Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

The Tamm–Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree–Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin–spin coupling constant. Particular attention is paid to the accuracy of the triplet spin–dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalised in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin–spin coupling constants is highlighted by this comparison.     

Theoretical study on the influence of ancillary ligand on the energy and optical properties of heteroleptic phosphorescent Ir(III) complexes

The geometries, energies, and electronic properties of a series of phosphorescent Ir(III) complexes including FIrpic, FIrmpic, FIrpca, and FIrprza have been characterized within density functional theory DFT calculations, which can reproduce and rationalize experimental results. The properties of excited states of the Ir(III) complexes were characterized by the configuration interaction with single-excitation (CIS) method. The ground- and excited-state geometries were optimized at the B3LYP/LANL2DZ and CIS/LANL2DZ levels, respectively. The absorption and phosphorescence wavelengths were computed based on the optimized ground- and excited-state geometries, respectively, by the time-dependent density functional theory (TD-DFT) methods. All the energies have been calculated by B3LYP method. The predictions revealed that the nature of the ancillary ligands can influence the distributions of frontier molecular orbitals and their energies, resulting in impact on the transition character and change in the emission color. In addition, the charge of transport quality has been estimated approximately by the predicted reorganization energy (λ). Our result also indicates that the substituent groups and different auxiliary ligand not only change the character of transition but also affect the rate and balance of charge transfer.     

双原子分子激发态势能的自旋相关局域Hartree-Fock密度泛函理论方法

基于自旋相关局域Hartree-Fock (SLHF)势函数,本文提出了一种计算双原子分子激发态势能的密度泛函理论(DFT)方法,并将该方法应用于和的激发态势能曲线的计算。在只考虑交换能的情况下,本文的DFT计算结果与文献中精确方法和Hartree-Fock (HF)方法的结果符合的非常好,说明采用SLHF势函数作为交换势的DFT方法是一个很好的计算激发态势能的方法。本文还计算和探讨了电子的关联势函数和关联能,发现传统的近似方法在较大核间距的情况下大大低估了电子的关联能.     

Density functional approximation for van der Waals fluids： based on hard sphere density functional approximation

A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.     

Excited-state hydrogen bonding dynamics of methyl isocyanide in methanol solvent: A DFT/TDDFT study

The time-dependent density functional theory (TDDFT) method was performed to investigate the hydrogenbonding dynamics of methyl cyanide (MeNC) as hydrogen bond acceptor in hydrogen donating methanol (MeOH) solvent. The ground-state geometry optimizations and electronic transition energies and corresponding oscillation strengths of the low-lying electronically excited states for the isolated MeNC and MeOH monomers, the hydrogen-bonded MeNC-MeOH dimer and MeNC-2MeOH trimer are calculated by the DFT and TDDFT methods, respectively. An intermolecular hydrogen bond N≡C…H-O is formed between MeNC and methanol molecule. According to Zhao’s rule on the excited-state hydrogen bonding dynamics, we find the intermolecular hydrogen bonds N≡C…H-O are strengthened in electronically excited states of the hydrogen-bonded MeNC-MeOH dimer and MeNC-2MeOH trimer, with the excitation energy of a related excited state being lowered and electronic spectral redshifts being induced. Furthermore, the hydrogen bond strengthening in the electronically excited state plays an important role on the photophysics and photochemistry of MeNC in solutions     

Excited states from range-separated density-functional perturbation theory

We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory and an extension of the Görling–Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the hydrogen molecule. The first-order correction within this perturbation theory improves significantly the total ground- and excited-state energies of the different systems. However, the excitation energies mostly deteriorate with respect to the zeroth-order ones, which may be explained by the fact that the ionisation energy is no longer correct for all interaction strengths. The second (Görling–Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.     

Opto-electronic properties of low band gap fused-ring thieno[3,4-b]pyrazine analogues – A theoretical study

The structural, optical and ionic properties of thieno[3,4-b]pyrazine (TP) analogues have been studied using quantum chemical methods. The density functional theory (DFT) and time-dependent density functional theory (TD-DFT) methods were employed to optimise the ground- and excited-state geometries of TP analogues. Based on the ground- and excited-state geometries, the absorption and emission spectra have been calculated by using TD-DFT method with 6-311G(d,p) basis set. All the calculations were carried out in gas phase and in acetonitrile and chloroform medium. The solvent-phase calculations were performed using the polarisable continuum model (PCM). It has been observed that the effect of medium on the calculated absorption and emission spectra of these analogues is negligible. The calculated absorption and emission spectra are in good agreement with the available experimental results. This theoretical investigation shows that the fused-ring thieno[3,4-b]pyrazine analogues dibenzo[f,h]thieno[3,4-b]quinoxalines and thieno[3′,4′:5,6]pyrazino[2,3-f][1,10] phenanthroline have lower band gap than the thieno[3,4-b]pyrazine. Hence, these analogues can be used for the production of low band gap conjugated polymers.     

The coupling constant averaged exchange–correlation energy density

ABSTRACT

The exchange–correlation energy, central to density-functional theory, may be represented in terms of the coupling constant averaged (CCA) exchange–correlation energy density. We present an approach to calculate the CCA energy density using accurate ab initio methods and its application to simple atomic systems. This function provides a link between intrinsically non-local, many-body electronic structure methods and simple local and semi-local density-functional approximations (DFAs). The CCA energy density is resolved into separate exchange and correlation terms and the features of each compared with those of quantities commonly used to construct DFAs. In particular, the more complex structure of the correlation energy density is found to exhibit features that align well with those present in the Laplacian of the density, suggesting its role as a key variable to be used in the construction of improved semi-local correlation functionals. The accurate results presented in this work are also compared with those provided by the Laplacian-dependent Becke–Roussel model for the exchange energy.     

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACT

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.     

Lowest Π–Π* electronic transitions in linear and two-dimensional polycyclic aromatic hydrocarbons: enhanced electron density edge effect

Polycyclic aromatic hydrocarbons (PAHs) form an important class of molecules as they are ubiquitous, pollute air and cause severe health problems. Lowest vertical π–π* singlet–singlet or triplet–triplet excitation energies and corresponding oscillator strengths were studied for several linear and two-dimensional PAHs employing time-dependent density functional theory. Excited-state electron density, molecular electrostatic potential (MEP) and spin density distributions in the PAHs, along with ground-state chemical hardness, were also studied. It has been found that, generally, excitation energies and oscillator strengths decrease with increase in PAH size, and excitation energies and chemical hardness are strongly linearly correlated. Enhanced electron density edge effect, which was found to occur in the ground states of the molecules, continues to hold in their excited states also. A strong similarity between the ground and π–π* excited-state MEP maps suggests that σ electrons are the main contributors to the enhanced electron density at the edges. Due to their strong electronic absorption transitions in the visible and infrared regions, the PAHs can be used for harnessing solar energy efficiently.     

Assessment of oscillator strengths with multiconfigurational short-range density functional theory for electronic excitations in organic molecules

ABSTRACT

We have in a series of recent papers investigated electronic excited states with a hybrid between a complete active space self-consistent field (CASSCF) wave function and density functional theory (DFT). This method has been dubbed the CAS short-range DFT method (CAS–srDFT). The previous papers have primarily focused on the excitation energies, and not on the oscillator strengths, although they comprise an important part of the absorption spectrum. In this study, we have carried out a quantitative analysis of oscillator strengths obtained with CAS–srDFT. As target molecules, we have considered the large collection of organic molecules whose excited states were investigated with a range of electronic structure methods by Thiel et al. As a by-product of our calculations of oscillator strengths, we also obtain electronic excitation energies, which enable us to compare the performance of CAS–srPBE for excitation energies, using a larger set of chromophores compared to previous studies.     

Fractional-charge and fractional-spin errors in range-separated density-functional theory

ABSTRACT

We investigate fractional-charge and fractional-spin errors in range-separated density-functional theory (DFT). Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation density functional, and the RSH+MP2 method which adds long-range, second-order Møller-Plesset (MP2) correlation. Results on atoms and molecules show that the fractional-charge errors obtained in RSH are much smaller than in the standard Kohn-Sham (KS) scheme applied with semilocal or hybrid approximations, and also generally smaller than in the standard HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than standard MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation density-functional approximations are smaller than the corresponding contributions for the full-range exchange and correlation density-functional approximations, RSH gives fractional-spin errors that are larger than in the standard KS scheme and only slightly smaller than in standard HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-separated DFT approaches for eliminating self-interaction and static-correlation errors.     

Electron correlation and the stability of substituted alkenes

Isomerization energies for hexenes (C₆H₁₂) were evaluated with ab initio (Hartree–Fock (HF), MP2, SCS‐MP2, and CCSD(T)) and several density functional approximation (DFA) methods. CCSD(T)/6‐311+G(2d,p) energies were taken as a benchmark standard. The HF method incorrectly predicts that monosubstituted alkenes are more stable than multiply‐substituted alkenes. DFAs generally predict the correct stability trends of alkenes (mono‐, < di‐, < tri‐, < tetra‐substituted alkenes) but errors in popular functionals, such as B3LYP, can be as large as errors found for alkane hydrocarbon thermochemistries. Some of the HF error is traced back to deficiencies in modeling 1,3‐geminal and 1,4‐vicinal alkyl–alkyl group interactions, called vinylbranches, and changes in C? C and C? H bond types (sp³–sp² C? C to sp³–sp³ C? C and sp³ C? H to sp² C? H). The latter is shown to be more significant. Comparison of CCSD(T) energies of trans‐2‐butene with 2‐methylpropylene and cis‐2‐butene suggests that geminal vinylbranches are stabilizing while vicinal vinylbranches are destabilizing. B3LYP and other DFAs have much smaller errors than HF theory due to inclusion of correlation energy that better reproduces bond type changes. Copyright © 2011 John Wiley & Sons, Ltd.     

Theoretical studies of the structures and optical properties of the bifluorene and its derivatives

The ground and excited structures of the molecules are compared basis on the calculated by HF and CIS, respectively. The ionization potentials (IPs), electron affinities (EAs) and HOMO–LUMO gaps (ΔE_HOMO–LUMO) of the oligomers are studied by the density functional theory (DFT) with B3LYP functional while the vertical excitation energies (E_gs) and the maximal absorption wavelength λ_abs of oligomers of bifluorene and its derivatives DFE, DFA, DFBT, FDBO, and FSCHD are studied employing the time dependent density functional theory (TD‐DFT) and ZINDO. Compared with BF, the derivatives DFE, DFA, and DFBT are better conjugated, easier to give an electron or a hole, as well as get an electron or a hole. Their HOMO–LUMO gaps are narrower and they have lower vertical excitation energies. The absorption and emission spectra of them are red shifting. However, FDBO and FSCHD are in the other way round. It is important that FDBO and FSCHD are good blue emitters. Copyright © 2007 John Wiley & Sons, Ltd.     

电子激发和溶剂效应对芴酮-甲醇分子间氢键增强现象的理论研究 (cited: 1)

理论研究了电子激发和溶剂效应导致的芴酮-甲醇复合体系中分子间氢键增强现象．通过基态和激发态性质的计算,不仅展示了分子间氢键键长的变化以及变化在振动光谱中的影响,而且揭示了导致氢键变化的内在物理机制：溶质分子的电子激发及溶剂化效应引起的电子重新分布,增大了溶质和溶剂分子的偶极矩,导致了它们之间的相互作用的增大,并最终加强了分子间氢键的强度．还分别对处于液相及气相中的复合体的基态和激发态的几何结构、红外谱、复合体及构成分子的偶极矩进行了理论计算,结果阐明了电子激发与溶剂化效应对氢键变化的贡献,同时还发现只有进一步引入溶剂化效应,复合体的基态、激发态的性质才能与实验达到精确一致．所有激发态均采用所开发的基于含时密度泛函理论解析计算一阶、二阶激发态能量导数的方法．     

Sum-rules of the response potential in the strongly-interacting limit of DFT

The response part of the exchange-correlation potential of Kohn–Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.     

Generalized density-functional theory: extended weighted density approaches

A third-order density-functional theory is introduced by an approach that may be used to find density-functional theories to any higher-order accuracy provided only that known homogeneous state correlation functions are utilized as input. It is constructed from the required knowledge of a single weight function at each order. By way of application results are presented for the melting of classical hard spheres using functionals accurate to a third-order functional Taylor series in the homogeneous limit. Within the framework of the modified weighted density approximation, there is a uniform improvement in the solid phase-free energies, pressures and melting parameters, and further improvement also results when these functionals are optimized in a way that utilizes the close packing limit. The sensitivity of the results to existing and proposed models of the third-order direct correlation function is discussed.     

Bayesian error estimation in density-functional theory

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.     

Density Functional Study on Relative Energies, Structures, and Bonding of Low-lying Electronic States of Lutetium Dimer

用密度泛函理论方法研究了镥二聚体(Lu₂)低能量电子态的性质,计算了电子态相对能量、平衡键长、振动频率以及基态解离能,考察了密度泛函性质、相对论有效势种类以及Hartree-Fock交换作用大小对计算结果的影响．结果表明,无论采用何种密度泛函和相对论有效势,体系的基态都为三重态,与其他一些基于分子轨道理论的从头计算方法得到的结论是一致的．另外,与分子轨道从头计算结果以及实验结果比较发现,采用杂化密度泛函理论和Stuttgart小核有效势计算得到的结果总体吻合最好．最后,特别分析研究了B3LYP计算中Hartree-Fock交换作用大小对基态键长和基态解离能的影响,发现随着交换作用的增大,键长增长,解离能减小,这是由于5d轨道杂化导致的共价成键作用减弱造成的．