| 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, 2The 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 3Three-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, 5In 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 6,7In 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, 9Motivated 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 10Very 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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