targets for drug design of osteoporosis. Their active sites are typical examples of the Fe(II)‐Fe(III) mixed‐valence system. We studied double exchange interaction of the mixed‐valence system, using the potential energy difference between the Fe(II)‐Fe(III) and the Fe(III)‐Fe(II) states. The pathway of the antiferromagnetic coupling between Fe(III) and Fe(II) were also discussed by using chemical indices, which are evaluated by the occupation numbers of singly occupied natural orbitals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Nature of the near‐IR band in the electronic absorption spectra of neutral bis(tetrapyrrole) rare earth(III) complexes: Time‐dependent density functional theory calculations

The nature of the near‐IR band in the electronic absorption spectra of bis(tetrapyrrole) rare earth(III) complexes Y(Pc)₂ (1), La(Pc)₂ (2), Y(Pc)(Por) (3), Y(Pc)[Pc(α‐OCH₃)₄] (4), Y(Pc)[Pc(α‐OCH₃)₈] (5), and Y(Pc)[Pc(β‐OCH₃)₈] (6) was studied on the basis of time‐dependent density functional theory (TD‐DFT) calculations. The electronic dipole moment along the z‐axis in the electronic transition of the near‐IR band in all the studied neutral bis(tetrapyrrole) yttrium(III) and lanthanum(III) double‐deckers is well explained on the basis of the composition analysis of the orbitals involved. The electronic transition in the near‐IR band causes the reversion of the orbital orientation of one tetrapyrrole ring in both homoleptic and heteroleptic bis(tetrapyrrole) rare earth complexes and induces electron transfer from the tetrapyrrole ring with lower orbital energy to the other ring in the heteroleptic bis(tetrapyrrole) rare earth(III) complexes. The near‐IR band can work as an ideal characteristic absorption band to reflect the π–π interaction between the two tetrapyrrole rings in bis(tetrapyrrole) rare earth(III) double‐decker complexes because of its peculiar electronic transition nature. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Calculation of the Vibrationally Resolved,Circularly Polarized Luminescence of d‐Camphorquinone and (S,S)‐trans‐β‐Hydrindanone

Circularly polarized luminescence (CPL), the differential emission of left‐ and right‐handed circularly polarized light from a molecule, is modeled by using time‐dependent density functional theory. Calculations of the CPL spectra for the first electronic excited states of d‐camphorquinone and (S,S)‐trans‐β‐hydrindanone under the Franck–Condon approximation and using various functionals are presented, as well as calculations of absorption, emission, and circular dichroism spectra. The functionals B3LYP, BHLYP, and CAM‐B3LYP are employed, along with the TZVP and aug‐cc‐pVDZ Gaussian‐type basis sets. For the lowest‐energy transitions, all functionals and basis sets perform comparably, with the long‐range‐corrected CAM‐B3LYP better reproducing the excitation energy of camphorquinone but leading to a blue shift with respect to experiment for hydrindanone. The vibrationally resolved spectra of camphorquinone are very well reproduced in terms of peak location, widths, shapes, and intensities. The spectra of hydrindanone are well reproduced in terms of overall envelope shape and width, as well as the lack of prominent vibrational structure in the emission and CPL spectra. Overall the simulated spectra compare well with experiment, and reproduce the band shapes, emission red shifts, and presence or absence of visible vibrational fine structure.     

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.     

On the achievement of high fidelity and scalability for large‐scale diagonalizations in grid‐based DFT simulations

Recent advance in high performance computing (HPC) resources has opened the possibility to expand the scope of density functional theory (DFT) simulations toward large and complex molecular systems. This work proposes a numerically robust method that enables scalable diagonalizations of large DFT Hamiltonian matrices, particularly with thousands of computing CPUs (cores) that are usual these days in terms of sizes of HPC resources. The well‐known Lanczos method is extensively refactorized to overcome its weakness for evaluation of multiple degenerate eigenpairs that is the substance of DFT simulations, where a multilevel parallelization is adopted for scalable simulations in as many cores as possible. With solid benchmark tests for realistic molecular systems, the fidelity of our method are validated against the locally optimal block preconditioned conjugated gradient (LOBPCG) method that is widely used to simulate electronic structures. Our method may waste computing resources for simulations of molecules whose degeneracy cannot be reasonably estimated. But, compared to LOBPCG method, it is fairly excellent in perspectives of both speed and scalability, and particularly has remarkably less (< 10%) sensitivity of performance to the random nature of initial basis vectors. As a promising candidate for solving electronic structures of highly degenerate systems, the proposed method can make a meaningful contribution to migrating DFT simulations toward extremely large computing environments that normally have more than several tens of thousands of computing cores.     

Influence of the protein and DFT method on the broken‐symmetry and spin states in nitrogenase

The enzyme nitrogenase contains a complicated MoFe₇CS₉ cofactor with 35 possible broken‐symmetry (BS) states. We have studied how the energies of these states depend on the geometry, the surrounding protein, the DFT functional and the basis set, studying the resting state, a one‐electron reduced state and a protonated state. We find that the effect of the basis set is small, up to 11 kJ/mol. Likewise, the effect of the surrounding protein is restricted, up to 10 and 7 kJ/mol for the electrostatic and van der Waals energy terms. Single‐point energies calculated on a single geometry give a good correlation (R² = 0.92‐0.98) to energies calculated after geometry optimization, but some BS states may be disfavored by up to 37 kJ/mol. A change from the pure TPSS functional to the hybrid B3LYP functional may change the relative energies by up to 58 kJ/mol and the correlation between the two results is only 0.57‐0.72. Both functionals agree that BS7 is the most stable BS state and that the ground spin state is the quartet for the resting state and the quintet for the reduced state. With the TPSS functional, the BS6 state is the second most stable state, always at least 21 kJ/mol less stable than the BS7 state. However, with the B3LYP functional, BS10 is the second most stable state and for the protonated state it comes close in energy. Based on these results, we suggest a procedure how to consider the 35 BS states in future investigations of the nitrogenase reaction mechanism.     

Time-dependent density functional study of the electronic spectra of oligoacenes in the charge states −1, 0, +1, and +2

We present a systematic theoretical study of the five smallest oligoacenes (naphthalene, anthracene, tetracene, pentacene, and hexacene) in their anionic, neutral, cationic, and dicationic charge states. We used density functional theory (DFT) to obtain the ground-state optimised geometries, and time-dependent DFT (TD-DFT) to evaluate the electronic absorption spectra. Total-energy differences enabled us to evaluate the electron affinities and first and second ionisation energies, the quasiparticle correction to the HOMO–LUMO energy gap and an estimate of the excitonic effects in the neutral molecules. Electronic absorption spectra have been computed by combining two different implementations of TD-DFT: the frequency–space method to study general trends as a function of charge-state and molecular size for the lowest-lying in-plane long-polarised and short-polarised π → π^* electronic transitions, and the real-time propagation scheme to obtain the whole photo-absorption cross-section up to the far-UV. Doubly ionised PAHs are found to display strong electronic transitions of π → π^* character in the near-IR, visible, and near-UV spectral ranges, like their singly charged counterparts. While, as expected, the broad plasmon-like structure with its maximum at about 17–18 eV is relatively insensitive to the charge-state of the molecule, a systematic decrease with increasing positive charge of the absorption cross-section between 6 and 12 eV is observed for each member of the class.     

Time‐dependent density functional calculations on the electronic spectra of the neutral nickel complex [Ni(LISQ)2] (LISQ = 3,5‐di‐tert‐butyl‐o‐diiminobenzosemiquinonate(1−)) and its monoanion and dication

The electronic spectrum of the neutral nickel complex [Ni(L^ISQ)₂] (L^ISQ = 3,5‐di‐tert‐butyl‐o‐diiminobenzosemiquinonate(1^?)) and the spectra of its anion and dication have been calculated by means of time‐dependent density functional theory. The electronic ground state of the neutral complex exhibits an open shell singlet diradical character. The mandatory multireference problem for this electronic ground state has been treated approximately by using the unrestricted and spin symmetry broken Kohn‐Sham Slater determinant as the wave function for the noninteracting reference system in the time‐dependent density functional calculations. A reasonable agreement with observed transition energies and band intensities has been achieved. This holds also for the long wavelength transitions that are shown to be of charge transfer type. The charge distributions in the electronic ground state and the corresponding low lying excited states, however, are rather similar. Thus, the known failure of standard time‐dependent density functional theory to describe improperly long range charge transfer transitions is absent in this work. The applied computational scheme might be adequate for calculating electronic spectra of transition metal complexes with noninnocent ligands. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

π-d-Interaction and the temperature dependent magnetic circular dichroism spectra of low spin Fe(III)-heme compounds

The magnetic circular dichroism (MCD) of metmyoglobin cyanide, ferricytochromec and horseradish peroxidase cyanide were measured in the region 340–800 nm over a range of temperatures from 293 to 15 K. All three species show the temperature dependent MCD (TheC-type effects ∼1/T) in both visibleQ and near UVB bands. While the MCD and absorption inB- region as well as the absorption inQ region are quite similar for all three species the MCD inQ- bands reveal the marked differences, especially at low temperatures. To explain these observations, the theoretical treatment based on our previous model (A. P. Mineyev and Yu. A. Sharonov, 1978, Theoret. Chim. Acta (Berl.)49, 295–307) is proposed. The key point of this consideration is the configuration π-d- interaction which in addition to our previous analysis involves the first excited Fe(III)-ion Kramers doublet and theB-Q-mixing effects. The simultaneous least square fit of MCD and absorption data allows to evaluate the π —d- parameters which appear to be of the order of 10²−10³ cm⁻¹. The role of the π -d- interaction in the forming of hemoprotein spectra are discussed.     

Theory of variational calculation with a scaling correct moment functional to solve the electronic schrödinger equation directly for ground state one‐electron density and electronic energy

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a nonlinear, approximate density functional of a three spatial dimension one‐electron density for an N electron system which is tractable in practice, is a long‐desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital‐free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree–Fock (HF) and Kohn–Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫g_i( r ₁)g_k( r ₂)rd r ₁d r ₂, etc.) to estimate electron‐electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation. © 2012 Wiley Periodicals, Inc.     

Acid/Base‐Triggered Switching of Circularly Polarized Luminescence and Electronic Circular Dichroism in Organic and Organometallic Helicenes

Electronic circular dichroism and circularly polarized luminescence acid/base switching activity has been demonstrated in helicene‐bipyridine proligand 1 a and in its “rollover” cycloplatinated derivative 2 a . Whereas proligand 1 a displays a strong bathochromic shift (>160 nm) of the nonpolarized and circularly polarized luminescence upon protonation, complex 2 a displays slightly stronger emission. This strikingly different behavior between singlet emission in the organic helicene and triplet emission in the organometallic derivative has been rationalized by using quantum‐chemical calculations. The very large bathochromic shift of the emission observed upon protonation of azahelicene‐bipyridine 1 a has been attributed to the decrease in aromaticity (promoting a charge‐transfer‐type transition rather than a π–π* transition) as well as an increase in the HOMO–LUMO character of the transition and stabilization of the LUMO level upon protonation.     

Ab initio simulations of two‐dimensional electronic spectra: The SOS//QM/MM approach

Two‐dimensional electronic spectroscopy (2DES) is a cutting‐edge technique for investigating with high temporal resolution energy transfer, structure, and dynamics in a wide range of systems in physical chemistry, energy sciences, biophysics, and biocatalysis. However, the interpretation of 2DES is challenging and requires computational modeling. This perspective provides a roadmap for the development of computational tools that could be routinely applied to simulate 2DES spectra of multichromophoric systems active in the UV region (2DUV) using state‐of‐the‐art ab initio electronic structure methods within a quatum mechanics/molecular mechanics (QM/MM) scheme and the sum‐over‐states (SOS) approach (here called SOS//QM/MM). Multiconfigurational and multireference perturbative methods, such as the complete active space self‐consistent field and second‐order multireference perturbation theory (CASPT2) techniques, can be applied to reliably calculate the electronic properties of multichromophoric systems. Hybrid QM/MM method and molecular dynamics techniques can be used to assess environmental and conformational effects, respectively, that shape the 2D electronic spectra. DNA and proteins are important biological targets containing UV chromophores. We report ab initio simulation of 2DUV spectra of a cyclic tetrapeptide containing two interacting aromatic side chains, a model system for the study of protein structure and dynamics by means of 2DUV spectroscopy. © 2013 Wiley Periodicals, Inc.     

Electronic structures and spectra of porphyrin with fused benzoheterocycles: DFT and TDDFT‐PCM investigations

Density functional theory (DFT) and time‐dependent DFT (TDDFT) are applied to study seven asymmetric π‐conjugated porphyrins with extended benzoheterocycles: quinoline, indole, benzoimidazole, benzothiazole, benzooxazole, 2,1,3‐benzothiadiazole, and 2,1,3‐benzoxadiazole. The solvation effects on the excitation energies for these porphyrin derivatives in chloroform are taken into account by using the continuum model (C‐PCM) combined with TDDFT, and this method makes a closer agreement with the experimental values, especially for the B‐bands of these objects. Great efforts have been made on investigating the influences of the fused aromatic units of the porphyrins on the absorption properties as these can be particularly important for many applications. Benzoheterocycle introduction and solvent effects have been systemically investigated, and close agreement is obtained between calculated and measured UV–vis spectra. These theoretical data could shed light on future synthetic chemistry. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007