Diabatic couplings for charge recombination via Boys localization and spin-flip configuration interaction singles

We describe a straightforward technique for obtaining diabatic couplings applicable to charge transfer from or charge recombination to the electronic ground state. Our method is nearly black box, requiring minimal chemical intuition from the user, and merges two well-established approaches in electronic structure theory: first, smooth and balanced adiabatic states are generated using spin-flip-configuration interaction singles (SF-CIS) based on a triplet HF state; second, Boys localization is applied to rotate all adiabatic states into charge-localized diabatic states. The method is computationally inexpensive, scaling only with the cost of CIS, and does not require a choice of active space, which is usually required for such intrinsically multiconfigurational problems. Molecular LiF in vacuum and LiF solvated by a single water molecule are examined as model systems. We find nearly smooth diabatic potential energy surfaces and couplings and we find that the Condon approximation is obeyed approximately for this model problem.     

Calculation of nonadiabatic couplings in density-functional theory

This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.     

9,10-二氰基蒽和杜烯间光诱导电子转移的电荷分离态和电子耦合

采用从头算方法,讨论了9,10-二氰基蒽(DCA)和杜烯(DUR)间光诱导电子转移反应的态-态跃迁.考虑基组重叠误差(BSSE)对相互作用能的校正,用MP₂方法优化得到重叠式[DCA…DUR]配合物的稳定构型.用单激发组态相互作用(CIS)方法讨论了[DCA…DUR]配合物的光诱导电荷分离和电荷复合过程.根据广义Mulliken-Hush(GMH)模型,计算了电荷复合过程的电子耦合矩阵元.结果表明,[DCA…DUR]配合物的S₀→S₁和S₀→S₂跃迁产生了两个强的局域激发态,S₀→S₃跃迁直接导致电荷分离态,小的振子强度预测该电荷转移(CT)跃迁是一弱跃迁,电荷分离态S₃衰变到低局域激发态或基态的电荷复合是可能的.     

Structural,Electronic and Optical Properties of Multifunctional Iridium(III) and Platinum(II) Metallophosphors for Organic Light‐Emitting Diodes

An elaborated theoretical investigation on the optical and electronic properties of three fluorene‐based platinum(II) and iridium(III) cyclometalated complexes Pt‐a , Ir‐a and Ir‐b is reported. The geometric and electronic structures of the complexes in the ground state are studied with density functional theory and Hartree Fock approaches, while the lowest triplet excited states are optimized by singles configuration interaction (CIS) methods. At the time‐dependent density functional theory (TD‐DFT) level, molecular absorption and emission properties were calculated on the basis of optimized ground‐ and excited‐state geometries, respectively. The computational results show that the appearance of triphenylamino (TPA) moiety at the 9‐position of fluorene ring favors the hole‐creation and leads to red‐shifts of absorption and emission spectra. Moreover, Pt‐a and Ir‐b are nice hole‐transporting materials whereas Ir‐a has good charge‐transfer balance, which render them useful for the realization of efficient OLEDs (Organic Light‐Emitting Diodes).     

Accurate theoretical study of PS(q) (q = 0,+1,-1) in the gas phase

Highly correlated ab initio methods were used in order to generate the potential energy curves and spin-orbit couplings of electronic ground and excited states of PS and PS(+). We also computed those of the bound parts of the electronic states of the PS(-) anion. We used standard coupled cluster CCSD(T) level with augmented correlation-consistent basis sets, internally contacted multi-reference configuration interaction, and the newly developed CCSD(T)-F12 methods in connection with the explicitly correlated basis sets. Core-valence correction and scalar relativistic effects were examined. Our data consist of a set of spectroscopic parameters (equilibrium geometries, harmonic vibrational frequencies, rotational constants, spin-orbit, and spin-spin constants), adiabatic ionization energies, and electron affinities. For the low laying electronic states, our calculations are consistent with previous works whereas the high excited states present rather different shapes. Based on these new computations, the earlier ultraviolet bands of PS and PS(+) were reassigned. For PS(-) and in addition to the already known anionic three bound electronic states (i.e., X(3)Σ(-), (1)Δ, and 1(1)Σ(+)), our calculations show that the (1)Σ(-), (3)Σ(+), and the (3)Δ states are energetically below their quartet parent neutral state (a(4)Π). The depletion of the J = 3 component of PS(-)((3)Δ) will mainly occur via weak interactions with the electron continuum wave.     

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.     

Correlation effects in EOM-CCSD for the excited states: evaluated by AIM localization index (LI) and delocalization index (DI)

We have extended the evaluation and interpretation of QTAIM (quantum theory of atoms in molecules) localization and delocalization indices lambda (LI) and delta (DI) to electronic excited states by studying ground states (at HF and CCSD levels) and excited states (at CIS and EOM-CCSD) of H2C=CH2, HCCH, H2C=O, H2C=S, CO2, CS2, and SO2. These molecules undergo extensive geometrical changes upon the excitation to the valence adiabatic excited singlet state. The importance of Coulomb correlation effects was demonstrated by comparing the LIs and DIs at none-correlated levels (HF and CIS) and those at correlated levels (CCSD and EOM-CCSD). In interpreting the changes in the magnitudes of the LIs and DIs, we made use of simple molecular orbital and Walsh-diagram analyses. Coulomb correlation is important in determining the magnitude of the LIs and DIs and obtaining geometries that are close to experiment.     

Theoretical modeling of the O-H stretching IR bands of hydrogen-bonded dimers of benzoic acid in S(0) and S(1) electronic states

Theoretical model for vibrational interactions in the hydrogen-bonded dimer of benzoic acid is presented. The model takes into account anharmonic-type couplings between the high-frequency O-H and the low-frequency O[cdots, three dots, centered]O stretching vibrations in two hydrogen bonds, resonance interactions (Davydov coupling) between two hydrogen bonds in the dimer, and Fermi resonance between the O-H stretching fundamental and the first overtone of the O-H in-plane bending vibrations. The vibrational Hamiltonians and selection rules for the C(2h) geometry in the S(0) state and for the C(s) in-plane bent geometry in the S(1) state of the dimer are derived. The model is used for theoretical simulation of the O-H stretching IR absorption bands of benzoic acid dimers in the gas phase in the electronic ground and first excited singlet states. Ab initio CIS and CIS(D)6-311++G(d,p) calculations have been performed to determine geometry, frequencies, and excited state energies of benzoic acid dimer in the S(1) state.     

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.     

A tetrathiafulvalene-functionalized naphthalene diimide: synthesis, electrochemical and photophysical properties

A tetrathiafulvalene donor has been attached to the naphthalene diimide core via a rigid bridge affording a new planar molecular dyad. Its electronic properties have been studied experimentally by the combination of electrochemistry and UV-vis-NIR spectroscopy. Various electronic excited charge-transfer states are generated in different oxidation states, leading to almost full absorption in the visible to near-IR region with high extinction coefficients. The observed electronic properties are explained on the basis of density-functional-theory. In particular, the oxidized radical species show a strong tendency to undergo aggregation, in which the long-distance attractive interactions overcome the electrostatic repulsions.     

Analytical Hessian of electronic excited states in time-dependent density functional theory with Tamm-Dancoff approximation

We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values.     

Ab initio characterization of electron transfer coupling in photoinduced systems: generalized Mulliken-Hush with configuration-interaction singles

To calculate electronic couplings for photoinduced electron transfer (ET) reactions, we propose and test the use of ab initio quantum chemistry calculation for excited states with the generalized Mulliken-Hush (GMH) method. Configuration-interaction singles (CIS) is proposed to model the locally excited (LE) and charge-transfer (CT) states. When the CT state couples with other high lying LE states, affecting coupling values, the image charge approximation (ICA), as a simple solvent model, can lower the energy of the CT state and decouple the undesired high-lying local excitations. We found that coupling strength is weakly dependent on many details of the solvent model, indicating the validity of the Condon approximation. Therefore, a trustworthy value can be obtained via this CIS-GMH scheme, with ICA used as a tool to improve and monitor the quality of the results. Systems we tested included a series of rigid, sigma-linked donor-bridge-acceptor compounds where "through-bond" coupling has been previously investigated, and a pair of molecules where "through-space" coupling was experimentally demonstrated. The calculated results agree well with experimentally inferred values in the coupling magnitudes (for both systems studied) and in the exponential distance dependence (for the through-bond series). Our results indicate that this new scheme can properly account for ET coupling arising from both through-bond and through-space mechanisms.     

Singlet excitation energies of thiophene derivatives of fluorene: TD‐DFT study

Fluorene‐thiophene (FT)‐based oligomers and polymers and their derivatives are good candidates for organic blue light‐emitting diodes. In this work, the intrinsic properties of the ground and excited states of FT monomer and its derivatives are studied. The ground‐state optimized structures and energies are obtained using molecular orbital theory and density functional theory (DFT). The ground‐state potential energy curves or surfaces of FT and its derivatives are also obtained. All derivatives are nonplanar in their electronic ground states. The character and energy of the first 20 singlet–singlet electronic transitions are investigated by applying the time‐dependent density functional theory (TD‐DFT) approximations to the correspondingly optimized ground‐state geometries. The lowest singlet state is studied with the configuration interaction (singles) approach (CIS). Excitation energies are red shifted when the FT unit or its derivatives are extended longitudinally. CIS results suggest geometry relaxation in the first singlet excited state. When available, a comparison is made with experimental results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Scaled second-order perturbation corrections to configuration interaction singles: efficient and reliable excitation energy methods

Two modifications of the perturbative doubles correction to configuration interaction with single substitutions (CIS(D)) are suggested, which are excited state analogues of ground state scaled second-order M?ller-Plesset (MP2) methods. The first approach employs two parameters to scale the two spin components of the direct term of CIS(D), starting from the two-parameter spin-component scaled (SCS) MP2 ground state, and is termed SCS-CIS(D). An efficient resolution-of-the-identity (RI) implementation of this approach is described. The second approach employs a single parameter to scale only the opposite-spin direct term of CIS(D), starting from the one-parameter scaled opposite-spin (SOS) MP2 ground state, and is called SOS-CIS(D). By utilizing auxiliary basis expansions and a Laplace transform, a fourth-order algorithm for SOS-CIS(D) is described and implemented. The parameters that describe SCS-CIS(D) and SOS-CIS(D) are optimized based on a training set that includes valence excitations of various organic molecules and Rydberg transitions of water and ammonia, and they significantly improve upon CIS(D) itself. The accuracy of the two methods is found to be comparable. This arises from a strong correlation between the same-spin and the opposite-spin portions of the excitation energy terms. The methods are successfully applied to the zincbacteriochlorin-bacteriochlorin charge-transfer transition, for which time-dependent density functional theory, with presently available exchange-correlation functionals, is known to fail. The methods are also successfully applied to describe various electronic transitions outside of the training set. The efficiency of the SOS-CIS(D) and the auxiliary basis implementation of CIS(D) and SCS-CIS(D) are confirmed with a series of timing tests.     

From electronic excited state theory to the property predictions of organic optoelectronic materials

We introduce here a work package for a National Natural Science Foundation of China Major Project. We propose to develop computational methodology starting from the theory of electronic excitation processes to predicting the opto-electronic property for organic materials, in close collaborations with experiments. Through developing methods for the electron dynamics, considering superexchange electronic couplings, spin-orbit coupling elements between excited states, electron-phonon relaxation, intermolecular Coulomb and exchange terms we combine the statistical physics approaches including dynamic Monte Carlo, Boltzmann transport equation and Boltzmann statistics to predict the macroscopic properties of opto-electronic materials such as light-emitting efficiency, charge mobility, and exciton diffusion length. Experimental synthesis and characterization of D-A type ambipolar transport material as well as novel carbon based material will provide a test ground for the verification of theory.     

Double-hybrid density functional theory for excited electronic states of molecules

Double-hybrid density functionals are based on a mixing of standard generalized gradient approximations (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixture of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), respectively. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chemistry applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent density functional theory (TD-DFT) or the closely related Tamm-Dancoff approximation (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to configuration interaction with singles (CIS(D)) wave functions developed some years ago by Head-Gordon et al. [Chem. Phys. Lett. 219, 21 (1994)] is computed on the basis of density functional data and added to the TD(A)-DFTGGA excitation energy. The method is implemented by applying the resolution of the identity approximation and the efficiency of the code is discussed. Extensive tests for a wide variety of molecules and excited states (of singlet, triplet, and doublet multiplicities) including electronic spectra are presented. In general, rather accurate excitation energies (deviations from reference data typically <0.2 eV) are obtained that are mostly better than those from standard functionals. Still, systematic errors are obtained for Rydberg (too low on average by about 0.3 eV) and charge-transfer transitions but due to the relatively large ax parameter (0.53), B2PLYP outperforms most other functionals in this respect. Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts. The (D) correction often works in the right direction and compensates for the overestimation of the transition energy at the TD level due to the elevated fraction of HF exchange in the hybrid GGA part. Finally, the limitations of the method are discussed for challenging systems such as transition metal complexes, cyanine dyes, and multireference cases.     

Third- and fourth-order perturbation corrections to excitation energies from configuration interaction singles

Complete third-order and partial fourth-order Rayleigh-Schrodinger perturbation corrections to excitation energies from configuration interaction singles (CIS) have been derived and termed CIS(3) and CIS(4)(P). They have been implemented by the automated system TENSOR CONTRACTION ENGINE into parallel-execution programs taking advantage of spin, spatial, and index permutation symmetries and applicable to closed- and open-shell molecules. The consistent use of factorization, first introduced by Head-Gordon et al. in the second-order correction to CIS denoted CIS(D), has reduced the computational cost of CIS(3) and CIS(4)(P) from O(n(8)) and O(n(6)) to O(n(6)) and O(n(5)), respectively, with n being the number of orbitals. It has also guaranteed the size extensivity of excited-state energies of these methods, which are in turn the sum of size-intensive excitation energies and the ground-state energies from the standard M?ller-Plesset perturbation theory at the respective orders. The series CIS(D), CIS(3), and CIS(4)(P) are usually monotonically convergent at values close to the accurate results predicted by coupled-cluster singles and doubles (CCSD) with a small fraction of computational costs of CCSD for predominantly singly excited states characterized by a 90%-100% overlap between the CIS and CCSD wave functions. When the overlap is smaller, the perturbation theory is incapable of adequately accounting for the mixing of the CIS states through higher-than-singles sectors of the Hamiltonian matrix, resulting in wildly oscillating series with often very large errors in CIS(4)(P). Hence, CIS(3) and CIS(4)(P) have a rather small radius of convergence and a limited range of applicability, but within that range they can be an inexpensive alternative to CCSD.     

Structures and binding energies of the (dibenzoylmethanato)boron difluoride complexes with aromatic hydrocarbons in the ground and excited states. Density functional theory calculations

Structures of the (dibenzoylmethanato)boron difluoride molecule (DBMBF2) and its complexes with a series of aromatic hydrocarbons (benzene; toluene; o-, m-, and p-xylenes, naphthalene; anthracene; and pyrene) in the ground and the first singlet excited states have been calculated. The calculations have been performed by the density functional theory (DFT) and time-dependent density functional theory (TDDFT) for the ground and excited states, respectively, with the empirical dispersion correction. It has been shown that the complexes in the ground and excited states have similar stacking structures and are characterized by short contacts between the F atom of DBMBF2 and H atoms of the hydrocarbon molecule, which decrease on transition from the ground to the excited state. The calculated binding energies in the complexes in the excited state are two to three times higher than those in the ground state. The charge transfer in the ground state of the complexes is insignificant and directed from DBMBF2 to the ligand, while in the excited state it is 0.6–0.8 e and directed from the ligand to DBMBF2.