多光子吸收与圆二色光学性质及其电子振动光谱的理论研究
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摘要
通过研究光与物质的相互作用,我们可以更好地了解周围的物质世界。使用传统的光源,只有线性光学现象被观测到,激光出现以后,非线性光学作为一门新兴学科迅速发展起来,并在现代激光技术、光学通讯、数据储存、光信息处理等方面显示出诱人的应用前景。寻找非线性光学特性强且响应速度快的新型材料成为这一领域的主要课题之一。本质上说,任何材料都具有非线性光学特性,而线性只是特定情况下的近似。由于有机分子非线性光学材料易于进行合成和加工,宽的响应波段、响应时间短等特点而倍受重视。量子化学计算可以提供有效信息,将分子结构与其光学响应联系起来。理论研究可以从理论上设计新型的分子材料,指导实验合成,提高实验效率。本论文着重解决理论计算与实验结果比较过程中的两大难题:溶剂环境和分子振动的影响。
大部分理论研究都是针对单个分子进行的,而实验上对分子材料光学性质的测量一般是在溶剂中进行的,周围的溶剂分子对溶质分子的结构及其光学性质可能有着重要影响,这就给理论与实验测量结果相比较带来了困难。因此,为了更好的与实验相比较,就需要在理论模型中考虑溶剂环境的影响。本论文采用极化连续模型(PCM)来模拟溶剂环境,将溶剂看作均匀连续电介质,并由其介电常数来表征。当存在外加电磁场时,溶剂分子受其影响会产生一感应场,该感应场反过来会起到屏蔽外加电磁场的作用,这部分效应可以通过所谓的局域场因子来描述。
另外,基于垂直跃迁的理论研究只考虑了电子能级之间的跃迁,忽略了振动能级的贡献,而很多实验往往包含了精细振动结构展开,此外,有很多重要的实验现象可能会隐藏在精细振动结构中,只有在考虑分子振动的影响后才能做出正确的理论解释。因此,正确理解分子振动对光谱性质的影响也是十分必要的。振动耦合理论的复杂性、构造理论模型的难度以及较大的计算量使得分子振动的研究较少。本文基于绝热近似和简谐近似两大理论基石对电子振动光谱进行研究。绝热近似假设电子的运动跟核的运动是可以分开的,当激发态能级离其它能级较远时,绝热近似能对其进行较为可靠的描述。简谐近似是引入分子振动效应时常用并行之有效的近似之一,该近似将原子看作小球(谐振子),把原子间的化学键看作质量可以忽略不计的弹簧。论文主要采用两种绝热简谐振动模型:一种是简谐绝热Franck-Condon(AFC)模型,基于优化后的初、终态平衡构型,可以给出高分辨率的电子振动光谱,并可以对特征峰进行有效标识。另一种是线性耦合模型(LCM),只能提供低分辨率的谱图,但是避免了通常较繁琐的激发态的构型优化,并可以描述电子振动光谱的主要特征。
随着高功率激光的出现,多光子光谱学已经成为研究热点,在生物、化学、材料科学、物理等领域均有着重要应用。由于不同的选择定则,多光子光谱可以给出单光子光谱中所没有给出的新的振动或电子跃迁态。多光子吸收光谱是研究分子结构主要的分析工具之一,本论文侧重研究电荷转移型有机分子的单(OPA)、双(TPA)、三(3PA)光子吸收性质。圆二色光谱,基于左、右旋圆偏振光吸收性质的不同,可以被看作是一种特殊的吸收光谱,是一种与手性相关的性质。这里我们着重研究手性分子的单(ECD)、双(TPCD)光子圆二色光谱性质。
论文研究内容大致可以分为两部分:一是对电子垂直跃迁光谱的研究,即只考虑电子能级的跃迁,而不考虑振动态的贡献;二是综合考虑电子、振动能级贡献,即电子振动光谱的研究。下面简要介绍一下论文的主要研究内容。
一、电子垂直跃迁光谱研究
(1)有机共轭分子多光子吸收性质的半经验量化研究。(论文1、2)
计算多光子吸收截面最直接的方法就是态求和(SOS)公式,而在从头算水平上,利用态求和方法处理分子体系的计算量非常大,因此一般在半经验水平上使用。本论文中,使用半经验的ZINDO程序,结合组态相互作用(CI)方法,计算得出态求和公式所需的分子的跃迁能、偶极矩以及态态之间的跃迁偶极矩,先求得非线性极化率,再进一步计算材料分子的多光子吸收截面。这种半经验方法使得计算精确度受到限制,但是使得在从头算水平上无法实现的较大分子体系多光子吸收性质的研究变为可能。半经验方法已大量用于不同种类分子的非线性光学性质的计算,能够较准确地预测分子性质的变化趋势,因此对于分子构效关系的研究具有重要意义。本论文侧重于构建和测试可靠的理论体系,因此选择了中等尺寸的分子进行研究。
论文1对一系列含有咪唑-噻唑核的Y-型分子的单、双、三光子吸收性质进行了系统研究,计算结果验证了实验结论,指出所研究的分子为很有潜力的多光子吸收材料。分子多光子吸收性质随着电子给体强度的增大而增大。研究发现杂环核心由于其富电子特性,可以提供更多的自由电子以增强分子内电荷转移,从而可以增强多光子吸收强度。另外,Y型设计以及硫磺基作为电子受体均对多光子吸收的增强有着重要作用。
论文2对一系列以三价硼为受体的D-π-A型有机化合物的双光子吸收性质进行了研究。研究表明三甲基苯可以很好的保护三价硼使其不受空气中氧的攻击。只要采用比较庞大的基团对三价硼实施保护,它可以成为很有效的电子受体。在构型优化的基础上,对该分子的双光子吸收强度和峰位进行了报道。
(2)有机共轭分子多光子吸收性质的第一性原理研究。(论文3)
三光子吸收属于五阶非线性光学行为,但是可以通过三阶响应函数的单留数得出的三阶跃迁矩阵元而求得。
论文3中首次应用三阶响应场理论结合极化连续模型对一种高共轭A-π-π-π-A对称芴-衍生体的三光子吸收性质以及溶剂效应进行了研究。文章中详细描述了溶剂环境以及分子构型(尤其是分子平面性)对吸收性质的影响。研究表明,相较气相下,溶剂的极性很大程度地增大了三光子吸收截面值。室温下,该分子可能存在对应于不同二面角的多种构型,而非一种单一平衡构型,因此,只针对单一构型的计算是不充分的。对于大尺寸体系,采用完整的响应理论方法使得计算量变得很大,少态模型的计算量要小得多。研究发现,对于我们所研究的体系,两态模型不能对其三光子吸收性质进行很好的描述,得出结果与完整的响应理论结果相差很大。另外,文中我们将计算结果与实验数据进行了详细比较。
(3)手性分子单、双光子圆二色性光谱第一性原理研究(论文4,5)
论文4中,基于第一性原理,采用密度泛函理论结合无原点依赖性的响应函数对R-(+)-3-methyl-cyclopentanone(R3MCP)分子单、双光子圆二色光谱进行了理论研究。文章对两种最低能量构型进行了分析,对单、双光子圆二色光谱进行了全面的分析和比较,并与其双光子吸收强度和特性进行了对比。几何构型、计算基组、交换相关泛函的影响也进行了详尽的讨论。结果表明新近发展的CAMB3LYP交换相关泛函比起常用的B3LYP泛函能更好地对里德堡态进行描述,得出的谱图能与实验较好的吻合。文章从分子轨道角度对激发态跃迁性质进行了表征,并对单、双光子过程不同的响应作出了相应解释。
论文5首次给出了一种轴向手性分子R-(+)-1,1'-bi(2-naphtol)(RBN)及其对映体S-(-)-1,1'-bi(2-naphtol)(SBN)在溶剂中的TPCD实验光谱。该光谱通过DoubleL-scan技术测得,文中同时给出了相应的理论计算结果。实验分别给出了对应于左、右旋圆偏振光的TPA光谱,两者差值即给出TPCD光谱。跟预期结果相同,实验清晰的指出对映异构体的TPCD光谱性质呈现镜像,即信号完全相反。所研究体系的TPCD光谱表现出与其ECD不同的特性,因而提供了一个很好的范例来说明TPCD可以为ECD的手性识别功能起到很好的补充作用,是一种很有潜力的手性识别工具。在B3LYP/PCM水平上得出的TPCD光谱很好的重复了实验谱型。由于两个相互垂直的萘酚之间只存在很弱的相互作用,导致出现很多简并态,为了涵盖实验给出的光谱范围200-350 nm,计算需要考虑前25个激发态的贡献。计算还表明,该体系的TPCD性质对溶剂环境的影响非常敏感,伴随着信号符号的变化。可以发现,实验谱图主要特征峰均来自不同激发态正负信号的相互抵消作用。
二、电子振动光谱研究
(1)振动效应对单、双光子吸收性质影响的第一性原理研究(论文6,7)
论文6应用LCM振动模型结合密度泛函响应理论对一种D-π-D型二苯乙烯衍生物分子的单、双光子电子振动性质做了系统研究,给出了最低四个激发态的Franck-Condon贡献、Herzberg-Teller贡献、以及总的电子振动光谱,分别用了0.1eV和0.01eV两种洛伦兹展宽系数。首先对于不同的优化方法该分子呈现不同的平面性,结果发现密度泛函方法使得分子趋于平面化,Hartree-Fock能更好的描述分子结构。用0.01eV的光谱展宽系数,显然可以得到更多的单光子吸收电子振动光谱的精细结构,计算发现0-0跃迁是最主要的跃迁方式,而高于2的振动能级可以安全地被忽略掉,而不会对计算结果有什么影响。对应于C-N-C和C-C-C扭曲的振动模式是主要贡献。文中还详细阐述了Herzberg-Teller贡献项的著名的“borrowing mechanism”,它在禁止跃迁态中起到非常重要作用。这项工作属于首次应用线性耦合模型对分子不同激发态的单、双光子吸收电子振动光谱的研究。
在Franck-Condon水平上,同一分子的单、双光子吸收光谱应该有着相同的谱型,而实验上给出的单、双光子吸收电子振动光谱却通常存在差异。论文7结合密度泛函响应理论和线性耦合模型对Franck-Condon和Herzberg-Teller振动贡献不同的作用机制进行分析,指出该差异是由Herzberg-Teller振动效应带来的。该理论机制成功解释了一种杂环分子单、双光子最大吸收峰之间的偏移,并且可推广至具有不同单、双光子吸收态的一般分子。另外值得一提的是,论文7属于首次综合考虑电子振动耦合和溶剂效应对双光子吸收光谱的影响,其中溶剂效应采用极化连续模型进行模拟。
(2)手性分子单光子圆二色电子振动光谱的第一性原理研究(论文8、9)
实验给出了R3MCP分子进行了振动能级展开的ECD光谱,论文8中我们采用LCM模型研究了电子振动耦合效应对该手性分子ECD光谱的影响,并全面考虑Franck-Condon和Herzberg-Teller振动贡献。研究表明后者能够导致单一电子态中存在正负两种相反信号,从而引起分子手性响应性质的变化。这说明对圆二色谱的理论计算如果只考虑垂直跃迁可能导致正负信号出错,振动效应的引入是十分必要的。因手性对映体圆二色信号始终符号相反,实验上常把圆二色信号作为分子构型表征的判据。研究结果无疑对相关实验有着重要的指导价值。
为了更准确的对实验特征峰进行标识,论文9采用能够给出高分辨率谱图的AFC振动模型,在精确描述基态激发态势能面基础上,全面考虑Franck-Condon,Herzberg-Teller,简正模式Duschinsky转动贡献及可能的频率变化对手性分子圆二色谱的影响,并分别对各贡献项进行了详尽的讨论。该方法能对振动精细结构进行准确指认。圆二色信号强度会随着温度的升高而降低,这与实验得出的结论是一致的。值得一提的是,该研究进一步证实了LCM模型所预测的单一电子态中正负信号的变化。但由于信号变化发生在Axial构型,与Equatorial构型的Boltzmann构型比仅为1:9,这就限制了文章给出的理论预测能得到实验验证的可能性。
(3)手性分子双光子圆二色电子振动光谱的第一性原理研究(论文10)
近来,对手性分子TPCD光谱的实验研究取得了很大进展,TPCD结合了ECD和TPA的优点,在手性分子识别应用方面有着巨大潜力,这使得对TPCD电子振动光谱的理论研究也变得重要起来。
论文10结合AFC振动模型与密度泛函响应理论对手性分子R3MCP的双光子圆二色电子振动光谱进行了研究,并与该分子的OPA、ECD、TPA光谱进行了对比。在FC水平上计算所得的分子不同性质的光谱具有相同的振动能级展开,谱型的区别是由HT贡献项带来的。研究发现对于双光子圆二色性这样较为复杂的光学过程,FC/HT干涉项变得相对重要,线性耦合模型在模拟类似性质时表现出局限性。对于双光子圆二色谱,HT同样可以在单一电子态中引入正负两种信号,并且较单光子圆二色谱更为明显,即使使用较大的谱线展宽系数并进行Boltzmann构型平均后,正负信号仍然存在,使其在实验上得到验证变得可能。论文10属于首次对双光子圆二色电子振动光谱的研究。
本论文共由九章组成。第一章为综述,首先简单介绍了线性光学与非线性光学的特点,接着对相关分子光谱进行了介绍,重点讨论了单、双、三光子吸收以及单、双光子圆二色光谱性质,然后对论文中使用的溶剂模型和电子振动光谱理论作了简单说明。第二章简单介绍了论文中用到的基本量子化学理论,主要阐述了以波函数为出发点的量子化学和密度泛函理论。第三章给出了多光子吸收性质的计算方法,其中包括含时微扰理论方法(又称为态求和方法)和响应理论方法。第四章给出了在半经验水平上对多光子吸收性质的研究结果,包括分别对一系列Y型咪唑-噻唑杂环分子和一系列三价硼为受体的共轭分子的研究。第五章给出了基于从头算理论的电子垂直跃迁光谱的研究结果,包括研究溶剂效应对高共轭芴衍生物分子三光子吸收性质的影响以及手性分子单、双光子圆二色光谱的研究。第六章给出了电子振动光谱理论及其计算方法。第七章和第八章分别使用线性耦合模型和简谐绝热Franck-Condon模型对分子的电子振动光谱进行了第一性原理研究。其中线性耦合模型的研究包括对单、双光子吸收以及单光子圆二色性质的电子振动耦合效应的模拟,基于简谐绝热Franck-Condon模型我们侧重对手性分子的单、双光子圆二色光谱进行了研究。第九章为总结与展望。
The study of the interaction of light with molecules has been and continues to be of great importance for understanding the natural world surrounding us. With the conventional light source, only linear optical processes can be detected. After the invent of laser light, nonlinear optics (NLO) has rapidly developed into an important branch of modern optics, and shown attractive perspective in many fields, such as photodynamic theopy, optical power limiting, 3D optical data storage, and so on. To design and synthesis materials which process large NLO responses is one of the main task in this field. Basically, all materials exhibit nonlinear optical properties, with linearity an approximation under certain circumstances. For the past decades, organic molecular materials have attracted more and more attention due to the advantages, like, easy and cheap to prepare and fabricate, wide response waverange, short response time. Theoretical computation can provide useful information on the relationship between molecular structure and optical responses, which should be helpful in guiding the often time-consuming and expensive experiments. The present thesis mainly takes care of two challenges in the comparison between the calculated results with the experiment: the effects of solvent environment and molecular vibrations.
The theoretical studies performed on an isolated molecule meet a difficulty in the directly comparison with the experimental measurements, which are usually carried out in solutions. The neighboring solvent molecules may have important influence on both the geometrical and optical responses of the solute molecule. For a better comparison with the experiment, it is of high relevance to include the effect of the solvent environment in the theoretical approaches. In this thesis, the solvent effect on the molecular optical properties of interest is modeled by means of the polarizable continuum model, which treats the solvent environment as a homogenous dielectric continuum medium characterized by its dielectric constant. With the presence of an external electromagnetic field, the induced field by the solvents can in turn screen the effects of the external field, which can be described by the so-called local field factor.
Theoretical studies rest on the approximation of vertical-transition, which only take into account the electronic transitions and neglects the contributions from the vibrational states, cannot reproduce the vibrational fine structures in many experimental spectra. Moreover, some important experimental phenomena hidden in the broad profiles can only be well explained by taking both the electronic and vibrational contributions into account. The complexity of the vibronic coupling theory, the difficulty in building the effective vibronic model, together with the huge computational cost, make seldom studies on vibronic coupling could be found. The present thesis studies the vibronically resolved spectra based on two foundation stones: the adiabatic approximation and the harmonic approximation. Adiabatic approximation assumes that the movements of electrons are separable with nuclei. It has been shown reliable when the excited states in concern are well-separated from each other. Harmonic approximation is a convenient and widely-used model to describe molecular vibrations, where the atoms are treated as harmonic oscillators and bonds between them as weightless springs. Two kinds of vibronic models have been applied: the adiabatic harmonic Franck-Condon (AFC) model, which requires the information of both minimum geometries of the initial and final states, can provide more accurate results and more confident assignment of the vibrational peaks. Linear coupling model (LCM), which avoids the often cumbersome excited-state optimization, less accurate but less computational intensive, is also applied to capture the major features of the vibronically resolved spectra.
With the development of powerful lasers, multiphoton spectroscopy has become one of the most interesting fields of research with wide applications in biology, chemistry, materials science, physics, and other disciplines. Because of different selection rules, new vibronic and electronic excited states, which were not found in ordinary one-photon spectroscopy, can be observed in a wide range. Molecular absorption spectroscopy has become one of the main analytical tools to understand the molecular structures. In this thesis, special attention has been paid to one-, two- and three-photon absorption properties of charge-transfer organic molecules. Circular dichroism, which can be regarded as a special kind of absorption spectroscopy, is highly related with chirality. It is based on the different absorption abilities between left and right polarized light. Here special attentions have been put on one- and two-photon circular dichroism spectra of chiral molecules.
The content of present thesis can be devided into two categories: electronic spectra, which are based on the vertical-transition approximation, without considering the contributions from vibrational states; vibronically resolved spectra, take both the electronic and vibrational transitions into account.
1. Electronic spectra
(1) Semi-empirical studies of multi-photon absorption: paper 1, 2
The direct way to calculate multi-photon cross section is the sum-over-state (SOS) formula. Since it is computational expensive at ab initio level, it is often applied at semi-empirical level. In present thesis, by using the semi-emipirical ZINDO program, in combination with the Configuration Interaction (CI) method, we can get the transition energies, permanent dipole moments, and transition dipole moments, which are needed in the SOS method to get the nonlinear poplarizabilities. Furthermore, we can get the multi-photon absorption cross sections. Compared with ab initio methods, semi-empirical results are less accurate but making the calculations on sizable molecules possible. Semi-empirical methods have been widely used for a huge number of systems, which could capture the major features of the nonlinear properties qualitively and are very useful for studing structure-property relationship. Since we focus on the build and test of a reliable calculation regime, rather than to perform a systematically study of large molecules, here only medium-size molecules are investigated.
In paper 1, we studied the one-, two- and three-photon absorption properties of a series of Y-shaped molecules which possess an imidazole-thiazole core. Our calculated results have confirmed the experimental findings that the investigated molecules are all promising multiphoton absorption materials and both the two-photon absorption and the three-photon absorption cross sections are seriatim increscent along with the increase of the electron-donor strength. The calculated results indicate that the heterocyclic core increases the two- and three-photon absorption cross sections due to itsπ-excessive nature, since it can provide more free electrons to enlarge the charge transfer within the molecule system. In addition, the design of Y shape and the sulfonyl-based electron-accepting group play a part in the enhancement of multiphoton absorption. It is notable that molecules with heterocyclic core will provide favorable condition for multiphoton absorption applications.
In paper 2, one- and two-photon absorption properties as well as the transition nature of a series of donor-π-acceptor-type compounds with trivalent boron as an acceptor have been theoretically studied. Our calculations indicate that the four o-methyl moieties on the two mesityl groups play an important part in protecting the trivalent boron from being attacked by oxygen in the air. The trivalent boron can be an all-right electron-acceptor with some bulky groups attached to it. On the basis of geometry optimization and UV-vis spectra, the positions and strengths of two-photon absorption for these molecules were reported.
(2) Ab initio studies of multi-photon absorption: paper 3
Three-photon absorption, known as a fifth-order nonlinear optical property, however, can be evaluated from the third-order transition matrix elements which can be obtained from the single residue of the appropriate cubic response function.
In paper 3 we present a theoretical study of the solvent-induced three-photon absorption cross-section of a highly conjugated fluorene derivative, performed using density functional cubic response theory in combination with the polarizable continuum model. The effects of solvent polarity and geometrical distortions have been carefully examined. It's found that dielectric medium enhances the three-photon absorption cross section remarkably. At room temperature, the molecule is expected to be observed with a wide distribution of geometries of different torsion angles rather than a unique equibrilium geometry. Therefore, it is not sufficient to perform calculations only on equibrilium geometry. For sizable molecules, the full response calculations often become really heavy. The applicability of the often used two-state model, which is less computational intensive, is examined by comparison against the full response theory results. It is found that the simplified model performs poorly for the three-photon absorption properties of our symmetric charge transfer molecule. A detailed comparison with experiment is also presented.
(3) Ab initio studies of one- and two-photon circular dichroism: paper 4, 5
In paper 4, the one- and two-photon circular dichroism spectra of R-(+)-3-methyl-cyclopentanone (R3MCP) have been calculated with an origin-invariant density functional theory approximation. Two low-lying conformers are analyzed, and a comparison of the intensities and characteristic features is made with the corresponding two-photon absorption for each species, also for the Boltzmann-averaged spectra. The effect of the choice of geometry, basis set and exchange-correlation functional is carefully analyzed. It is found that the recently developed CAMB3LYP functional can describe the Rydberg-state characteristics more appropriately than the popular B3LYP functional. With the combination with the correlation-consistent basis sets of double-zeta quality, we can reproduce the experimental electronic circular dichroism spectra very well. The features appearing in experiment are characterized in terms of molecular excitations, and the differences in the response of each state in the one- and two- photon processes are highlighted.
In Paper 5 the first experimental measurement of TPCD spectra is given on an axial chiral system, R-(+)-1,1'-bi(2-naphtol) (RBN) and its enantiomer S-(-)-1,1'-bi(2-naphtol) (SBN), in tetrahydrofunan. The double L-scan technique is applied. The corresponding theoretical efforts are also given. One can identify the differences in TPA between left and right circularly polarized lights, which determines TPCD. It is clearly indicated that the spectrum of one enantiomer is the specular image of the other as expected. It is worth to stress that the spectral features obtained by TPCD are different from those reported by ECD, which provides a nice example of the complementary fingerprinting capability of TPCD with respect to ECD. The calculated TPCD result at the B3LYP/PCM level well reproduces the experimental shapes. Due to the weak interaction between the two single naphthols, many near-degenerated states have been explored, and the first 25 states have to be included in the calculation in order to cover the experimental frequency range of 200-350 nm. The calculation indicates that TPCD is very sensitive to the solvent environment, accompanying with sign changes of the signals. A detailed analysis of the stick bands reveals that each experimental band results from a complicated balance of contributions, of opposite sign, from several electronic excited states
2. Vibronically resolved spectra
(1) One- and two-photon absorption: paper 6,7
In paper 6, both the electronic and the vibronic contributions to one-, and two-photon absorption of a D-π-D charge-transfer molecule are studied by means of density functional response theory combined with LCM vibronic model. Vibronic profiles of the first four excited states are fully explored. Franck-Condon, Herzberg-Teller contributions and the total spectra are expanded with respectively the Lorentzian parameters of 0.1 eV and 0.01 eV. The molecule under study is sensitive to different methods used for the geometry optimization. It is found that density functional theory tends to make the molecular more planar and Hartree-Fock can describe better the molecular structure. By applying the lineshape of 0.01 eV, we can get more fine vibrational structures. It is found 0-0 transition plays the dominant role and the levels with quantum numbers more than 2 can be safely neglected. The modes corresponding to the C-C-C and C-N-C bendings dominate the spectrum. The 'borrowing mechanism' of Herzberg-Teller contribution has been analyzed in detail, which often play a dominant role for forbidden transitions. A similar vibronic coupling behavior is found for both one- and two-photon absorptions. This is the first study on the vibronically resolved one- and two-photon absorption spectra for different electronic states.
At Franck-Condon level, the one- and two-photon absorption spectra of the same molecule are predicted to have the same shape. However, the experiments often give a strong violation of this statement, with differences between experimental one- and two-photon absorption spectra. In paper 7, we successfully explained the shifts between one- and two-photon absorption of a heterocyclic molecule by inspecting the different mechanisms between Franck-Condon and Herzberg-Teller contributions. The study applies density functional response theory in combination with Linear Coupling Model, and the proposed theoretical mechanism can be extended to general cases for molecules possessing different strong one- and two-photon absorption states. It is worth to say that paper 7 is the first study to take both the vibronic coupling and solvent effects into the two-photon absorption spectrum, where the Polarizable Continuum Model is applied for the solvent effect.
(2) One-photon circular dichroism: paper 8, 9
Motivated by a recent experiment which gives the Vibronically resolved ECD spectra of R3MCP, a corresponding computational study by use of LCM vibronic model is performed in paper 8, including both Franck-Condon and Herzberg-Teller contributions. It shows that Herzberg-Teller can introduce a change of sign on the chiral response of an electronic excited state, which breaks the usual belief that the sign reversion only occurs with the involvement of different electronic states. As we all know that the enantiomers show exactly the opposite ECD signals, therefore, this sign inversion within the Vibronically resolved electronic band, which can be interpreted as a change of the chirality of the system, has in principle important consequences in comparisons of theoretical and experimental ECD spectra employed for the assignment of absolute configurations.
In order to perform a confident assignment of the experimental peaks, in paper 9 we also applied the more accurate but also more computational intensive AFC model, which can give high-resolution spectra, on the same system, with a full account of Franck-Condon and Herzberg-Teller vibrational contributions and also Duschinsky rotation effect and possible frequency changes between the two sets of normal modes, within the harmonic approximation. The calculation allows a confident assignment of the CD fine vibrational structure. The computed decrease of the CD intensity in the gas phase upon increase of the temperature of the sample follows the trend observed experimentally in different solvents. It is worth to mention that the AFC result confirms the sign-reversion observed with LCM in paper 8. The fact that the change of sign occurs in the axial-methyl conformer of R3MCP, which is in ratio of 1:9 with respect to the predominant equatorial-methyl conformer, limits the chance that our theoretical prediction might be easily confirmed by experiment.
(3) Two-photon circular dichroism: paper 10
Very recently, the experimentalists have been made very striking progress on the measurement of TPCD responses on chiral species, which together with the fact that TPCD combines the advantages of both ECD and TPA, makes TPCD might become a very promising tools for fingerprinting applications and also evokes our theoretical study on the Vibronically resolved TPCD spectra.
In paper 10, the AFC vibronic model in combination with density functional response theory for computing two-photon Vibronically resolved circular dichroism spectra of R3MCP is presented, with comparisons with OPA, ECD, TPA spectra of the same system. The shapes of different properties are same on the Franck-Condon level, and the differences are brought by Herzberg-Teller term. Interesting interference effects between Franck-Condon and Herzberg-Teller contributions becomes more important for the more complex processes as TPCD. The more approximate and less computationally intensive LCM vibronic model shows its limitation in the simulation of this kind of processes. It is found that the change of sign can also occur in TPCD responses, introduced by the Herzberg-Teller contribution. Different from ECD, the sign-reversion survives even after Boltzmann averaging and also with larger lineshape parameters, which makes it might be amenable to experimental verification. Paper 10 is the first study on Vibronically resolved spectra of two-photon circular dichroism.
The present thesis is devided into nine chapters. Chapter 1 is the review, with brief introductions on the linear and nonlinear optics and the related spectroscopies. Special attentions are paid to one-, two-, three-photon absorption and one-, two-photon circular dichroism. Introductions on the solvent model and Vibronically resolved spectra are also given. Chapter 2 collects the basic quantum chemistry methods used in the thesis, briefly devided into the wave-function based methods and density functional theory. Chapter 3 presents the methods to calculate the multi-photon absorption focusing on the time-dependent perturbation theory (also known as Sum-Over-State) and response theory. Chapter 4 collects the results of the semi-empirical studies of the multi-photon absorption, which includes studies on a series of Y-shaped molecules possessing an imidazole-thiazole core and a series of conjugated molecules with trivalent boron as an acceptor. Chapter 5 gives the results of ab initio studies of the electronic spectra, which consists of studies of the solvent effects on the three-photon absorption of a high-conjugated fluorene derivative, and one- and two-photon circular dichroism properties of a chiral molecule. Chapter 6 shows the theory of Vibronically resolved spectra and the computational methods. Chapter 7 and 8 give the calculated Vibronically resolved spectra by using respectively Linear Coupling Model and Harmonic adiabatic Franck-Condon model. We focus on one-, two-photon absorption and one-photon circular dichroism spectra for Linear Coupling Model, and mainly on one- and two-photon circular dichroism for Harmonic adiabatic Franck-Condon model. Chapter 9 is the summary and perspective.
大部分理论研究都是针对单个分子进行的,而实验上对分子材料光学性质的测量一般是在溶剂中进行的,周围的溶剂分子对溶质分子的结构及其光学性质可能有着重要影响,这就给理论与实验测量结果相比较带来了困难。因此,为了更好的与实验相比较,就需要在理论模型中考虑溶剂环境的影响。本论文采用极化连续模型(PCM)来模拟溶剂环境,将溶剂看作均匀连续电介质,并由其介电常数来表征。当存在外加电磁场时,溶剂分子受其影响会产生一感应场,该感应场反过来会起到屏蔽外加电磁场的作用,这部分效应可以通过所谓的局域场因子来描述。
另外,基于垂直跃迁的理论研究只考虑了电子能级之间的跃迁,忽略了振动能级的贡献,而很多实验往往包含了精细振动结构展开,此外,有很多重要的实验现象可能会隐藏在精细振动结构中,只有在考虑分子振动的影响后才能做出正确的理论解释。因此,正确理解分子振动对光谱性质的影响也是十分必要的。振动耦合理论的复杂性、构造理论模型的难度以及较大的计算量使得分子振动的研究较少。本文基于绝热近似和简谐近似两大理论基石对电子振动光谱进行研究。绝热近似假设电子的运动跟核的运动是可以分开的,当激发态能级离其它能级较远时,绝热近似能对其进行较为可靠的描述。简谐近似是引入分子振动效应时常用并行之有效的近似之一,该近似将原子看作小球(谐振子),把原子间的化学键看作质量可以忽略不计的弹簧。论文主要采用两种绝热简谐振动模型:一种是简谐绝热Franck-Condon(AFC)模型,基于优化后的初、终态平衡构型,可以给出高分辨率的电子振动光谱,并可以对特征峰进行有效标识。另一种是线性耦合模型(LCM),只能提供低分辨率的谱图,但是避免了通常较繁琐的激发态的构型优化,并可以描述电子振动光谱的主要特征。
随着高功率激光的出现,多光子光谱学已经成为研究热点,在生物、化学、材料科学、物理等领域均有着重要应用。由于不同的选择定则,多光子光谱可以给出单光子光谱中所没有给出的新的振动或电子跃迁态。多光子吸收光谱是研究分子结构主要的分析工具之一,本论文侧重研究电荷转移型有机分子的单(OPA)、双(TPA)、三(3PA)光子吸收性质。圆二色光谱,基于左、右旋圆偏振光吸收性质的不同,可以被看作是一种特殊的吸收光谱,是一种与手性相关的性质。这里我们着重研究手性分子的单(ECD)、双(TPCD)光子圆二色光谱性质。
论文研究内容大致可以分为两部分:一是对电子垂直跃迁光谱的研究,即只考虑电子能级的跃迁,而不考虑振动态的贡献;二是综合考虑电子、振动能级贡献,即电子振动光谱的研究。下面简要介绍一下论文的主要研究内容。
一、电子垂直跃迁光谱研究
(1)有机共轭分子多光子吸收性质的半经验量化研究。(论文1、2)
计算多光子吸收截面最直接的方法就是态求和(SOS)公式,而在从头算水平上,利用态求和方法处理分子体系的计算量非常大,因此一般在半经验水平上使用。本论文中,使用半经验的ZINDO程序,结合组态相互作用(CI)方法,计算得出态求和公式所需的分子的跃迁能、偶极矩以及态态之间的跃迁偶极矩,先求得非线性极化率,再进一步计算材料分子的多光子吸收截面。这种半经验方法使得计算精确度受到限制,但是使得在从头算水平上无法实现的较大分子体系多光子吸收性质的研究变为可能。半经验方法已大量用于不同种类分子的非线性光学性质的计算,能够较准确地预测分子性质的变化趋势,因此对于分子构效关系的研究具有重要意义。本论文侧重于构建和测试可靠的理论体系,因此选择了中等尺寸的分子进行研究。
论文1对一系列含有咪唑-噻唑核的Y-型分子的单、双、三光子吸收性质进行了系统研究,计算结果验证了实验结论,指出所研究的分子为很有潜力的多光子吸收材料。分子多光子吸收性质随着电子给体强度的增大而增大。研究发现杂环核心由于其富电子特性,可以提供更多的自由电子以增强分子内电荷转移,从而可以增强多光子吸收强度。另外,Y型设计以及硫磺基作为电子受体均对多光子吸收的增强有着重要作用。
论文2对一系列以三价硼为受体的D-π-A型有机化合物的双光子吸收性质进行了研究。研究表明三甲基苯可以很好的保护三价硼使其不受空气中氧的攻击。只要采用比较庞大的基团对三价硼实施保护,它可以成为很有效的电子受体。在构型优化的基础上,对该分子的双光子吸收强度和峰位进行了报道。
(2)有机共轭分子多光子吸收性质的第一性原理研究。(论文3)
三光子吸收属于五阶非线性光学行为,但是可以通过三阶响应函数的单留数得出的三阶跃迁矩阵元而求得。
论文3中首次应用三阶响应场理论结合极化连续模型对一种高共轭A-π-π-π-A对称芴-衍生体的三光子吸收性质以及溶剂效应进行了研究。文章中详细描述了溶剂环境以及分子构型(尤其是分子平面性)对吸收性质的影响。研究表明,相较气相下,溶剂的极性很大程度地增大了三光子吸收截面值。室温下,该分子可能存在对应于不同二面角的多种构型,而非一种单一平衡构型,因此,只针对单一构型的计算是不充分的。对于大尺寸体系,采用完整的响应理论方法使得计算量变得很大,少态模型的计算量要小得多。研究发现,对于我们所研究的体系,两态模型不能对其三光子吸收性质进行很好的描述,得出结果与完整的响应理论结果相差很大。另外,文中我们将计算结果与实验数据进行了详细比较。
(3)手性分子单、双光子圆二色性光谱第一性原理研究(论文4,5)
论文4中,基于第一性原理,采用密度泛函理论结合无原点依赖性的响应函数对R-(+)-3-methyl-cyclopentanone(R3MCP)分子单、双光子圆二色光谱进行了理论研究。文章对两种最低能量构型进行了分析,对单、双光子圆二色光谱进行了全面的分析和比较,并与其双光子吸收强度和特性进行了对比。几何构型、计算基组、交换相关泛函的影响也进行了详尽的讨论。结果表明新近发展的CAMB3LYP交换相关泛函比起常用的B3LYP泛函能更好地对里德堡态进行描述,得出的谱图能与实验较好的吻合。文章从分子轨道角度对激发态跃迁性质进行了表征,并对单、双光子过程不同的响应作出了相应解释。
论文5首次给出了一种轴向手性分子R-(+)-1,1'-bi(2-naphtol)(RBN)及其对映体S-(-)-1,1'-bi(2-naphtol)(SBN)在溶剂中的TPCD实验光谱。该光谱通过DoubleL-scan技术测得,文中同时给出了相应的理论计算结果。实验分别给出了对应于左、右旋圆偏振光的TPA光谱,两者差值即给出TPCD光谱。跟预期结果相同,实验清晰的指出对映异构体的TPCD光谱性质呈现镜像,即信号完全相反。所研究体系的TPCD光谱表现出与其ECD不同的特性,因而提供了一个很好的范例来说明TPCD可以为ECD的手性识别功能起到很好的补充作用,是一种很有潜力的手性识别工具。在B3LYP/PCM水平上得出的TPCD光谱很好的重复了实验谱型。由于两个相互垂直的萘酚之间只存在很弱的相互作用,导致出现很多简并态,为了涵盖实验给出的光谱范围200-350 nm,计算需要考虑前25个激发态的贡献。计算还表明,该体系的TPCD性质对溶剂环境的影响非常敏感,伴随着信号符号的变化。可以发现,实验谱图主要特征峰均来自不同激发态正负信号的相互抵消作用。
二、电子振动光谱研究
(1)振动效应对单、双光子吸收性质影响的第一性原理研究(论文6,7)
论文6应用LCM振动模型结合密度泛函响应理论对一种D-π-D型二苯乙烯衍生物分子的单、双光子电子振动性质做了系统研究,给出了最低四个激发态的Franck-Condon贡献、Herzberg-Teller贡献、以及总的电子振动光谱,分别用了0.1eV和0.01eV两种洛伦兹展宽系数。首先对于不同的优化方法该分子呈现不同的平面性,结果发现密度泛函方法使得分子趋于平面化,Hartree-Fock能更好的描述分子结构。用0.01eV的光谱展宽系数,显然可以得到更多的单光子吸收电子振动光谱的精细结构,计算发现0-0跃迁是最主要的跃迁方式,而高于2的振动能级可以安全地被忽略掉,而不会对计算结果有什么影响。对应于C-N-C和C-C-C扭曲的振动模式是主要贡献。文中还详细阐述了Herzberg-Teller贡献项的著名的“borrowing mechanism”,它在禁止跃迁态中起到非常重要作用。这项工作属于首次应用线性耦合模型对分子不同激发态的单、双光子吸收电子振动光谱的研究。
在Franck-Condon水平上,同一分子的单、双光子吸收光谱应该有着相同的谱型,而实验上给出的单、双光子吸收电子振动光谱却通常存在差异。论文7结合密度泛函响应理论和线性耦合模型对Franck-Condon和Herzberg-Teller振动贡献不同的作用机制进行分析,指出该差异是由Herzberg-Teller振动效应带来的。该理论机制成功解释了一种杂环分子单、双光子最大吸收峰之间的偏移,并且可推广至具有不同单、双光子吸收态的一般分子。另外值得一提的是,论文7属于首次综合考虑电子振动耦合和溶剂效应对双光子吸收光谱的影响,其中溶剂效应采用极化连续模型进行模拟。
(2)手性分子单光子圆二色电子振动光谱的第一性原理研究(论文8、9)
实验给出了R3MCP分子进行了振动能级展开的ECD光谱,论文8中我们采用LCM模型研究了电子振动耦合效应对该手性分子ECD光谱的影响,并全面考虑Franck-Condon和Herzberg-Teller振动贡献。研究表明后者能够导致单一电子态中存在正负两种相反信号,从而引起分子手性响应性质的变化。这说明对圆二色谱的理论计算如果只考虑垂直跃迁可能导致正负信号出错,振动效应的引入是十分必要的。因手性对映体圆二色信号始终符号相反,实验上常把圆二色信号作为分子构型表征的判据。研究结果无疑对相关实验有着重要的指导价值。
为了更准确的对实验特征峰进行标识,论文9采用能够给出高分辨率谱图的AFC振动模型,在精确描述基态激发态势能面基础上,全面考虑Franck-Condon,Herzberg-Teller,简正模式Duschinsky转动贡献及可能的频率变化对手性分子圆二色谱的影响,并分别对各贡献项进行了详尽的讨论。该方法能对振动精细结构进行准确指认。圆二色信号强度会随着温度的升高而降低,这与实验得出的结论是一致的。值得一提的是,该研究进一步证实了LCM模型所预测的单一电子态中正负信号的变化。但由于信号变化发生在Axial构型,与Equatorial构型的Boltzmann构型比仅为1:9,这就限制了文章给出的理论预测能得到实验验证的可能性。
(3)手性分子双光子圆二色电子振动光谱的第一性原理研究(论文10)
近来,对手性分子TPCD光谱的实验研究取得了很大进展,TPCD结合了ECD和TPA的优点,在手性分子识别应用方面有着巨大潜力,这使得对TPCD电子振动光谱的理论研究也变得重要起来。
论文10结合AFC振动模型与密度泛函响应理论对手性分子R3MCP的双光子圆二色电子振动光谱进行了研究,并与该分子的OPA、ECD、TPA光谱进行了对比。在FC水平上计算所得的分子不同性质的光谱具有相同的振动能级展开,谱型的区别是由HT贡献项带来的。研究发现对于双光子圆二色性这样较为复杂的光学过程,FC/HT干涉项变得相对重要,线性耦合模型在模拟类似性质时表现出局限性。对于双光子圆二色谱,HT同样可以在单一电子态中引入正负两种信号,并且较单光子圆二色谱更为明显,即使使用较大的谱线展宽系数并进行Boltzmann构型平均后,正负信号仍然存在,使其在实验上得到验证变得可能。论文10属于首次对双光子圆二色电子振动光谱的研究。
本论文共由九章组成。第一章为综述,首先简单介绍了线性光学与非线性光学的特点,接着对相关分子光谱进行了介绍,重点讨论了单、双、三光子吸收以及单、双光子圆二色光谱性质,然后对论文中使用的溶剂模型和电子振动光谱理论作了简单说明。第二章简单介绍了论文中用到的基本量子化学理论,主要阐述了以波函数为出发点的量子化学和密度泛函理论。第三章给出了多光子吸收性质的计算方法,其中包括含时微扰理论方法(又称为态求和方法)和响应理论方法。第四章给出了在半经验水平上对多光子吸收性质的研究结果,包括分别对一系列Y型咪唑-噻唑杂环分子和一系列三价硼为受体的共轭分子的研究。第五章给出了基于从头算理论的电子垂直跃迁光谱的研究结果,包括研究溶剂效应对高共轭芴衍生物分子三光子吸收性质的影响以及手性分子单、双光子圆二色光谱的研究。第六章给出了电子振动光谱理论及其计算方法。第七章和第八章分别使用线性耦合模型和简谐绝热Franck-Condon模型对分子的电子振动光谱进行了第一性原理研究。其中线性耦合模型的研究包括对单、双光子吸收以及单光子圆二色性质的电子振动耦合效应的模拟,基于简谐绝热Franck-Condon模型我们侧重对手性分子的单、双光子圆二色光谱进行了研究。第九章为总结与展望。
The study of the interaction of light with molecules has been and continues to be of great importance for understanding the natural world surrounding us. With the conventional light source, only linear optical processes can be detected. After the invent of laser light, nonlinear optics (NLO) has rapidly developed into an important branch of modern optics, and shown attractive perspective in many fields, such as photodynamic theopy, optical power limiting, 3D optical data storage, and so on. To design and synthesis materials which process large NLO responses is one of the main task in this field. Basically, all materials exhibit nonlinear optical properties, with linearity an approximation under certain circumstances. For the past decades, organic molecular materials have attracted more and more attention due to the advantages, like, easy and cheap to prepare and fabricate, wide response waverange, short response time. Theoretical computation can provide useful information on the relationship between molecular structure and optical responses, which should be helpful in guiding the often time-consuming and expensive experiments. The present thesis mainly takes care of two challenges in the comparison between the calculated results with the experiment: the effects of solvent environment and molecular vibrations.
The theoretical studies performed on an isolated molecule meet a difficulty in the directly comparison with the experimental measurements, which are usually carried out in solutions. The neighboring solvent molecules may have important influence on both the geometrical and optical responses of the solute molecule. For a better comparison with the experiment, it is of high relevance to include the effect of the solvent environment in the theoretical approaches. In this thesis, the solvent effect on the molecular optical properties of interest is modeled by means of the polarizable continuum model, which treats the solvent environment as a homogenous dielectric continuum medium characterized by its dielectric constant. With the presence of an external electromagnetic field, the induced field by the solvents can in turn screen the effects of the external field, which can be described by the so-called local field factor.
Theoretical studies rest on the approximation of vertical-transition, which only take into account the electronic transitions and neglects the contributions from the vibrational states, cannot reproduce the vibrational fine structures in many experimental spectra. Moreover, some important experimental phenomena hidden in the broad profiles can only be well explained by taking both the electronic and vibrational contributions into account. The complexity of the vibronic coupling theory, the difficulty in building the effective vibronic model, together with the huge computational cost, make seldom studies on vibronic coupling could be found. The present thesis studies the vibronically resolved spectra based on two foundation stones: the adiabatic approximation and the harmonic approximation. Adiabatic approximation assumes that the movements of electrons are separable with nuclei. It has been shown reliable when the excited states in concern are well-separated from each other. Harmonic approximation is a convenient and widely-used model to describe molecular vibrations, where the atoms are treated as harmonic oscillators and bonds between them as weightless springs. Two kinds of vibronic models have been applied: the adiabatic harmonic Franck-Condon (AFC) model, which requires the information of both minimum geometries of the initial and final states, can provide more accurate results and more confident assignment of the vibrational peaks. Linear coupling model (LCM), which avoids the often cumbersome excited-state optimization, less accurate but less computational intensive, is also applied to capture the major features of the vibronically resolved spectra.
With the development of powerful lasers, multiphoton spectroscopy has become one of the most interesting fields of research with wide applications in biology, chemistry, materials science, physics, and other disciplines. Because of different selection rules, new vibronic and electronic excited states, which were not found in ordinary one-photon spectroscopy, can be observed in a wide range. Molecular absorption spectroscopy has become one of the main analytical tools to understand the molecular structures. In this thesis, special attention has been paid to one-, two- and three-photon absorption properties of charge-transfer organic molecules. Circular dichroism, which can be regarded as a special kind of absorption spectroscopy, is highly related with chirality. It is based on the different absorption abilities between left and right polarized light. Here special attentions have been put on one- and two-photon circular dichroism spectra of chiral molecules.
The content of present thesis can be devided into two categories: electronic spectra, which are based on the vertical-transition approximation, without considering the contributions from vibrational states; vibronically resolved spectra, take both the electronic and vibrational transitions into account.
1. Electronic spectra
(1) Semi-empirical studies of multi-photon absorption: paper 1, 2
The direct way to calculate multi-photon cross section is the sum-over-state (SOS) formula. Since it is computational expensive at ab initio level, it is often applied at semi-empirical level. In present thesis, by using the semi-emipirical ZINDO program, in combination with the Configuration Interaction (CI) method, we can get the transition energies, permanent dipole moments, and transition dipole moments, which are needed in the SOS method to get the nonlinear poplarizabilities. Furthermore, we can get the multi-photon absorption cross sections. Compared with ab initio methods, semi-empirical results are less accurate but making the calculations on sizable molecules possible. Semi-empirical methods have been widely used for a huge number of systems, which could capture the major features of the nonlinear properties qualitively and are very useful for studing structure-property relationship. Since we focus on the build and test of a reliable calculation regime, rather than to perform a systematically study of large molecules, here only medium-size molecules are investigated.
In paper 1, we studied the one-, two- and three-photon absorption properties of a series of Y-shaped molecules which possess an imidazole-thiazole core. Our calculated results have confirmed the experimental findings that the investigated molecules are all promising multiphoton absorption materials and both the two-photon absorption and the three-photon absorption cross sections are seriatim increscent along with the increase of the electron-donor strength. The calculated results indicate that the heterocyclic core increases the two- and three-photon absorption cross sections due to itsπ-excessive nature, since it can provide more free electrons to enlarge the charge transfer within the molecule system. In addition, the design of Y shape and the sulfonyl-based electron-accepting group play a part in the enhancement of multiphoton absorption. It is notable that molecules with heterocyclic core will provide favorable condition for multiphoton absorption applications.
In paper 2, one- and two-photon absorption properties as well as the transition nature of a series of donor-π-acceptor-type compounds with trivalent boron as an acceptor have been theoretically studied. Our calculations indicate that the four o-methyl moieties on the two mesityl groups play an important part in protecting the trivalent boron from being attacked by oxygen in the air. The trivalent boron can be an all-right electron-acceptor with some bulky groups attached to it. On the basis of geometry optimization and UV-vis spectra, the positions and strengths of two-photon absorption for these molecules were reported.
(2) Ab initio studies of multi-photon absorption: paper 3
Three-photon absorption, known as a fifth-order nonlinear optical property, however, can be evaluated from the third-order transition matrix elements which can be obtained from the single residue of the appropriate cubic response function.
In paper 3 we present a theoretical study of the solvent-induced three-photon absorption cross-section of a highly conjugated fluorene derivative, performed using density functional cubic response theory in combination with the polarizable continuum model. The effects of solvent polarity and geometrical distortions have been carefully examined. It's found that dielectric medium enhances the three-photon absorption cross section remarkably. At room temperature, the molecule is expected to be observed with a wide distribution of geometries of different torsion angles rather than a unique equibrilium geometry. Therefore, it is not sufficient to perform calculations only on equibrilium geometry. For sizable molecules, the full response calculations often become really heavy. The applicability of the often used two-state model, which is less computational intensive, is examined by comparison against the full response theory results. It is found that the simplified model performs poorly for the three-photon absorption properties of our symmetric charge transfer molecule. A detailed comparison with experiment is also presented.
(3) Ab initio studies of one- and two-photon circular dichroism: paper 4, 5
In paper 4, the one- and two-photon circular dichroism spectra of R-(+)-3-methyl-cyclopentanone (R3MCP) have been calculated with an origin-invariant density functional theory approximation. Two low-lying conformers are analyzed, and a comparison of the intensities and characteristic features is made with the corresponding two-photon absorption for each species, also for the Boltzmann-averaged spectra. The effect of the choice of geometry, basis set and exchange-correlation functional is carefully analyzed. It is found that the recently developed CAMB3LYP functional can describe the Rydberg-state characteristics more appropriately than the popular B3LYP functional. With the combination with the correlation-consistent basis sets of double-zeta quality, we can reproduce the experimental electronic circular dichroism spectra very well. The features appearing in experiment are characterized in terms of molecular excitations, and the differences in the response of each state in the one- and two- photon processes are highlighted.
In Paper 5 the first experimental measurement of TPCD spectra is given on an axial chiral system, R-(+)-1,1'-bi(2-naphtol) (RBN) and its enantiomer S-(-)-1,1'-bi(2-naphtol) (SBN), in tetrahydrofunan. The double L-scan technique is applied. The corresponding theoretical efforts are also given. One can identify the differences in TPA between left and right circularly polarized lights, which determines TPCD. It is clearly indicated that the spectrum of one enantiomer is the specular image of the other as expected. It is worth to stress that the spectral features obtained by TPCD are different from those reported by ECD, which provides a nice example of the complementary fingerprinting capability of TPCD with respect to ECD. The calculated TPCD result at the B3LYP/PCM level well reproduces the experimental shapes. Due to the weak interaction between the two single naphthols, many near-degenerated states have been explored, and the first 25 states have to be included in the calculation in order to cover the experimental frequency range of 200-350 nm. The calculation indicates that TPCD is very sensitive to the solvent environment, accompanying with sign changes of the signals. A detailed analysis of the stick bands reveals that each experimental band results from a complicated balance of contributions, of opposite sign, from several electronic excited states
2. Vibronically resolved spectra
(1) One- and two-photon absorption: paper 6,7
In paper 6, both the electronic and the vibronic contributions to one-, and two-photon absorption of a D-π-D charge-transfer molecule are studied by means of density functional response theory combined with LCM vibronic model. Vibronic profiles of the first four excited states are fully explored. Franck-Condon, Herzberg-Teller contributions and the total spectra are expanded with respectively the Lorentzian parameters of 0.1 eV and 0.01 eV. The molecule under study is sensitive to different methods used for the geometry optimization. It is found that density functional theory tends to make the molecular more planar and Hartree-Fock can describe better the molecular structure. By applying the lineshape of 0.01 eV, we can get more fine vibrational structures. It is found 0-0 transition plays the dominant role and the levels with quantum numbers more than 2 can be safely neglected. The modes corresponding to the C-C-C and C-N-C bendings dominate the spectrum. The 'borrowing mechanism' of Herzberg-Teller contribution has been analyzed in detail, which often play a dominant role for forbidden transitions. A similar vibronic coupling behavior is found for both one- and two-photon absorptions. This is the first study on the vibronically resolved one- and two-photon absorption spectra for different electronic states.
At Franck-Condon level, the one- and two-photon absorption spectra of the same molecule are predicted to have the same shape. However, the experiments often give a strong violation of this statement, with differences between experimental one- and two-photon absorption spectra. In paper 7, we successfully explained the shifts between one- and two-photon absorption of a heterocyclic molecule by inspecting the different mechanisms between Franck-Condon and Herzberg-Teller contributions. The study applies density functional response theory in combination with Linear Coupling Model, and the proposed theoretical mechanism can be extended to general cases for molecules possessing different strong one- and two-photon absorption states. It is worth to say that paper 7 is the first study to take both the vibronic coupling and solvent effects into the two-photon absorption spectrum, where the Polarizable Continuum Model is applied for the solvent effect.
(2) One-photon circular dichroism: paper 8, 9
Motivated by a recent experiment which gives the Vibronically resolved ECD spectra of R3MCP, a corresponding computational study by use of LCM vibronic model is performed in paper 8, including both Franck-Condon and Herzberg-Teller contributions. It shows that Herzberg-Teller can introduce a change of sign on the chiral response of an electronic excited state, which breaks the usual belief that the sign reversion only occurs with the involvement of different electronic states. As we all know that the enantiomers show exactly the opposite ECD signals, therefore, this sign inversion within the Vibronically resolved electronic band, which can be interpreted as a change of the chirality of the system, has in principle important consequences in comparisons of theoretical and experimental ECD spectra employed for the assignment of absolute configurations.
In order to perform a confident assignment of the experimental peaks, in paper 9 we also applied the more accurate but also more computational intensive AFC model, which can give high-resolution spectra, on the same system, with a full account of Franck-Condon and Herzberg-Teller vibrational contributions and also Duschinsky rotation effect and possible frequency changes between the two sets of normal modes, within the harmonic approximation. The calculation allows a confident assignment of the CD fine vibrational structure. The computed decrease of the CD intensity in the gas phase upon increase of the temperature of the sample follows the trend observed experimentally in different solvents. It is worth to mention that the AFC result confirms the sign-reversion observed with LCM in paper 8. The fact that the change of sign occurs in the axial-methyl conformer of R3MCP, which is in ratio of 1:9 with respect to the predominant equatorial-methyl conformer, limits the chance that our theoretical prediction might be easily confirmed by experiment.
(3) Two-photon circular dichroism: paper 10
Very recently, the experimentalists have been made very striking progress on the measurement of TPCD responses on chiral species, which together with the fact that TPCD combines the advantages of both ECD and TPA, makes TPCD might become a very promising tools for fingerprinting applications and also evokes our theoretical study on the Vibronically resolved TPCD spectra.
In paper 10, the AFC vibronic model in combination with density functional response theory for computing two-photon Vibronically resolved circular dichroism spectra of R3MCP is presented, with comparisons with OPA, ECD, TPA spectra of the same system. The shapes of different properties are same on the Franck-Condon level, and the differences are brought by Herzberg-Teller term. Interesting interference effects between Franck-Condon and Herzberg-Teller contributions becomes more important for the more complex processes as TPCD. The more approximate and less computationally intensive LCM vibronic model shows its limitation in the simulation of this kind of processes. It is found that the change of sign can also occur in TPCD responses, introduced by the Herzberg-Teller contribution. Different from ECD, the sign-reversion survives even after Boltzmann averaging and also with larger lineshape parameters, which makes it might be amenable to experimental verification. Paper 10 is the first study on Vibronically resolved spectra of two-photon circular dichroism.
The present thesis is devided into nine chapters. Chapter 1 is the review, with brief introductions on the linear and nonlinear optics and the related spectroscopies. Special attentions are paid to one-, two-, three-photon absorption and one-, two-photon circular dichroism. Introductions on the solvent model and Vibronically resolved spectra are also given. Chapter 2 collects the basic quantum chemistry methods used in the thesis, briefly devided into the wave-function based methods and density functional theory. Chapter 3 presents the methods to calculate the multi-photon absorption focusing on the time-dependent perturbation theory (also known as Sum-Over-State) and response theory. Chapter 4 collects the results of the semi-empirical studies of the multi-photon absorption, which includes studies on a series of Y-shaped molecules possessing an imidazole-thiazole core and a series of conjugated molecules with trivalent boron as an acceptor. Chapter 5 gives the results of ab initio studies of the electronic spectra, which consists of studies of the solvent effects on the three-photon absorption of a high-conjugated fluorene derivative, and one- and two-photon circular dichroism properties of a chiral molecule. Chapter 6 shows the theory of Vibronically resolved spectra and the computational methods. Chapter 7 and 8 give the calculated Vibronically resolved spectra by using respectively Linear Coupling Model and Harmonic adiabatic Franck-Condon model. We focus on one-, two-photon absorption and one-photon circular dichroism spectra for Linear Coupling Model, and mainly on one- and two-photon circular dichroism for Harmonic adiabatic Franck-Condon model. Chapter 9 is the summary and perspective.
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