密度矩阵重正化群计算电子激发态的算法比较研究

激发态电子结构计算是理论与计算化学领域中的重要问题.本文测试了密度矩阵重正化群理论的state specific激发态算法,并在Pariser-Parr-Pople(PPP)模型下以并苯体系和聚乙炔体系为例对state specific算法和传统的态平均激发态算法进行了比较.计算结果表明,state specific算法可以正确地跟踪较低的激发态,并能得到比态平均算法更精确的能量本征值;在高激发态的计算过程中,state specific算法可能出现收敛于错误本征态的问题.     

理论研究连接方式对低聚(3-己基噻吩)结构和电子光谱的影响

用密度泛函理论优化了不同连接方式的低聚(3-己基噻吩)((3HT)n,n=2~8)异构体的几何结构,并得到了相对能量,接着用含时密度泛函理论计算了不同异构体的垂直激发能,并优化了(3HT)8第一激发态的几何结构.结果表明,不同连接方式异构体的相对能量接近,但它们的轨道能级和垂直激发能差异都较大;第一激发态比基态共平面性更好.     

PP体系双荧光及分子内电荷转移的理论研究

用含时密度泛函理论（TDDFF）对PP（5-phenyl-5H-phenanthridin-6-one）分子进行了量子化学计算．实验观察到该分子具有双荧光和分子内电荷转移（ICT）特征．理论计算采用B3LYP泛函和6-311＋G（2d,p）基组,并用可极化连续介质模型（PCM）处理溶剂效应．基态结构优化表明PP分子为非平面状,苯环和菲啶酮平面的二面角近似等于90．0°．气相和溶剂中低激发态的计算结果表明这些激发态均为局域激发（LE）．通过构建气相和溶液中LE—ICT反应和荧光发射的势能曲线,得到了ICT反应的焓变△H、能垒Ea以及由于结构弛豫所产生的能量差δEFC．势能曲线的分析和发射能的计算显示PP是一个双荧光体系,包含一个LE发射谱和一个红移的ICT谱．考虑了溶剂效应的计算结果表明,双荧光的产生是由于在ICT反应过程中分子构型的变化,即苯环和菲啶酮单元由相互垂直变成了共平面．     

3,9-咔唑聚合物基态和激发态性质的理论研究

用密度泛函B3LYP方法对3,9-咔唑低聚物[(3,9-carbazole)n(n=1,2,3,4,6,8)]体系进行了全优化, 计算得到电离能、电子亲合势、空穴抽取能及电子抽取能等相关能量, 用ZINDO和TD-DFT方法计算得到吸收光谱; 分析了各种能量的变化及光谱规律. 用外推法由低聚物分子的各种性质与聚合度n相联系得到高聚物的性质, 将所得结果与2,7-咔唑(2,7-carbazole)及类似聚合物进行了比较分析. 结果表明, 3,9位聚合的咔唑整体共轭程度降低, 光谱蓝移, 其IP值和聚芴相近, 可以作为空穴接受材料应用于多层电子荧光器件的空穴传输层. 用CIS方法进行优化得到部分分子的S1激发态结构, 用ZINDO和TD-DFT方法得到对应的发射光谱.     

9,9’-螺双芴的光电性能

采用密度泛函理论(DFT)-B3LYP/6-31G(d)方法对9,9'-螺双芴低聚物[(SBF)n(n=1-4)]体系进行全优化, 得到各分子的最高占据轨道(HOMO)和最低空轨道(LUMO)能量及HOMO-LUMO能隙, 结果表明各分子整体表现出很好的共轭性质. 并在分子的阳离子和阴离子状态的优化结构基础上, 计算得到电离势(IP)、电子亲和势(EA)、空穴抽取能(HEP)、电子抽取能(EEP)和重组能等相关能量. 利用单激发组态相互作用(CIS)/3-21G方法优化得到9,9'-螺双芴单体的S1激发态的几何构型. 用含时密度泛函理论(TD-DFT)方法计算得到了分子吸收光谱和荧光光谱的相关数据. 随着聚合长度的增加, 能隙变窄, 空穴注入和电子转移的能力都相应提高, 吸收光所需能量减小, 吸收强度(f)增大, 光谱红移. 采用线性外推法, 利用低聚物分子的各种性质与聚合度n之间的关系, 得到高聚物的相应性质.为考察9位螺芴化的影响, 将(SBF)n的相关性质与母体芴的低聚物[(FL)n(n=1-4)]进行比较, 由两者的计算结果对比显示, 在芴的9位螺芴化可以提高电子和空穴的传输能力, 并同时保留芴优良的发光性质.     

9,9′-螺双芴的光电性能

采用密度泛函理论(DFT)-B3LYP/6-31G(d)方法对9,9'-螺双芴低聚物[(SBF)_n(n=1-4)]体系进行全优化,得到各分子的最高占据轨道(HOMO)和最低空轨道(LUMO)能量及HOMO-LUMO能隙,结果表明各分子整体表现出很好的共轭性质.并在分子的阳离子和阴离子状态的优化结构基础上,计算得到电离势(IP)、电子亲和势(EA)、空穴抽取能(HEP)、电子抽取能(EEP)和重组能等相关能量.利用单激发组态相瓦作用(CIS)/3-21G方法优化得到9,9'-螺双芴单体的S_1激发态的几何构型.用含时密度泛函理论(TD-DFT)方法计算得到了分子吸收光谱和荧光光谱的相关数据.随着聚合长度的增加,能隙变窄,空穴注入和电子转移的能力都相应提高,吸收光所需能量减小,吸收强度(f)增大,光谱红移.采用线性外推法,利用低聚物分子的各种性质与聚合度n之间的关系,得到高聚物的相应性质.为考察9位螺芴化的影响,将(SBF)_n的相关性质与母体芴的低聚物[(FL)_n(n=1-4)]进行比较,由两者的计算结果对比显示,在芴的9位螺芴化可以提高电子和空穴的传输能力,并同时保留芴优良的发光性质.     

芴与苯并硒化二唑共聚物的电子结构和光谱性质的理论研究

用密度泛函B3LYP方法对低聚体(DEF-BSeD)n(n=1~4)[其中9,9二乙基芴(DEF)单元与苯并硒化二唑(BSeD)单元的摩尔比分别为1∶1和2∶1]进行全优化, 计算电离能(PI)、电子亲和势(EA)和能隙(ΔH-L), 在基态结构的基础上用TD-DFT和ZINDO方法计算激发能和电子吸收光谱, 并利用外推法得到高聚物的相应性质. 从外推结果看出, 随着聚合物中BSeD比例的增大, 聚合物的最低单激发能呈减小的趋势, 最大电子吸收光谱红移. 用CIS方法优化得到单体的S1激发态结构, 计算结果表明, 激发态的结构更趋近于平面构型.     

线性响应和两种态特定方法模拟AF350电子跃迁的溶剂效应

在极化连续模型框架下比较了线性响应与两种不同态特定方法计算的溶液中Alexa Fluor 350(AF350)分子激发能和光谱移动值的差异. AF350的第一激发态S0→S1电子跃迁属于π→π^*跃迁, 主要对应于最高占据分子轨道(HOMO)到最低空轨道(LUMO)的跃迁. 该分子激发态偶极矩大于基态偶极矩, 激发态时溶质溶剂相互作用比基态时更强, 随着溶剂极性增大, 会发生光谱红移的现象. 与实验值相比, 线性响应和两种态特定方法均高估了激发能, 其中以IBSF(Improta-Barone-Scalmani-Frisch)方法得到的激发能最小, 矫正的基态反应场方法(cGSRF)得到的激发能最大. 对于光谱移动值, 3种方法与实验值相比都偏小, 线性响应方法(LR)计算出的误差最大, 而IBSF方法得到的结果与实验值最吻合, 是预测溶液中AF350分子激发能和光谱移动值最准确的方法. 对比了Marcus传统理论和基于约束平衡的非平衡溶剂化理论的结果, 发现后者得到的激发能和光谱移动值更接近于实验值.     

四氢二嵌萘衍生物在不同环境中的电子结构及光谱特征的理论研究

采用密度泛函理论的B3LYP泛函和单激发组态相关方法(CIS)在6-31+G*基组水平下分别优化了四氢二嵌萘衍生物(THP)基态和第一单重激发态的结构,并在此基础上利用含时密度泛函理论计算了THP在不同环境中的电子结构和光谱性质.溶剂效应采用连续极化介质模型(PCM)计算.结构分析发现在酸性环境中,基态时THP二甲氨基上的N原子容易质子化.计算结果表明,尽管THP的第一单重激发态是一个电荷转移态,但是它本身并不发射双荧光.在酸性溶剂中,THP的双峰发射来源于两种物质:跃迁能为2.71eV的发射峰由激发的THP发射,而3.69eV的发射峰则来源于质子化的THP.根据计算结果,我们建议了THP在酸性溶剂中的激发与驰豫途径.理论预测的吸收和发射光谱与实验结果一致.     

三维荧光光谱二阶校正方法测定血浆样中喷昔洛韦及泛昔洛韦含量

利用三维荧光光谱即激发发射矩阵荧光光谱与化学计量学的基于平行因子分析(PARAFAC)算法的二阶校正方法相结合,尝试对血浆样中泛昔洛韦及其活性代谢物喷昔洛韦的含量进行同时定量测定.当算法选取组分数为3时,解析得到血浆样中泛昔洛韦和喷昔洛韦的平均回收率分别为(102.4±3.4)%和(105.1±2.3)%.结果表明该分析策略可准确可靠地实现血浆样中泛昔洛韦和喷昔洛韦的直接同时快速定量测定.     

Local pair natural orbitals for excited states

We explore how in response calculations for excitation energies with wavefunction based (e.g., coupled cluster) methods the number of double excitation amplitudes can be reduced by means of truncated pair natural orbital (PNO) expansions and localized occupied orbitals. Using the CIS(D) approximation as a test model, we find that the number of double excitation amplitudes can be reduced dramatically with minor impact on the accuracy if the excited state wavefunction is expanded in state-specific PNOs generated from an approximate first-order guess wavefunction. As for ground states, the PNO truncation error can also for excitation energies be controlled by a single threshold related to generalized natural occupation numbers. The best performance is found with occupied orbitals which are localized by the Pipek-Mezey localization. For a large test set of excited states we find with this localization that already a PNO threshold of 10(-8)-10(-7), corresponding to an average of only 40-80 PNOs per pair, is sufficient to keep the PNO truncation error for vertical excitation energies below 0.01 eV. This is a significantly more rapid convergence with the number doubles amplitudes than in domain-based local response approaches. We demonstrate that the number of significant excited state PNOs scales asymptotically linearly with the system size in the worst case of completely delocalized excitations and sub-linearly whenever the chromophore does not increase with the system size. Moreover, we observe that the flexibility of state-specific PNOs to adapt to the character of an excitation allows for an almost unbiased treatment of local, delocalized and charge transfer excited states.     

Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

Potential-energy surfaces of local excited states from subsystem- and selective Kohn-Sham-TDDFT

Calculating excited-state potential-energy surfaces for systems with a large number of close-lying excited states requires the identification of the relevant electronic transitions for several geometric structures. Time-dependent density functional theory (TDDFT) is very efficient in such calculations, but the assignment of local excited states of the active molecule can be difficult. We compare the results of the frozen-density embedding (FDE) method with those of standard Kohn-Sham density-functional theory (KS-DFT) and simpler QM/MM-type methods. The FDE results are found to be more accurate for the geometry dependence of excitation energies than classical models. We also discuss how selective iterative diagonalization schemes can be exploited to directly target specific excitations for different structures. Problems due to strongly interacting orbital transitions and possible solutions are discussed. Finally, we apply FDE and the selective KS-TDDFT to investigate the potential energy surface of a high-lying π → π^∗ excitation in a pyridine molecule approaching a silver cluster.     

Calculation of excited-state properties using general coupled-cluster and configuration-interaction models

Using string-based algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupled-cluster (CC) models within CC linear-response (LR) theory which is equivalent to the equation-of-motion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linear-response theory. The presented procedures are applicable to both single-reference-type and multireference-type CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LR-CC/EOM-CC and configuration-interaction approaches for excited states is compared. The effect of higher excitations on excited-state properties is demonstrated in benchmark calculations for NH(2) and NH(3). As a first application, the stationary points of the S(1) surface of acetylene are characterized by high-accuracy calculations.     

Ligand localized triplet excited states in platinum(II) bipyridyl and terpyridyl peryleneacetylides

An investigation of the photophysics of two complexes, [Pt((t)Bu3tpy)(C triple bond C-perylene)]BF4 (1) and Pt((t)Bu2bpy)(C triple bond C-perylene)2 (2), where (t)Bu3tpy is 4,4',4'-tri( tert-butyl)-2,2':6',2'-terpyridine, (t)Bu2bpy is 4,4'-di( tert-butyl)-2,2'-bipyridine, and C triple bond C-perylene is 3-ethynylperylene, reveals that they both exhibit perylene-centered ligand localized excited triplet states ((3)IL) upon excitation with visible light. These complexes do not display any significant photoluminescence at room temperature but readily sensitize (1)O2 in aerated CH2Cl2 solutions, as evidenced by its characteristic emission near 1270 nm. The transient absorption difference spectra were compared to bi- and tridentate phosphine peryleneacetylides intended to model the (3)IL peryleneacetylide excited states in addition to the related phenylacetylide-bearing polyimine analogues, with the latter model being the respective triplet charge-transfer ((3)CT) excited states. The transient difference spectra of the two title compounds display excited-state absorptions largely attributable to perylene localized (3)IL states yet exhibit somewhat attenuated excited-state lifetimes relative to those of the phosphine model chromophores. The abbreviated lifetimes in 1 and 2 may suggest the involvement of the energetically proximate (3)CT triplet state exerting an influence on excited-state decay, and the effect appears to be stronger in 1 relative to 2, consistent with the energies of their respective (3)CT states.     

Self-consistent field calculations of excited states using the maximum overlap method (MOM)

We present a simple algorithm, which we call the maximum overlap method (MOM), for finding excited-state solutions to self-consistent field (SCF) equations. Instead of using the aufbau principle, the algorithm maximizes the overlap between the occupied orbitals on successive SCF iterations. This prevents variational collapse to the ground state and guides the SCF process toward the nearest, rather than the lowest energy, solution. The resulting excited-state solutions can be treated in the same way as the ground-state solution and, in particular, derivatives of excited-state energies can be computed using ground-state code. We assess the performance of our method by applying it to a variety of excited-state problems including the calculation of excitation energies, charge-transfer states, and excited-state properties.     

On the accuracy of computed excited-state dipole moments

The dipole moments of furan and pyrrole in many electronically excited singlet states have been determined using coupled cluster theory including large one-electron basis sets. The inclusion of connected triple excitations is shown to uniformly decrease the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) excitation energies by 0.04-0.24 eV, with an average reduction of 0.08 eV. Using a basis set larger than DZP (++)D (double-zeta plus polarization augmented with atom- and molecule-centered diffuse functions) uniformly increases the computed EOM-CCSD excitation energies by 0.03-0.29 eV, with an average increase of 0.20 eV. The corresponding shifts in excited-state dipole moments are more erratic. Including connected triple excitations changes the computed dipole moments by an rms amount of 0.17 au. More importantly, using a larger basis set shifts the dipole moments by an rms amount of 0.52 au, with an increase or a decrease being equally likely. The CC dipole moments are compared to those from time-dependent density functional theory (TD-DFT) computed by Burcl, Amos, and Handy [ Chem. Phys. Lett. 2002, 355, 8]. For 29 excited states of furan and pyrrole, the predicted TD-DFT dipole moments differ from the CC results by rms amounts of 1.6 au (HCTH functional) and 1.5 au (B97-1 functional). Including the asymptotic correction to TD-DFT developed by Tozer and Handy [ J. Chem. Phys. 1998, 109, 10180; J. Comput. Chem. 1999, 20, 106] reduces the rms differences for both functionals to 1.2 au. If those Rydberg excited states with very large polarizabilities are excluded, the rms differences from the CC results for the remaining 17 excited states become 1.31 au (HCTH) and 0.88 au (B97-1). For asymptotically corrected functionals and this subset of states, the rms differences from the CC results are only 0.54 au (HCTHc) and 0.34 au (B97-1c). Thus, the Tozer-Handy asymptotic correction for TD-DFT significantly improves the predictions of excited-state dipole moments. For excited states without very large polarizabilities, good agreement is achieved between excited-state dipole moments computed by coupled cluster theory and by the asymptotically corrected B97-1c density functional.     

Hybrid coupled cluster and molecular dynamics approach: application to the excitation spectrum of cytosine in the native DNA environment

Evolution of the excited state energies of cytosine base in the native DNA environment was investigated using a hybrid coupled cluster and classical molecular dynamics approach. The time averaged excitation energies obtained with the variant of the completely renormalized equation-of-motion with singles, doubles, and non-iterative triples approach that includes a bulk of the correlation effects for excited states, are compared with the analogous calculations in the gas phase. Significant blue shifts for the two lowest singlet excitation energies can be observed as a result of the interaction of the quantum system with the surrounding environment.     

Review of biorthogonal coupled cluster representations for electronic excitation

Single-reference coupled-cluster (CC) methods for electronic excitation are based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in terms of excited CC states, also referred to as correlated excited (CE) states, and an associated set of states biorthogonal to the CE states, the latter being essentially configuration interaction (CI) configurations. The bCC representation generates a non-hermitian secular matrix, the eigenvalues representing excitation energies, while the corresponding spectral intensities are to be derived from both the left and right eigenvectors. Using the perspective of the bCC representation, a systematic and comprehensive analysis of the excited-state CC methods is given, extending and generalizing previous such studies. Here, the essential topics are the truncation error characteristics and the separability properties, the latter being crucial for designing size-consistent approximation schemes. Based on the general order relations for the bCC secular matrix and the (left and right) eigenvector matrices, formulas for the perturbation-theoretical order of the truncation errors (TEO) are derived for energies, transition moments, and property matrix elements of arbitrary excitation classes and truncation levels. In the analysis of the separability properties of the transition moments, the decisive role of the so-called dual ground state is revealed. Due to the use of CE states, the bCC approach can be compared to so-called intermediate state representation (ISR) methods based exclusively on suitably orthonormalized CE states. As the present analysis shows, the bCC approach has decisive advantages over the conventional CI treatment, but also distinctly weaker TEO and separability properties in comparison to a full (and hermitian) ISR method.     

Excited states of GFP chromophore and active site studied by the SAC-CI method: effect of protein-environment and mutations

Excited states of fluorescent proteins were studied using symmetry-adapted cluster-configuration interaction (SAC-CI) method. Protein-environmental effect on the excitation and fluorescence energies was investigated. In green fluorescent protein (GFP), the overall protein-environmental effect on the first excitation energy is not significant. However, glutamine (Glu) 94 and arginine (Arg96) have the red-shift contribution as reported in a previous study (Laino et al., Chem Phys 2004, 298, 17). The excited states of GFP active site (GFP-W22-Ser205-Glu222-Ser65) were also calculated. Such large-scale SAC-CI calculations were performed with an improved code containing a new algorithm for the perturbation selection. The SAC-CI results indicate that a charge-transfer state locates at 4.19 eV, which could be related to the channel of the photochemistry as indicated in a previous experimental study. We also studied the excitation and fluorescence energies of blue fluorescent protein, cyan fluorescent protein, and Y66F. The SAC-CI results are very close to the experimental ones. The protonation state of blue fluorescent protein was determined. Conformation of cyan fluorescent protein indicated by the present calculation agrees to the experimentally observed structure.