一维体系的DMRG方法和缩水甘油及其水复合物VCD的理论研究
摘要
密度矩阵重整化群方法是由Wilson的数值重整化群方法发展而成的，该方法继承了数值重整化群方法的重整化思想，但不再以哈密顿量本征值大小作为保留状态的判据，而是根据密度矩阵本征值大小来确定哪些状态保留，哪些状态舍弃，从而克服了数值重整化群方法在处理强关联体系时的困难。自S.White于1992年提出实空间密度矩阵重整化群方法以来，密度矩阵重整化群方法目前已经发展成处理一维强关联体系最精确的数值计算方法之一。与严格对角化方法相比，密度矩阵重整化群方法可以处理的体系要比严格对角化方法所能处理的体系大许多倍；另外，密度矩阵重整化群方法也避免了量子蒙特卡洛方法的负几率问题，而负几率问题是把量子蒙特卡洛方法应用到有自旋阻挫作用以及费米子体系的主要障碍。
利用密度矩阵重整化群方法可以计算有限格点系统的基态能量、低激发态能量、关联函数；借助于转移矩阵可以计算体系的热力学性质，比如：比热、内能、磁化率、自由能等；结合格林函数，密度矩阵重整化群方法可以处理体系的电磁响应及其它动力学性质问题，如：电导、光电导、热导、动力学自旋-自旋关联函数等。密度矩阵重整化群方法在量子化学方面的应用也取得很大的进展，比如：在Paiser-Parr-Pople模型下运用密度矩阵重整化群方法研究环聚多烯的性质；把分子轨道看作密度矩阵重整化群方法中的“格点”(site)，并且按照HF能量和轨道占据数将这些轨道(格点)排序，相应地，分子轨道集合就是密度矩阵重整化群方法中的“块”(block)，计算一些小分子的基态和低激发态能量。密度矩阵重整化群方法的优点就是能够以很高的精度计算非常大的体系，并且这种方法的理论基础保证了，计算中保留的状态越多，计算结果就越精确；缺点是目前这种方法还主要集中在一维体系中的应用。但人们在把密度矩阵重整化群方法应用到二维甚至三维体系的努力已经取得一些突破。
从三维空间上了解分子的结构与性能，尤其与生命过程有关的化学问题，如药物分子的立体构型与受体之间的相互作用、跟药理作用和药效之间的关系；生化反应过程的立体选择性与分子的立体构型之间的关系；各类天然有机物分子的立体构型与它们表现出的生物活性之间的关系；还有高分子材料的立体构型与性能之间的关系等等，已经成为当今化学的一个非常重要的研究领域。在自然界，特别是在生物体中，手性(chirality)化合物是广泛存在的。手性这个命题对于化学、分子生物学、医学和药学的理论和实践都有重大的意义。
由于自然界生命体存在的手性属性，也就产生了药物的手性问题。手性药物是手性化合物的重要组成部分，在许多情况下，手性化合物的一对对映体在生物体内的药理活性、代谢过程、代谢速率及毒性等均存在显著的差异，可能存在以下不同的情况：
(1)只有一种对映体有活性，而另一种无显著的药理作用；
(2)两个对映体具有等同或相近的同一药理活性；
(3)两个对映体具有完全不同的生理活性；
(4)两个对映体中一个有活性，另一个不仅没有活性，反而有毒副作用；
(5)对映体中两个都有相近的活性，而从全面平衡仍宜选用单一异构体；
(6)对映体中，一个有活性而另一个不但没有活性而且发生拮抗作用。
由此可见，对手性化合物分子构型的鉴定是非常重要的，目前测定手性化合物绝对构型的方法有以下几种：
(1)应用圆二色性光谱和旋光谱测定分子构型；
(2)X射线衍射法；
(3)似外消旋的Fredge方法；
(4)利用非对映异构体性质的经验关系；
(5)用化学相关法确定手性化合物的绝对构型。
其中圆二色谱方法具有：使用简便快速，需要的样品量相对较少，且对样品无破坏等优点，所以它已经成为现代分子生物学研究的重要手段。圆二色谱方法可以测定手性分子的构型，在核酸、多糖等生物聚合物的研究方面也有大量的应用。圆二色光谱在测定子性化合物的构型和构象、确定某些官能团(如羰基)在手性分子中的位置方面有独到之处，是其他光谱无法代替的。
缩水甘油(glycidol)分子具有手性，是一种十分重要的环氧化合物(epoxides)。主要用作环氧树脂稀释剂、塑料和纤维改性剂、卤代烃类稳定剂、食品保藏剂、杀菌剂、制冷系统干燥剂、芳烃萃取剂等。其衍生物是树脂、塑料和助剂等重要的工业原料。缩水甘油及其衍生物也是合成抗癌药的前体(starting materials)。另外，缩水甘油具有毒性，它能中度刺激皮肤和粘膜，可使中枢神经系统兴奋继而抑郁。工业生产主要是以烯丙醇为原料，采用过氧化氢环氧化法和过乙酸环氧化法制备。然而，对缩水甘油的分子结构的研究却非常有限，我们从理论上研究了(S)-缩水甘油及其水复合物的振动吸收光谱和圆二色性光谱，对它们的不同构型的稳定性以及分子内、分子间氢键的作用作了详细深入的探讨。
本论文在简单介绍一些量子力学基础理论及密度矩阵重整化群方法常用到的几个哈密顿模型后，详细推导了密度矩阵重整化群方法中无限链长算法和有限链长算法的计算公式，讨论了密度矩阵重整化群方法的一些内禀性质，运用所编写的密度矩阵重整化群方法的程序对一维及准一维体系进行了计算，另外，推导出计算圆二色性光谱强度所需的基本物理量的公式，计算了(S)—缩水甘油及其水复合物圆二色性光谱，从理论上详细分析了(S)—缩水甘油及其水复合物不同构型的稳定性以及不同构象、构型间圆二色性光谱的区别。主要取得如下结果：
(Ⅰ)从模型哈密顿出发，推导了密度矩阵重整化群方法的基本公式，例如：新系统块(系统块加计算原胞)、新环境块(环境块加计算原胞)以及体系超块哈密顿量的构造公式，由基态波函数构造密度矩阵公式等。并且对传统的密度矩阵重整化群方法加以改进，即在构造环境块的哈密顿量时，不再简单地使用系统块的映射，而是根据具体问题重新构造环境块哈密顿量。编写了密度矩阵重整化群方法无限链长算法和有限链长算法的Fortran程序，并对一维Heisenberg链以及准二维体系的聚省和聚菲苯环链进行了计算，计算结果令人满意。
(Ⅱ)运用密度泛函理论研究了(S)-缩水甘油各种稳定构型的能量、振动吸收光谱以及圆二色性光谱。找到(S)-缩水甘油8个稳定构型，分析了分子内氢键以及环状结构对分子稳定性的作用，根据(S)-缩水甘油不同构型振动吸收光谱中O-H伸缩振动频率的红移，以及C-O-H弯曲频率的篮移，可以推断哪些构型中有分子内氢键形成；为了进一步鉴定两个含有分子内氢键的构象之间几何结构的区别，可以根据(S)-缩水甘油不同构型的圆二色性光谱的差别，推断两个有分子内氢键的构型的绝对结构。从理论上说明圆二色性光谱是研究手性分子绝对构型的主要手段。
(Ⅲ)运用密度泛函理论研究了(S)-缩水甘油水复合物的各种稳定构型的能量、振动吸收光谱以及圆二色性光谱。结果表明，非手性分子(水)与手性分子(缩水甘油)形成复合物时也表现出光活性；同时为开发圆二色性光谱在研究手性分子与非手性分子复合物构型方面的应用提供了理论支持。
The density-matrix renormalization group (DMRG) were established on the basis of the Wilson's numerical renormalization group method, the key point of which was that the decimation procedure of the Hilbert space is to take the lowest-lying eigenstates of the compound block. However, the truncation procedure to system states of DMRG preserves a maximum of system-environment entanglement basing on the eigenvalues of the reduced density-matrix. Since the density-matrix renormalization group was origined by S. White in 1992, it is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. DMRG can be used to calculate more large many-body problem than exact diagonalization (ED), and DMRG has no negative-sign problem that plagues the quantum Monte Carlo (QMC) method. It was the negative-sign problem that limited QMC been used for frustrated spin or fermionic system.
DMRG has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic (with the help of Green function method), and thermodynamic quantities (combined with the transfer matrix renormalization group, TMRG) in these systems are developed. A field in which DMRG will make increasingly important contributions in the next few years is quantum chemistry. While the first quantum-chemical DMRG calculations on cyclic polyene and polyacetylene were still very much in the spirit of extended Hubbard models, more recent work has moved on to calculations in generic bases with arbitrary interactions. The major drawback of DMRG is that it displays its full force mainly for one-dimensional systems; nevertheless, interesting forays into higher dimensions have been made.
It is now the very important field in chemitry, considering the absolute 3D-structures of a molecular. Especially, the structures of the biologic molecule are very vital, since they are relavtive to the living progress. Many biologic molecule are chiral. Two enantiomers of chiral molecule have different effects:
(1) one has living effect, the other has not;
(2) both enantiomers have the same or similar effects;
(3) two enantiomers have the contrary effects;
(4) one has living effect, the other has poisonous effect;
(5) both enantiomers have living effects, however, one of them is perfected;
(6) one has living effect, the other has antagonistic effect.
So, it is necessary to determine the absolute structure of chiral molecule. There are about five such methods: (1) The vibrational circular dichroism (VCD) and rotational spectroscopies; (2) X radial method; (3)Fredge method; (4) experiential method; (5) chemical method. The first method is broadly used because of its excellences.
The vibrational circular dichroism spectroscopies plays an important role in determining the molecular configurations. The VCD spectrum provides unique fingerprint information for a chiral molecule, which has at least one chiral center and so exhibits chirality and optical activity.
There is a growing interest in the study on epoxides because they are versatile intermediates in organic synthesis. Particularly, glycidol and its derivatives have a compact skeleton of glycerol and wide potential for synthesis. They are considered to be versatile chiral synthesis units. Both enantiomers of glycidol have become widely used as starting materials for the synthesis of many interesting compounds, such as anticancer drugs, protein synthesis inhibitors, as well as a 2-oxazolidinone derivative used against depression. Glycidol has also been demonstrated to be carcinogenic and mutagenic in many mutagenicity test systems, because the alkylating glycidol could introduce dihydroxypropyl groups onto nitrogens in protein and thus damage protein. Both from theoretical and experimental point of view, glycidol is a suitable model for investigation of epoxides and alcohols.
This article is started with a discussion of the basis theory of quantum mechnics and the key algorithmic ideas needed to deal with the most conventional DMRG problem, the study the properties of a onedimensional quantum Hamiltonian. In section III, it is discussed the properties of the quantum states generated by DMRG smatrix-product statesd and the properties of the density matrices that are essential for its success. The Fortran programe of infinite- and finite-DMRG is designed, and is performed to calculate the ground state energes of S=1/2 Heisenberg model and polyacene, polyphenanthrene. Additionaly, the conformational stability, intramolecular and intermolecular H-bond strength, vibrational absorption (VA) and vibrational circular dichroism (VCD) spectra for conformers of (S)-glycidol and their complexes with water are investigated in the two last sections. There are three conclusions can be drawn:
(Ⅰ) The equations that the DMRG needed are derivated from the model Harmilton. For example, the formula how to add site to block system and enviroment, how to get the Harmilton of the superblock and the density matrix, are discussed in detail. We designe the Fortran programe of infinite- and finite-DMRG, and use it to calculate the ground state energes of S=1/2 Heisenberg model and polyacene, polyphenanthrene. The results of our programe are very closed to the results of exact diagonalization, when considering little system.
(Ⅱ) The electronic energies, the vibrational absorption harmonic frequencies, IR intensities and VCD spectra of eight (S)-glycidol conformers are calculated. The effection of intramolecular H-bond and ring structure on the stablity of molecule is discussed. The red-shift of O-H stretching frequency is using to determine whether there is intramolecular H-bond in a molecule. The absolute structure of (S)-glycidol can be determined by the vibrational circular dichroism (VCD) spectra for conformers of (S)-glycidol.
(Ⅲ) The energies, the vibrational absorption harmonic frequencies and VCD spectra of six (S)-glycidol-water complexes are calculated. The calculated results indicate that the VCD spectra are sensitive to conformational changes of both monomer and complexes and that alter complex formation with a chiral molecule, an achiral molecule becomes active in VCD spectra. Using the theoretical prediction, we demonstrate that the VCD technique is a powerful approach for determining conformational behavior of chiral molecules.
利用密度矩阵重整化群方法可以计算有限格点系统的基态能量、低激发态能量、关联函数；借助于转移矩阵可以计算体系的热力学性质，比如：比热、内能、磁化率、自由能等；结合格林函数，密度矩阵重整化群方法可以处理体系的电磁响应及其它动力学性质问题，如：电导、光电导、热导、动力学自旋-自旋关联函数等。密度矩阵重整化群方法在量子化学方面的应用也取得很大的进展，比如：在Paiser-Parr-Pople模型下运用密度矩阵重整化群方法研究环聚多烯的性质；把分子轨道看作密度矩阵重整化群方法中的“格点”(site)，并且按照HF能量和轨道占据数将这些轨道(格点)排序，相应地，分子轨道集合就是密度矩阵重整化群方法中的“块”(block)，计算一些小分子的基态和低激发态能量。密度矩阵重整化群方法的优点就是能够以很高的精度计算非常大的体系，并且这种方法的理论基础保证了，计算中保留的状态越多，计算结果就越精确；缺点是目前这种方法还主要集中在一维体系中的应用。但人们在把密度矩阵重整化群方法应用到二维甚至三维体系的努力已经取得一些突破。
从三维空间上了解分子的结构与性能，尤其与生命过程有关的化学问题，如药物分子的立体构型与受体之间的相互作用、跟药理作用和药效之间的关系；生化反应过程的立体选择性与分子的立体构型之间的关系；各类天然有机物分子的立体构型与它们表现出的生物活性之间的关系；还有高分子材料的立体构型与性能之间的关系等等，已经成为当今化学的一个非常重要的研究领域。在自然界，特别是在生物体中，手性(chirality)化合物是广泛存在的。手性这个命题对于化学、分子生物学、医学和药学的理论和实践都有重大的意义。
由于自然界生命体存在的手性属性，也就产生了药物的手性问题。手性药物是手性化合物的重要组成部分，在许多情况下，手性化合物的一对对映体在生物体内的药理活性、代谢过程、代谢速率及毒性等均存在显著的差异，可能存在以下不同的情况：
(1)只有一种对映体有活性，而另一种无显著的药理作用；
(2)两个对映体具有等同或相近的同一药理活性；
(3)两个对映体具有完全不同的生理活性；
(4)两个对映体中一个有活性，另一个不仅没有活性，反而有毒副作用；
(5)对映体中两个都有相近的活性，而从全面平衡仍宜选用单一异构体；
(6)对映体中，一个有活性而另一个不但没有活性而且发生拮抗作用。
由此可见，对手性化合物分子构型的鉴定是非常重要的，目前测定手性化合物绝对构型的方法有以下几种：
(1)应用圆二色性光谱和旋光谱测定分子构型；
(2)X射线衍射法；
(3)似外消旋的Fredge方法；
(4)利用非对映异构体性质的经验关系；
(5)用化学相关法确定手性化合物的绝对构型。
其中圆二色谱方法具有：使用简便快速，需要的样品量相对较少，且对样品无破坏等优点，所以它已经成为现代分子生物学研究的重要手段。圆二色谱方法可以测定手性分子的构型，在核酸、多糖等生物聚合物的研究方面也有大量的应用。圆二色光谱在测定子性化合物的构型和构象、确定某些官能团(如羰基)在手性分子中的位置方面有独到之处，是其他光谱无法代替的。
缩水甘油(glycidol)分子具有手性，是一种十分重要的环氧化合物(epoxides)。主要用作环氧树脂稀释剂、塑料和纤维改性剂、卤代烃类稳定剂、食品保藏剂、杀菌剂、制冷系统干燥剂、芳烃萃取剂等。其衍生物是树脂、塑料和助剂等重要的工业原料。缩水甘油及其衍生物也是合成抗癌药的前体(starting materials)。另外，缩水甘油具有毒性，它能中度刺激皮肤和粘膜，可使中枢神经系统兴奋继而抑郁。工业生产主要是以烯丙醇为原料，采用过氧化氢环氧化法和过乙酸环氧化法制备。然而，对缩水甘油的分子结构的研究却非常有限，我们从理论上研究了(S)-缩水甘油及其水复合物的振动吸收光谱和圆二色性光谱，对它们的不同构型的稳定性以及分子内、分子间氢键的作用作了详细深入的探讨。
本论文在简单介绍一些量子力学基础理论及密度矩阵重整化群方法常用到的几个哈密顿模型后，详细推导了密度矩阵重整化群方法中无限链长算法和有限链长算法的计算公式，讨论了密度矩阵重整化群方法的一些内禀性质，运用所编写的密度矩阵重整化群方法的程序对一维及准一维体系进行了计算，另外，推导出计算圆二色性光谱强度所需的基本物理量的公式，计算了(S)—缩水甘油及其水复合物圆二色性光谱，从理论上详细分析了(S)—缩水甘油及其水复合物不同构型的稳定性以及不同构象、构型间圆二色性光谱的区别。主要取得如下结果：
(Ⅰ)从模型哈密顿出发，推导了密度矩阵重整化群方法的基本公式，例如：新系统块(系统块加计算原胞)、新环境块(环境块加计算原胞)以及体系超块哈密顿量的构造公式，由基态波函数构造密度矩阵公式等。并且对传统的密度矩阵重整化群方法加以改进，即在构造环境块的哈密顿量时，不再简单地使用系统块的映射，而是根据具体问题重新构造环境块哈密顿量。编写了密度矩阵重整化群方法无限链长算法和有限链长算法的Fortran程序，并对一维Heisenberg链以及准二维体系的聚省和聚菲苯环链进行了计算，计算结果令人满意。
(Ⅱ)运用密度泛函理论研究了(S)-缩水甘油各种稳定构型的能量、振动吸收光谱以及圆二色性光谱。找到(S)-缩水甘油8个稳定构型，分析了分子内氢键以及环状结构对分子稳定性的作用，根据(S)-缩水甘油不同构型振动吸收光谱中O-H伸缩振动频率的红移，以及C-O-H弯曲频率的篮移，可以推断哪些构型中有分子内氢键形成；为了进一步鉴定两个含有分子内氢键的构象之间几何结构的区别，可以根据(S)-缩水甘油不同构型的圆二色性光谱的差别，推断两个有分子内氢键的构型的绝对结构。从理论上说明圆二色性光谱是研究手性分子绝对构型的主要手段。
(Ⅲ)运用密度泛函理论研究了(S)-缩水甘油水复合物的各种稳定构型的能量、振动吸收光谱以及圆二色性光谱。结果表明，非手性分子(水)与手性分子(缩水甘油)形成复合物时也表现出光活性；同时为开发圆二色性光谱在研究手性分子与非手性分子复合物构型方面的应用提供了理论支持。
The density-matrix renormalization group (DMRG) were established on the basis of the Wilson's numerical renormalization group method, the key point of which was that the decimation procedure of the Hilbert space is to take the lowest-lying eigenstates of the compound block. However, the truncation procedure to system states of DMRG preserves a maximum of system-environment entanglement basing on the eigenvalues of the reduced density-matrix. Since the density-matrix renormalization group was origined by S. White in 1992, it is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. DMRG can be used to calculate more large many-body problem than exact diagonalization (ED), and DMRG has no negative-sign problem that plagues the quantum Monte Carlo (QMC) method. It was the negative-sign problem that limited QMC been used for frustrated spin or fermionic system.
DMRG has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic (with the help of Green function method), and thermodynamic quantities (combined with the transfer matrix renormalization group, TMRG) in these systems are developed. A field in which DMRG will make increasingly important contributions in the next few years is quantum chemistry. While the first quantum-chemical DMRG calculations on cyclic polyene and polyacetylene were still very much in the spirit of extended Hubbard models, more recent work has moved on to calculations in generic bases with arbitrary interactions. The major drawback of DMRG is that it displays its full force mainly for one-dimensional systems; nevertheless, interesting forays into higher dimensions have been made.
It is now the very important field in chemitry, considering the absolute 3D-structures of a molecular. Especially, the structures of the biologic molecule are very vital, since they are relavtive to the living progress. Many biologic molecule are chiral. Two enantiomers of chiral molecule have different effects:
(1) one has living effect, the other has not;
(2) both enantiomers have the same or similar effects;
(3) two enantiomers have the contrary effects;
(4) one has living effect, the other has poisonous effect;
(5) both enantiomers have living effects, however, one of them is perfected;
(6) one has living effect, the other has antagonistic effect.
So, it is necessary to determine the absolute structure of chiral molecule. There are about five such methods: (1) The vibrational circular dichroism (VCD) and rotational spectroscopies; (2) X radial method; (3)Fredge method; (4) experiential method; (5) chemical method. The first method is broadly used because of its excellences.
The vibrational circular dichroism spectroscopies plays an important role in determining the molecular configurations. The VCD spectrum provides unique fingerprint information for a chiral molecule, which has at least one chiral center and so exhibits chirality and optical activity.
There is a growing interest in the study on epoxides because they are versatile intermediates in organic synthesis. Particularly, glycidol and its derivatives have a compact skeleton of glycerol and wide potential for synthesis. They are considered to be versatile chiral synthesis units. Both enantiomers of glycidol have become widely used as starting materials for the synthesis of many interesting compounds, such as anticancer drugs, protein synthesis inhibitors, as well as a 2-oxazolidinone derivative used against depression. Glycidol has also been demonstrated to be carcinogenic and mutagenic in many mutagenicity test systems, because the alkylating glycidol could introduce dihydroxypropyl groups onto nitrogens in protein and thus damage protein. Both from theoretical and experimental point of view, glycidol is a suitable model for investigation of epoxides and alcohols.
This article is started with a discussion of the basis theory of quantum mechnics and the key algorithmic ideas needed to deal with the most conventional DMRG problem, the study the properties of a onedimensional quantum Hamiltonian. In section III, it is discussed the properties of the quantum states generated by DMRG smatrix-product statesd and the properties of the density matrices that are essential for its success. The Fortran programe of infinite- and finite-DMRG is designed, and is performed to calculate the ground state energes of S=1/2 Heisenberg model and polyacene, polyphenanthrene. Additionaly, the conformational stability, intramolecular and intermolecular H-bond strength, vibrational absorption (VA) and vibrational circular dichroism (VCD) spectra for conformers of (S)-glycidol and their complexes with water are investigated in the two last sections. There are three conclusions can be drawn:
(Ⅰ) The equations that the DMRG needed are derivated from the model Harmilton. For example, the formula how to add site to block system and enviroment, how to get the Harmilton of the superblock and the density matrix, are discussed in detail. We designe the Fortran programe of infinite- and finite-DMRG, and use it to calculate the ground state energes of S=1/2 Heisenberg model and polyacene, polyphenanthrene. The results of our programe are very closed to the results of exact diagonalization, when considering little system.
(Ⅱ) The electronic energies, the vibrational absorption harmonic frequencies, IR intensities and VCD spectra of eight (S)-glycidol conformers are calculated. The effection of intramolecular H-bond and ring structure on the stablity of molecule is discussed. The red-shift of O-H stretching frequency is using to determine whether there is intramolecular H-bond in a molecule. The absolute structure of (S)-glycidol can be determined by the vibrational circular dichroism (VCD) spectra for conformers of (S)-glycidol.
(Ⅲ) The energies, the vibrational absorption harmonic frequencies and VCD spectra of six (S)-glycidol-water complexes are calculated. The calculated results indicate that the VCD spectra are sensitive to conformational changes of both monomer and complexes and that alter complex formation with a chiral molecule, an achiral molecule becomes active in VCD spectra. Using the theoretical prediction, we demonstrate that the VCD technique is a powerful approach for determining conformational behavior of chiral molecules.
引文
[1] D. R. Hartree, Proc. Camb. Phil. Soc. 24 (1928) 111
[2] V. Fock, NSherungsmethoden zur Losung des Quantenmechanischen Mehrkorperproblems, Zeit. Phys. 61 (1930) 126
[3] C. C. J. Roothaan, New developments in Molecular Orbital Theory, Rev. Mod. Phys. 23 (1951) 69
[4] J. B. Foresman, M. Head-Gordon, J. A. Pople and M. J. Frisch, Toward a systematic molecular orbital theory for excited states, J. Phys. Chem. 96 (1992)135
[5] E. A. Hylleraas, Zeit. Physik, 48 (1928) 469
[6] C. Moller and M. S. Plesset, Note on an Approximation Treatment for Many-Electron Systems, Phys. Rev. 46 (1934) 618
[7] M. Head-Gordon, J. A. Pople and M. J. Frisch, MP2 energy evaluation by direct methods, Chem. Phys. Lett. 153 (1988) 503
[8] M. J. Frisch, M. Head-Gordon and J. A. Pople, A direct MP2 gradient method, Chem. Phys. Lett. 166 (1990) 275
[9] M. J. Frisch, M. Head-Gordon and J. A. Pople, Semi-direct algorithms for the MP2 energy and gradient, Chem. Phys. Lett. 166 (1990) 281
[10] M. Head-Gordon and T. Head-Gordon, Analytic MP2 frequencies without fifth-order storage. Theory and application to bifurcated hydrogen bonds in the water hexamer, Chem. Phys. Lett. 220 (1994) 122
[11] S. Saebo and J. Almlof, Avoiding the integral storage bottleneck in LCAO calculations of electron correlation, Chem. Phys. Lett. 154 (1989) 83
[12] H.Thomas, The Calculation of Atomic Fields, Pro. Camb. Phil. Soc. 23 (1927)545
[13] R. Fermi, A Statistical Method for Determining Some Properties of the Atom, Atti Accad Lincei 6 (1927) 602
[14] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964) B864
[15] W. Kohn, L. J. Sham, Self-consistent Eguations Including Exchange and Correlation Effects, Phys. Rev. A 140 (1965) 1133
[16] 徐树方，矩阵计算的理论与方法，北京大学出版社，北京，1995年，
[17] White S R, Density Matrix Formulation for Quantum Renormalization Groups, Phys. Rev. Lett, 69 (1992) 2863
[1] J. A. Pople, Trans. Faraday Soc. 49 (1953) 1375
[2] R. Pariser and R. G. Parr, A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I, J. Chem. Phys. 21 (1953) 466
[3] R. Padser and R. G. Parr, A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. Ⅱ, J. Chem. Phys. 21 (1953) 767
[3] I. Ohmine, M. Karplus and K. Schulten, Renormalized configuration interaction method for electron correlation in the excited states of polyenes, J. Chem. Phys. 68 (1978) 2298
[4] J. Hubbard, Electron Correlations in Narrow Energy Bands, Proc. R. Soc. London Ser. A 276 (1963) 238
[5] E. Huckel, Zeit. Phys. 60 (1930) 423
[6] B. H. Brandow, Linked-Cluster Expansions for the Nuclear Many-Body Problem, Rev. Mod. Phys. 39 (1967) 771
[7] G. Hose, U. Kaldor, Diagrammatic many-body perturbation theory for general model spaces, J. Phys. B 12 (1979) 3827
[8] B. H. Brandow, Formal theory of effective-electron hamiltonians, Int. J. Quantum Chem. 15 (1979) 207
[9] P. W. Anderson, New approach to the theory of superexchange interactions, Phys. Rev. 115,2-13 (1959).
[10] P. A. Dirac, The Principles of Quantum Mechanics, Oxford University Press,Clarendon,1930
[11] J. H. Van Vleck, A. Sherman, Zeit. Phys. 49 (1935) 619
[12] L. Pauling and G. W. Wheland, The Nature of the Chemical Bond. V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals, J. Chem. Phys.1 (1933) 362
[13] C. K. Majumdar, Antiferromagnetic model with known ground state, J. Phys. C, 3 (1970)911
[14] C. K. Majumdar, D. K. Ghosh, J. Math. Phys. 10 (1969) 1399
[15] P. M. van den Broek, Exact value of the ground state energy of the linearantiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interaction, Phys. Lett. A, 77 (1980) 261
[16] B. S. Shastry, B. Sutherland, Excitation Spectrum of a Dimerized Next-Neighbor Antiferromagnetic Chain, Phys. Rev. Lett. 47 (1981) 964
[17] A. W. Garrett, Magnetic Excitations in the S=1/2 Alternating Chain Compound (VO)_2P_2O_7, Phys. Rev. Lett. 79 (1997)745
[18] K. M. Diedrix, Theoretical and experimental study of the magnetic properties of the singlet-ground-state system Cu (NO_3)_2·2. 5H_2O: An alternating linear Heisenberg antiferromagnet, Phys. Rev. B, 19 (1979) 420
[19] M. Base, Observation of the Spin-Peierls Transition in Linear Cu(Spin-1/2) Chains in an Inorganic Compound CuGeO_3, Phys. Rev. Lett. 70 (1993) 3651
[20] M. Isobe, Y. Ueda, Magnetic Susceptibility of QuasiOne-Dimensional Compound-NaV_2O_5 Possible Spin-Peierls Compound with High Critical Temperature of 34 K, J. Phys. Soc. Jpn, 65 (1996) 1178
[21] Azuma M, Observation of a Spin Gap in SrCu_2O_3 Comprising Spin-1/2 Quasi-1D Two-Leg Ladders, Phys. Rev. Lett. 73 (1994) 3463
[22] Chaboussant G, etc., Experimental phase diagram of Cu_2(C_5H_(12)N_2)_2C_(14): A quasi-one-dimensional antiferromagnetic spin-Heisenberg ladder, Phys. Rev. B 55 (1997) 3046
[1] K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47 (1975) 773
[2] (a) H. R. Krishna-Murthy, J. K. Wilkins and K. G. Wilson, Renormalization-group approach to the Anderson model of dilute magnetic alloys. Ⅰ. Static properties for the symmetric case, Phys. Rev. B 21 (1980) 1003; (b) Renormalization-group approach to the Anderson model of dilute magnetic alloys. Ⅱ. Static properties for the asymmetric case, Phys. Rev. B 21 (1980) 1044
[3] J. Kondo, Solid State Physics, Vol23, New York, (1969)
[4] P. A. Lee, Real-Space Scaling Studies of Localization, Plays. Rev. Lett. 42 (1979) 1492
[5] P. A. Lee and D. S. Fisher, Anderson Localization in Two Dimensions, Phys. Rev. Lett. 47 (1981) 882
[6] S. T. Chui and J. W. Bray, Computer renormalization-group technique applied to the Hubbard model, Phys. Rev. B 18 (1978) 2426
[7] J. W. Bray and S. T. Chui, Computer renormalization-group calculations of 2kF and 4kF correlation functions of the one-dimensional Hubbard model, Phys. Rev. B 19 (1979) 4876
[8] J. E. Hirsch, Renormalization-group study of the Hubbard model, Phys. Rev. B 22 (1980) 5259
[9] C. Dasgupta and P. Pfeuty, Comment on empirical photoionisation thresholds, J. Phys. C 14 (1981) 717
[10] S. R. White and R. M. Noack, Real-space quantum renormalization groups, Phys. Rev. Lett. 68 (1992) 3487
[11] S. R. White, Strongly correlated electron systems and the density matrix renormalization group, Phys. Rep. 301 (1998) 187
[13] S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69 (1992) 2863
[14] S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48 (1993) 10345
[15] S. Liang and H. Pang, Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective, Phys. Key. B 49 (1994) 9214
[16] S. R. White and D. A. Hase, Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S=1 Heisenberg chain, Phys. Rev. B 48 (1993) 3844
[17] S. Qin, X. Wang and L. Yu, Universality class of integer quantum spin chains: S=1/2 case study, Phys. Rev. B 46 (1997) R14251
[18] X. Wang, S. Qin and L. Yu, Haldane gap for the S=2 antiferromagnetic Heisenberg chain revisited, Phys. Rev. B 60 (1999) 14529
[19] S. Qin, S. Liang, Z. B. Su and L. Yu, Density-matrix renormalization-group calculation of correlation functions in the one-dimensional Hubbard model, Phys. Rev. B 52 (1995) R5475
[20] S. Qin and L. Yu, Momentum-distribution critical exponents for the one-dimensional largc-U Hubbard model in the thermodynamic limit, Phys. Rev. B 54 (1996) 1447
[21] K. Penc, K. Hallberg, F. Mila and H. Shiba, Shadow Band in the One-Dimensional Infinite-U Hubbard Model, Phys. Rev. Lett. 77 (1996) 1390
[22] S. Moukouri and L. G. Caron, Ground-state properties of the one-dimensional Kondo lattice at partial band filling, Phys. Rev. B 52 (1995) 15723
[23] J. Z. Lou, S. J. Qin and C. F. Chen, String Order in Half-Integer-Spin Antiferromagnetic Heisenberg Chains, Phys. Rev. Lett. 91 (2003) 087204
[24] S. J. Qin, J. Z. Lou, L. Q. Sun and C. F. Chen, Nonlocal Topological Order in Antiferromagnetic Heisenberg Chains, Phys. Rev. Lett. 90 (2003) 067202
[25] K. Hida, Magnetization Plateaux in Random Frustrated S=1/2 Heisenberg Chains J. Phys. Soc. Jpn. 72 (2003) 911
[26] H. E. Boos, V. E. Korepin, Y. Nishiyama and M. Shiroishi, J. Phys. A 35 (2002) 4443
[27] T. Hikihara and A. Furusaki, Spin correlations in the two-leg antiferromagnetic ladder in a magnetic field, Phys. Rev. B 63 (2001) 134438
[28] A. Kawaguchi, A. Koga, K. Okunishi and N. Kawakami, Magnetization process for a quasi-one-dimensional S=1 antiferromagnet, Phys. Rev. B 65 (2002) 214405
[29] L. Urba and A. Rosengren, Density-matrix renormalization-group analysis of the spin-1/2 XXZ chain in an XY symmetric random magnetic field, Phys. Rev. B 67 (2003) 104406
[30] J. Rotureau, N. Michel, W. Nazarewicz, M. Ploszajczak and J. Dukelsky Density Matrix Renormalization Group Approach for Many-Body Open Quantum Systems, Phys. Rev. Lett. 97 (2006) 110603
[31] O. Legeza and J. Solyom, Quantum data compression, quantum information generation, and the density-matrix renormalization-group method, Phys. Rev. B 70 (2004) 205118
[32] G. Hager, G. Wellein, E. Jeckelmann and H. Fehske, Stripe formation in doped Hubbard ladders, Phys. Rev. B 71 (2005) 075108
[33] M. Clemancey, H. Mayaffre, C. Berthier, M. Horvatic, J. -B. Fouet, S. Miyahara, F. Mila, B. Chiari and O. Piovesana, Field-Induced Staggered Magnetization and Magnetic Ordering in Cu2(CSH12N2)2Cl4, Phys. Rev. Lett. 97 (2006) 167204
[34] S. Liang and H. Pang, Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective, Phys. Rev. B 49 (1994) 9214
[35] R. M. Noack, S. R. White and D. J. Scalapino, in Computer Simulations in Condensed Matter Physics Ⅶ, Eds. D. P. Landau, K. K. Mon and H. B. Schuttler (Spinger Verlag, Heidelberg, Berlin, 1994)
[36] S. R. White and D. J. Scalapino, Density Matrix Renormalization Group Study of the Striped Phase in the 2D t-J Model, Phys. Rev. Lett. 80 (1998) 1272
[37] S. R. White and D. J. Scalapino, Energetics of Domain Walls in the 2D t-J Model, Phys. Rev. Lett. 81 (1998) 3227
[38] C. Zhang, E. Jeckelmann and S. R. White, Density Matrix Approach to Local Hilbert Space Reduction, Phys. Rev. Lett. 80 (1998) 2661
[39] E. Jeckelmann, C. Zhang and S. R. White, Metal-insulator transition in the one-dimensional Holstein model at half filling, Phys. Rec. B 60 (1999) 7950
[40] S. R. White and R. L. Martin, Ab initio quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 110 (1999) 4127
[41] J. Dukelsky and G. Sierra, Density Matrix Renormalization Group Study of Ultrasmall Superconducting Grains, Phys. Rev. Lett. 83 (1999) 172
[42] R. J. Bursill, T. Xiang and G. A. Gehring, J. Phys. Cond. Matt. 8 (1996) 1583
[43] X. Wang and T. Xiang, Transfer-matrix density-matrix renormalization-group theory for thermodynamics of one-dimensional quantum systems, Phys. Rev. B 56 (1997) 5061
[44] T. D. Kuhner and S. R. White, Dynamical correlation functions using the density matrix renormalization group, Phys. Rev. B 60 (1999) 335
[45] T. Xiang, Density-matrix renormalization-group method in momentum space, Phys. Rev. B 53 (1995) 10445
[46] M. A. Martin-Delgado and G. Sierra, Density Matrix Renormalization Group Approach to an Asymptotically Free Model with Bound States, Phys. Rev. Lett. 83 (1999) 1514
[47] S. R. White, Strongly correlated electron systems and the density matrix renormalization group, Phys. Rep. 301 (1998) 187
[48] J. Gaite, Angular Quantization And The Density Matrox Renormalization Group, Mod. Phys. Lett. A 16 (2001) 1109
[49] T. Xiang, Density-matrix renormalization-group method in momentum space, Phys. Rev. B 53 (1996) 10445
[50] S. Nishimoto, E. Jeckelmann, F. Gebhard and R. Noack, Application of the density matrix renormalization group in momentum space, Phys. Rev. B 65 (2002) 165114
[51] O. Legeza, J. Roder and B. Hess, Controlling the accuracy of the density-matrix renorrnalization-group method: The dynamical block state selection approach, Phys. Rev. B 67 (2003) 125114
[52] O. Legeza and J. Solyom, Optimizing the density-matrix renormalization group method using quantum information entropy, Phys. Rev. B 68 (2003) 195116
[53] T. Nishino and K. Okunishi, Product Wave Function Renormalization Group, J. Phys. Soc. Jpn. 64 (1995) 4084
[54] R. J. Bursill, T. Wang and G. A. Gehring, The density matrix renormalization group for a quantum spin chain at non-zero temperature, J. Phys. Cond. Matt. 8 (1996) L583
[55] G. Fano, F. Ortolani and L. Ziosi, The density matrix renormalization group method: Application to the PPP model of a cyclic polyene chain, J. Chem. Phys. 108 (1998) 9246
[56] G. L. Bendazzoli, S. Evangelisti, G. Fano, F. Ortolani and L. Ziosi, Density matrix renormalization group study of dirnerization of the Pariser-Parr-Pople model of polyacetilene, J. Chem. Phys. 110 (1999) 1277
[57] G. K.-L. Chan and M. Head-Gordon, Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group, J. Chem. Phys. 116 (2002) 4462
[58] S. Daul, I. Ciofini, C. Daul, and S. R. White, Full-CI quantum chemistry using the density matrix renormalization group, Int. J. Quantum Chem. 79 (2000) 331
[59] O. Legeza, J. Roder, and B. A. Hess, Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach, Phys. Rev. B 67 (20.03) 125114
[60] A. O. Mitrushenkov, G. Fano, F. Ortolani, R. Linguerri, and P. Palmieri, Quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 115(2001)6815
[61] Yi Gao, Chun-Gen Liu and Yuan-Sheng Jiang, The Valence Bond Study for Benzenoid Hydrocarbons of Medium to Infinite Sizes, J. Phys. Chem. A 106(2002)2592
[62] Haibo Ma, Fei Cai, Chungen Liu and Yuansheng Jiang, Spin distribution in neutral polyene radicals: Pariser-Parr-Pople model studied with the density matrix renormalization group method, J. Chem. Phys. 122 (2005) 104909
[63] S White and R Martin, Ab initio quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 110 (1999) 4127
[64] S. Daul and R. M. Noack, Phase diagram of the half-filled Hubbard chain with next-nearest-neighbor hopping, Phys. Rev. B 61 (2000) 1646
[65] A. O. Mitrushenkov, G. Fano, F. Ortolani, R. Linguerri and P. Palmieri, Quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 115(2001)6815
[66] A. O. Mitrushenkov, R. Linguerri, P. Palmieri and G. Fano, Quantum chemistry using the density matrix renormalization group II, J. Chem. Phys. 119(2003)4148
[1] P. Schmitteckert and U. Eckern, Phase coherence in a random one-dimensional system of interacting fermions: A density-matrix renormalization-group study, Phys. Rev. B 53 (1996) 15397
[2] S. Rapsch, U. Schollwock and W. Zwerger, Density matrix renormalization group for disordered bosons in one dimension, Europhys. Lett. 46 (1999) 559
[3] S. R. White, I. Affleck and D. J. Scalapino, Local versus nonlocal order-parameter field theories for quantum phase transitions, Phys. Rev. B 65 (2002) 165122
[4] R. P. Feynman, Statistical Mechanics: A Set of Lectures, Benjamin, Reading, MA, 1972
[5] E. R. Davidson, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices, J. Comput. Phys. 17 (1975) 87
[6] P. Hennlius, Two-dimensional infinite-system density matrix renormalization group algorithm, Phys. Rev. B 60 (1999) 9561
[7] R. Bursill, Density matrix renormalization group algorithm for quantum lattice systems with a large number of states per site, Phys. Rev. B 60 (1999) 1643
[8] Yi Gao, Chun-Gen Liu and Yuan-Sheng Jiang, The Valence Bond Study for Benzenoid Hydrocarbons of Medium to Infinite Sizes, J. Phys. Chem. A 106 (2002) 2592
[1] 常建华 董绮功，波谱原理及解析，科学出版社，北京，2001年，352-378
[2] Z. Dubinsky, T. Berman, Seasonal changes in the spectral composition of down-Telling irradiance in Lake Kinneret, Limnol. Oceanogr, 24 (1979) 652
[3] L. A. Nafie, Polarization Modulation FTIR Spectroscopy, in Advances in Applied FTIR Spectroscopy, ed. M. W. Mackenzie, John Wiley and Sons, New York, 1988, 67-104
[4] 尤田耙，手性化合物的现代研究方法，中国科技大学出版社，合肥，1993年，122-218
[5] 黄量 戴立信，手性药物的化学与生物学，化学工业出版社，北京，2002年，1-5
[6] L. A. Nafie, R. K. Dukor and T. B. Freedman, Vibrational Circular Dichroism in Handbook of Vibrational Spectroscopy, John Wiley & Sons Ltd, Chichester, 2002, 731-744
[7] P. J. Stephens, F. J. Devlin, C. S. Ashvar, C. F. Chabalowski and M. J. Frisch, Theoretical calculation of vibrational circular dichroism spectra, Faraday Discuss., 1994, 99, 103-119.
[8] P. J. Stephens, Theory of Vibrational Circular Dichroism, J. Phys. Chem. 89 (1985) 748
[9] P. J. Stephens, Mechanisms of vectorial transmembrane reduction of viologens across phosphatidylcholine bilayer membranes, J. Phys. Chem. 91 (1987) 1712
[10] P. J. Stephens, K. J. Jalkanen, R. D. Amos, P. Lazzeretti and R. Zanasi, Ab initio calculations of atomic polar and axial tensors for hydrogen fluoride, water, ammonia, and methane, J. Phys. Chem. 94 (1990) 1811
[11] Stephens, P. J. ; Devlin, F. J. ; Chabalowski, C. F. ; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields, J. Phys. Chem. 1994, 98, 11623.
[12] Devlin, F. J. ; Finley, J. W. ; Stephens, P. J. ; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields: A Comparison of Local, Nonlocal, and Hybrid Density Functionals J. Phys. Chem. 1995, 99, 16883.
[13] R. Liu, D. R. Tate, J. A. Clark, P. R. Moody, A. S. Van Buren and J. A. Krauser, Density Functional Theory Study of Molecular Structures and Vibrational Spectra of 3, 4- and 2, 3-Pyridyne, J. Phys. Chem. 100 (1996) 3430
[14] S. Abdali, K. J. Jalkanen, H. Bohr, S. Suhai and R. M. Nieminen, The VA and VCD spectra of various isotopomers of -alanine in aqueous solution, Chem. Phys. 282 (2002) 219
[15] C. N. Tam, P. Bour and T. A. Keiderling, Vibrational Optical Activity of (3S, 6S)-3,6-Dimethyl-1, 4-dioxane-2, 5-dione, J. Am. Chem. Soc. 118 (1996) 10285
[16] F. J. Devlin, P. J. Stephens, C. Osterle, K. B. Wiberg, J. R. Cheeseman and M. J. Frisch, Configurational and Conformational Analysis of Chiral Molecules Using IR and VCD Spectroscopies: Spiropentylcarboxylic Acid Methyl Ester and Spiropentyl Acetate, J. Org. Chem. 67 (2002) 8090
[17] Frisch, M. J. Prediction of Vibrational Circular Dichroism Spectra Using Density Functional Theory: Camphor and Fenchone, J. Am. Chem. Soc. 118 (1996) 6327
[1] C. H. Heathcock, M. McLaughlin, J. Medina, J. L. Hubbs, G. A. Wallace, R. Scott, M. M. Claffey, C. J. Hayes, G. R. Ott, J. Am. Chem. Soc. 125 (2003) 12844.
[2] Y. Kiyotsuka, J. Igarashi, Y. Kobayashi, A study toward a total synthesis of fostriecin, Tetrahedron Lett. 43 (2002) 2725.
[3] J. Wouters, F. Moureau, G. Evrard, J. J. Koenig, S. Jegham, P. Gorge, F. Durant, A reversible monoamine oxidase a inhibitor, befloxatone: structural approach of its mechanism of action, Bioorg. Med. Chem. 7 (1999) 1683.
[4] W. Lijinsky, R. M. Kovatch, Toxicol. Ind. Health 8 (1992) 267.
[5] R. D. Irwin, S. L. Eustis, S. Stefanski, J. K. Haseman, Carcinogenicity of Glycidol in F344 Rats and B6C3F1 Mice, J. Appl. Toxicol. 16 (1996) 201.
[6] L. Ehrenberg and S. Hussian, Genetic toxicity of some important epoxides, Mutat. Res./Genetic Toxicology and Environmental Mutagenesis 86 (1981) 1.
[7] S. De Flora, P. Zanacehi, A. Camoirano, C. Bennicelli, G. S. Badolati, Genotoxic activity and potency of 135 compounds in the Ames reversion test and in a bacterial DNA-repair test, Mutat. Res./Reviews in Genetic Toxicology 133 (1984) 161.
[8] A. D. Becke, Density-functional thermochemistry. Ⅲ. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648
[9] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys. 88 (1988) 2547
[10] C. Lee, W. Yang and R. G. Parr, Development of the CoUe-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785
[11] J. P. Perdew, K. Burke and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Rev. B 54 (1996) 16533
[12] K. Burke, J. P. Perdew and Y. Wang, in Electronic Density Functional Theory: Recent Progress and New Directions, ed. J. F. Dobson, G. Vignale and M. P. Das, Plenum, New York, 1998.
[13] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople, GAUSSIAN 98 (Revision A.7), Craussian, Inc., Pittsburgh PA, 1998.
[14] J. H. Jensen, M. S. Gordon, Conformational potential energy surface of glycine: a theoretical study, J. Am. Chem. Soc. 113 (1991) 7917
[15] S. Wolfe, Gauche effect. Stereochemical consequences of adjacent electron pairs and polar bonds, Acc. Chem. Res. 5 (1972) 102
[16] C. S. Callam, S. J. Singer, T. L. Lowary and C. M. Hadad, Computational Analysis of the Potential Energy Surfaces of Glycerol in the Gas and Aqueous Phases: Effects of Level of Theory, Basis Set, and Solvation on Strongly Intramolecularly Hydrogen-Bonded Systems, J. Am. Chem. Soc. 123 (2001) 11743
[17] A. P. Mauricio, Scaling factors for the prediction of vibrational spectra. Ⅰ. Benzene molecule, Int. J. Quantum. Chem. 77 (2000) 661
[18] F. J. Devlin, P. J. Stephens, J. R. Chceseman and M. J. Frisch, Ab Initio Prediction of Vibrational Absorption and Circular Dichroism Spectra of Chiral Natural Products Using Density Functional Theory: Camphor and Fenchone, J. Phys. Chem. A, 101 (1997) 6322
[19] Y. He, X. Cao, L. A. Nafie and T. B. Freedman, Ab Initio VCD Calculation of a Transition-Metal Containing Molecule and a New Intensity Enhancement Mechanism for VCD, J. Am. Chem. Soc. 123 (2001) 11320
[20] W.-G. Han, K. J. Jalkanen, M. Elstner, S. Suhai, Theoretical Study of Aqueous N-Acetyl-L-alanine N'-Methylamide: Structures and Raman, VCD, and ROA Spectra, J. Phys. Chem. B. 102 (1998) 2587
[21] K. Monde, T. Taniguchi, N. Miura, S.-I. Nishimura, Specific Band Observed in VCD Predicts the Anomeric Configuration of Carbohydrates, J. Am. Chem. Soc. 126 (2004) 9496
[22] I. Alkorta and J. Elfuero, Discrimination of hydrogen-bonded complexes with axial chirality, J. Chem. Phys., 117 (2002) 6463
[23] J. Sadlej, J. Cz. Dobrowolski, J. E. Rode, M. H. Jamroz, DFT study of vibrational circular dichroism spectra of D-lactic acid-water complexesw, Phys. Chem. Chem. Phys. 8 (2006) 101
[24] S. F. Boys and F. Bemardi, Mol. Phys. 112 (1970) 553
[25] L. Turi and J. J. Dannenberg, Correcting for basis set superposition error in aggregates containing more than two molecules: ambiguities in the calculation of the counterpoise correction, J. Phys. Chem. 97 (1993) 2488
[1] C. H. Heatheock, M. McLaughlin, J. Medina, J. L. Hubbs, G. A. Wallace, R. Scott, M. M. Claffey, C. J. Hayes, G. R. Ott, J. Am. Chem. Soc. 125 (2003) 12844.
[2] Y. Kiyotsuka, J. Igarashi, Y.Kobayashi, Tetrahedron Lett. 43 (2002) 2725.
[3] J. Wouters, F. Moureau, G. Evrard, J. J. Koenig, S. Jegham, P. Gorge, F. Durant, Bioorg. Med. Chem. 7 (1999) 1683.
[4] W. Lijinsky, R. M. Kovateh, Toxicol. Ind. Health 8 (1992) 267.
[5] R. D. Irwin, S. L. Eustis, S. Stefanski, J. K. Haseman, J. Appl. Toxieol. 16 (1996)201.
[6] L. Ehrenberg, S. Hussian, Mutat. Res. 86 (1981) 1.
[7] S. De Flora, P. Zanacchi, A. Camoirano, C. Bennicelli, G S. Badolati, Murat. Res. 133 (1984) 161.
[8] T. B. Freedman, X. Cao, R. K. Dukor, L. A. Nafie, Chirality 15 (2003) 743.
[9] L. A. Nafie, Polarization Modulation FTIR Spectroscopy, in Advances in Applied FTIR Spectroscopy, ed. M. W. Mackenzie, John Wiley and Sons, New York, 1988, pp. 67-104.
[10] A. D. Becke, J. Chem. Phys. 98 (1993) 1372, 5648.
[11] R. Liu, D. R. Tate, J. A. Clark, P. R. Moody, A. S. Van Buren and J. A. Krauser, J. Phys. Chem., 100 (1996) 3430.
[12] S. Abdali, K. J. Jalkanen, H. Bohr, S. Suhai and R. M. Nieminen, Chem. Phys., 282 (2002) 219.
[13] F. J. Devlin, P. J. Stephens, J. R. Cheeseman and M. J. Frisch, J. Phys. Chem. A, 101 (1997)6322.
[14] (a) A. D. Becke, J. Chem. Phys., 98 (1993) 5648; (b) A. D. Becke, J. Chem. Phys., 88 (1988) 2547; (c) C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 37 (1988) 785; (d) J. P. Perdew, K. Burke and Y. Wang, Phys. Rev. B, 54 (1996) 16533.
[15] J. H. Jensen, M. S. Gordon, J.Am. Chem. Soc. 113 (1991) 7917.
[16] E. R. Joanna, Cz. D. Jan, Chem. Phys. Lett. 360 (2002) 123.
[17] (a) S. F. Boys and F. Bernardi, Mol. Phys. 112 (1970) 553; (b) L. Turi and J. J. Dannenberg, J. Phys. Chem. 97 (1993) 2488.
[18] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople, GAUSSIAN 98 (Revision A.7), Gaussian, Inc., Pittsburgh PA, 1998.
[19] S. Wolfe, Acc. Chem. Res. 5 (1972) 102.
[20] A. P. Mauricio, Int. J. Quantum. Chem. 77 (2000) 661.
[21] J. E. Rode, J. Cz. Dobrowolski, J. Mol. Struct. (THEOCHEM). 637 (2003) 81.
[22] J. Sadlej, J. Cz. Dobrowolski, J. E. Rode, M. H. Jamroz, Phys. Chem. Chem. Phys. 8 (2006) 101.
[23] T. Steiner, Angew. Chem. Int. Ed. 41 (2002) 48.
[1] F. Remize, L. Bamavon, S. Dequin, Metabol. Eng. 3 (2001) 301.
[2] O. Bastiansen, Acta Chem. Scand. 3 (1949)415.
[3] R. Chelli, F. L. Gervasio, C. Gellini, P. Procacci, G. Cardini, V. Schettino, J. Phys. Chem. A 104 (2000) 5351.
[4] C. S. Callam, S. J. Singer, T. L. Lowary, C. M. Hadad, J. Am. Chem. Soc. 123 (2001) 11743.
[5] C. H. Heathcock, M. McLaughlin, J. Medina, J. L. Hubbs, G. A. Wallace, R. Scott, M. M. Claffey, C. J. Hayes, G. R. Ott, J. Am. Chem. Soc. 125 (2003) 12844.
[6] Y. Kiyotsuka, J. Igarashi, Y. Kobayashi, Tetrahedron Lett. 43 (2002) 2725.
[7] J. Wouters, F. Moureau, G. Evrard, J. J. Koenig, S.Jegham, P.Gorge, F. Durant, Bioorg. Med. Chem. 7 (1999) 1683.
[8] L. Ehrenberg, S. Hussian, Mutat. Res. 86 (1981) 1.
[9] S. De Flora, P. Zanacchi, A. Camoirano, C. Bennicelli, G. S. Badolati, Mutat. Res. 133 (1984) 161.
[10] W. Lijinsky, R. M. Kovatch, Toxicol. Ind. Health 8 (1992) 267.
[11] R. D. Irwin, S. L. Eustis, S. Stefanski, J. K. Haseman, J. Appl. Toxicol. 16 (1996) 201.
[12] H. Landin, E. Tareke, P. Rydberg, U. Olsson, M. Tornqvist, Food Chem. Toxicol. 38 (2000) 963.
[13] M. J. Frisch, G. W. Trucks, H.B. Schlegel, G. E. Scuseria, M. A. Robb, J.R. Cheeseman, J. A. Montgomery, Jr. T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomclli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewsld, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Forcsman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chcn, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision B.01, (Gaussian, Inc., Pittsburgh PA, 2003.).
[14] R. Hauschid, J. Petit, Bulletin de la Societe Chimique de France, Memoires (1956) 878.
[2] V. Fock, NSherungsmethoden zur Losung des Quantenmechanischen Mehrkorperproblems, Zeit. Phys. 61 (1930) 126
[3] C. C. J. Roothaan, New developments in Molecular Orbital Theory, Rev. Mod. Phys. 23 (1951) 69
[4] J. B. Foresman, M. Head-Gordon, J. A. Pople and M. J. Frisch, Toward a systematic molecular orbital theory for excited states, J. Phys. Chem. 96 (1992)135
[5] E. A. Hylleraas, Zeit. Physik, 48 (1928) 469
[6] C. Moller and M. S. Plesset, Note on an Approximation Treatment for Many-Electron Systems, Phys. Rev. 46 (1934) 618
[7] M. Head-Gordon, J. A. Pople and M. J. Frisch, MP2 energy evaluation by direct methods, Chem. Phys. Lett. 153 (1988) 503
[8] M. J. Frisch, M. Head-Gordon and J. A. Pople, A direct MP2 gradient method, Chem. Phys. Lett. 166 (1990) 275
[9] M. J. Frisch, M. Head-Gordon and J. A. Pople, Semi-direct algorithms for the MP2 energy and gradient, Chem. Phys. Lett. 166 (1990) 281
[10] M. Head-Gordon and T. Head-Gordon, Analytic MP2 frequencies without fifth-order storage. Theory and application to bifurcated hydrogen bonds in the water hexamer, Chem. Phys. Lett. 220 (1994) 122
[11] S. Saebo and J. Almlof, Avoiding the integral storage bottleneck in LCAO calculations of electron correlation, Chem. Phys. Lett. 154 (1989) 83
[12] H.Thomas, The Calculation of Atomic Fields, Pro. Camb. Phil. Soc. 23 (1927)545
[13] R. Fermi, A Statistical Method for Determining Some Properties of the Atom, Atti Accad Lincei 6 (1927) 602
[14] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964) B864
[15] W. Kohn, L. J. Sham, Self-consistent Eguations Including Exchange and Correlation Effects, Phys. Rev. A 140 (1965) 1133
[16] 徐树方，矩阵计算的理论与方法，北京大学出版社，北京，1995年，
[17] White S R, Density Matrix Formulation for Quantum Renormalization Groups, Phys. Rev. Lett, 69 (1992) 2863
[1] J. A. Pople, Trans. Faraday Soc. 49 (1953) 1375
[2] R. Pariser and R. G. Parr, A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I, J. Chem. Phys. 21 (1953) 466
[3] R. Padser and R. G. Parr, A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. Ⅱ, J. Chem. Phys. 21 (1953) 767
[3] I. Ohmine, M. Karplus and K. Schulten, Renormalized configuration interaction method for electron correlation in the excited states of polyenes, J. Chem. Phys. 68 (1978) 2298
[4] J. Hubbard, Electron Correlations in Narrow Energy Bands, Proc. R. Soc. London Ser. A 276 (1963) 238
[5] E. Huckel, Zeit. Phys. 60 (1930) 423
[6] B. H. Brandow, Linked-Cluster Expansions for the Nuclear Many-Body Problem, Rev. Mod. Phys. 39 (1967) 771
[7] G. Hose, U. Kaldor, Diagrammatic many-body perturbation theory for general model spaces, J. Phys. B 12 (1979) 3827
[8] B. H. Brandow, Formal theory of effective-electron hamiltonians, Int. J. Quantum Chem. 15 (1979) 207
[9] P. W. Anderson, New approach to the theory of superexchange interactions, Phys. Rev. 115,2-13 (1959).
[10] P. A. Dirac, The Principles of Quantum Mechanics, Oxford University Press,Clarendon,1930
[11] J. H. Van Vleck, A. Sherman, Zeit. Phys. 49 (1935) 619
[12] L. Pauling and G. W. Wheland, The Nature of the Chemical Bond. V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals, J. Chem. Phys.1 (1933) 362
[13] C. K. Majumdar, Antiferromagnetic model with known ground state, J. Phys. C, 3 (1970)911
[14] C. K. Majumdar, D. K. Ghosh, J. Math. Phys. 10 (1969) 1399
[15] P. M. van den Broek, Exact value of the ground state energy of the linearantiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interaction, Phys. Lett. A, 77 (1980) 261
[16] B. S. Shastry, B. Sutherland, Excitation Spectrum of a Dimerized Next-Neighbor Antiferromagnetic Chain, Phys. Rev. Lett. 47 (1981) 964
[17] A. W. Garrett, Magnetic Excitations in the S=1/2 Alternating Chain Compound (VO)_2P_2O_7, Phys. Rev. Lett. 79 (1997)745
[18] K. M. Diedrix, Theoretical and experimental study of the magnetic properties of the singlet-ground-state system Cu (NO_3)_2·2. 5H_2O: An alternating linear Heisenberg antiferromagnet, Phys. Rev. B, 19 (1979) 420
[19] M. Base, Observation of the Spin-Peierls Transition in Linear Cu(Spin-1/2) Chains in an Inorganic Compound CuGeO_3, Phys. Rev. Lett. 70 (1993) 3651
[20] M. Isobe, Y. Ueda, Magnetic Susceptibility of QuasiOne-Dimensional Compound-NaV_2O_5 Possible Spin-Peierls Compound with High Critical Temperature of 34 K, J. Phys. Soc. Jpn, 65 (1996) 1178
[21] Azuma M, Observation of a Spin Gap in SrCu_2O_3 Comprising Spin-1/2 Quasi-1D Two-Leg Ladders, Phys. Rev. Lett. 73 (1994) 3463
[22] Chaboussant G, etc., Experimental phase diagram of Cu_2(C_5H_(12)N_2)_2C_(14): A quasi-one-dimensional antiferromagnetic spin-Heisenberg ladder, Phys. Rev. B 55 (1997) 3046
[1] K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47 (1975) 773
[2] (a) H. R. Krishna-Murthy, J. K. Wilkins and K. G. Wilson, Renormalization-group approach to the Anderson model of dilute magnetic alloys. Ⅰ. Static properties for the symmetric case, Phys. Rev. B 21 (1980) 1003; (b) Renormalization-group approach to the Anderson model of dilute magnetic alloys. Ⅱ. Static properties for the asymmetric case, Phys. Rev. B 21 (1980) 1044
[3] J. Kondo, Solid State Physics, Vol23, New York, (1969)
[4] P. A. Lee, Real-Space Scaling Studies of Localization, Plays. Rev. Lett. 42 (1979) 1492
[5] P. A. Lee and D. S. Fisher, Anderson Localization in Two Dimensions, Phys. Rev. Lett. 47 (1981) 882
[6] S. T. Chui and J. W. Bray, Computer renormalization-group technique applied to the Hubbard model, Phys. Rev. B 18 (1978) 2426
[7] J. W. Bray and S. T. Chui, Computer renormalization-group calculations of 2kF and 4kF correlation functions of the one-dimensional Hubbard model, Phys. Rev. B 19 (1979) 4876
[8] J. E. Hirsch, Renormalization-group study of the Hubbard model, Phys. Rev. B 22 (1980) 5259
[9] C. Dasgupta and P. Pfeuty, Comment on empirical photoionisation thresholds, J. Phys. C 14 (1981) 717
[10] S. R. White and R. M. Noack, Real-space quantum renormalization groups, Phys. Rev. Lett. 68 (1992) 3487
[11] S. R. White, Strongly correlated electron systems and the density matrix renormalization group, Phys. Rep. 301 (1998) 187
[13] S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69 (1992) 2863
[14] S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48 (1993) 10345
[15] S. Liang and H. Pang, Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective, Phys. Key. B 49 (1994) 9214
[16] S. R. White and D. A. Hase, Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S=1 Heisenberg chain, Phys. Rev. B 48 (1993) 3844
[17] S. Qin, X. Wang and L. Yu, Universality class of integer quantum spin chains: S=1/2 case study, Phys. Rev. B 46 (1997) R14251
[18] X. Wang, S. Qin and L. Yu, Haldane gap for the S=2 antiferromagnetic Heisenberg chain revisited, Phys. Rev. B 60 (1999) 14529
[19] S. Qin, S. Liang, Z. B. Su and L. Yu, Density-matrix renormalization-group calculation of correlation functions in the one-dimensional Hubbard model, Phys. Rev. B 52 (1995) R5475
[20] S. Qin and L. Yu, Momentum-distribution critical exponents for the one-dimensional largc-U Hubbard model in the thermodynamic limit, Phys. Rev. B 54 (1996) 1447
[21] K. Penc, K. Hallberg, F. Mila and H. Shiba, Shadow Band in the One-Dimensional Infinite-U Hubbard Model, Phys. Rev. Lett. 77 (1996) 1390
[22] S. Moukouri and L. G. Caron, Ground-state properties of the one-dimensional Kondo lattice at partial band filling, Phys. Rev. B 52 (1995) 15723
[23] J. Z. Lou, S. J. Qin and C. F. Chen, String Order in Half-Integer-Spin Antiferromagnetic Heisenberg Chains, Phys. Rev. Lett. 91 (2003) 087204
[24] S. J. Qin, J. Z. Lou, L. Q. Sun and C. F. Chen, Nonlocal Topological Order in Antiferromagnetic Heisenberg Chains, Phys. Rev. Lett. 90 (2003) 067202
[25] K. Hida, Magnetization Plateaux in Random Frustrated S=1/2 Heisenberg Chains J. Phys. Soc. Jpn. 72 (2003) 911
[26] H. E. Boos, V. E. Korepin, Y. Nishiyama and M. Shiroishi, J. Phys. A 35 (2002) 4443
[27] T. Hikihara and A. Furusaki, Spin correlations in the two-leg antiferromagnetic ladder in a magnetic field, Phys. Rev. B 63 (2001) 134438
[28] A. Kawaguchi, A. Koga, K. Okunishi and N. Kawakami, Magnetization process for a quasi-one-dimensional S=1 antiferromagnet, Phys. Rev. B 65 (2002) 214405
[29] L. Urba and A. Rosengren, Density-matrix renormalization-group analysis of the spin-1/2 XXZ chain in an XY symmetric random magnetic field, Phys. Rev. B 67 (2003) 104406
[30] J. Rotureau, N. Michel, W. Nazarewicz, M. Ploszajczak and J. Dukelsky Density Matrix Renormalization Group Approach for Many-Body Open Quantum Systems, Phys. Rev. Lett. 97 (2006) 110603
[31] O. Legeza and J. Solyom, Quantum data compression, quantum information generation, and the density-matrix renormalization-group method, Phys. Rev. B 70 (2004) 205118
[32] G. Hager, G. Wellein, E. Jeckelmann and H. Fehske, Stripe formation in doped Hubbard ladders, Phys. Rev. B 71 (2005) 075108
[33] M. Clemancey, H. Mayaffre, C. Berthier, M. Horvatic, J. -B. Fouet, S. Miyahara, F. Mila, B. Chiari and O. Piovesana, Field-Induced Staggered Magnetization and Magnetic Ordering in Cu2(CSH12N2)2Cl4, Phys. Rev. Lett. 97 (2006) 167204
[34] S. Liang and H. Pang, Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective, Phys. Rev. B 49 (1994) 9214
[35] R. M. Noack, S. R. White and D. J. Scalapino, in Computer Simulations in Condensed Matter Physics Ⅶ, Eds. D. P. Landau, K. K. Mon and H. B. Schuttler (Spinger Verlag, Heidelberg, Berlin, 1994)
[36] S. R. White and D. J. Scalapino, Density Matrix Renormalization Group Study of the Striped Phase in the 2D t-J Model, Phys. Rev. Lett. 80 (1998) 1272
[37] S. R. White and D. J. Scalapino, Energetics of Domain Walls in the 2D t-J Model, Phys. Rev. Lett. 81 (1998) 3227
[38] C. Zhang, E. Jeckelmann and S. R. White, Density Matrix Approach to Local Hilbert Space Reduction, Phys. Rev. Lett. 80 (1998) 2661
[39] E. Jeckelmann, C. Zhang and S. R. White, Metal-insulator transition in the one-dimensional Holstein model at half filling, Phys. Rec. B 60 (1999) 7950
[40] S. R. White and R. L. Martin, Ab initio quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 110 (1999) 4127
[41] J. Dukelsky and G. Sierra, Density Matrix Renormalization Group Study of Ultrasmall Superconducting Grains, Phys. Rev. Lett. 83 (1999) 172
[42] R. J. Bursill, T. Xiang and G. A. Gehring, J. Phys. Cond. Matt. 8 (1996) 1583
[43] X. Wang and T. Xiang, Transfer-matrix density-matrix renormalization-group theory for thermodynamics of one-dimensional quantum systems, Phys. Rev. B 56 (1997) 5061
[44] T. D. Kuhner and S. R. White, Dynamical correlation functions using the density matrix renormalization group, Phys. Rev. B 60 (1999) 335
[45] T. Xiang, Density-matrix renormalization-group method in momentum space, Phys. Rev. B 53 (1995) 10445
[46] M. A. Martin-Delgado and G. Sierra, Density Matrix Renormalization Group Approach to an Asymptotically Free Model with Bound States, Phys. Rev. Lett. 83 (1999) 1514
[47] S. R. White, Strongly correlated electron systems and the density matrix renormalization group, Phys. Rep. 301 (1998) 187
[48] J. Gaite, Angular Quantization And The Density Matrox Renormalization Group, Mod. Phys. Lett. A 16 (2001) 1109
[49] T. Xiang, Density-matrix renormalization-group method in momentum space, Phys. Rev. B 53 (1996) 10445
[50] S. Nishimoto, E. Jeckelmann, F. Gebhard and R. Noack, Application of the density matrix renormalization group in momentum space, Phys. Rev. B 65 (2002) 165114
[51] O. Legeza, J. Roder and B. Hess, Controlling the accuracy of the density-matrix renorrnalization-group method: The dynamical block state selection approach, Phys. Rev. B 67 (2003) 125114
[52] O. Legeza and J. Solyom, Optimizing the density-matrix renormalization group method using quantum information entropy, Phys. Rev. B 68 (2003) 195116
[53] T. Nishino and K. Okunishi, Product Wave Function Renormalization Group, J. Phys. Soc. Jpn. 64 (1995) 4084
[54] R. J. Bursill, T. Wang and G. A. Gehring, The density matrix renormalization group for a quantum spin chain at non-zero temperature, J. Phys. Cond. Matt. 8 (1996) L583
[55] G. Fano, F. Ortolani and L. Ziosi, The density matrix renormalization group method: Application to the PPP model of a cyclic polyene chain, J. Chem. Phys. 108 (1998) 9246
[56] G. L. Bendazzoli, S. Evangelisti, G. Fano, F. Ortolani and L. Ziosi, Density matrix renormalization group study of dirnerization of the Pariser-Parr-Pople model of polyacetilene, J. Chem. Phys. 110 (1999) 1277
[57] G. K.-L. Chan and M. Head-Gordon, Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group, J. Chem. Phys. 116 (2002) 4462
[58] S. Daul, I. Ciofini, C. Daul, and S. R. White, Full-CI quantum chemistry using the density matrix renormalization group, Int. J. Quantum Chem. 79 (2000) 331
[59] O. Legeza, J. Roder, and B. A. Hess, Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach, Phys. Rev. B 67 (20.03) 125114
[60] A. O. Mitrushenkov, G. Fano, F. Ortolani, R. Linguerri, and P. Palmieri, Quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 115(2001)6815
[61] Yi Gao, Chun-Gen Liu and Yuan-Sheng Jiang, The Valence Bond Study for Benzenoid Hydrocarbons of Medium to Infinite Sizes, J. Phys. Chem. A 106(2002)2592
[62] Haibo Ma, Fei Cai, Chungen Liu and Yuansheng Jiang, Spin distribution in neutral polyene radicals: Pariser-Parr-Pople model studied with the density matrix renormalization group method, J. Chem. Phys. 122 (2005) 104909
[63] S White and R Martin, Ab initio quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 110 (1999) 4127
[64] S. Daul and R. M. Noack, Phase diagram of the half-filled Hubbard chain with next-nearest-neighbor hopping, Phys. Rev. B 61 (2000) 1646
[65] A. O. Mitrushenkov, G. Fano, F. Ortolani, R. Linguerri and P. Palmieri, Quantum chemistry using the density matrix renormalization group, J. Chem. Phys. 115(2001)6815
[66] A. O. Mitrushenkov, R. Linguerri, P. Palmieri and G. Fano, Quantum chemistry using the density matrix renormalization group II, J. Chem. Phys. 119(2003)4148
[1] P. Schmitteckert and U. Eckern, Phase coherence in a random one-dimensional system of interacting fermions: A density-matrix renormalization-group study, Phys. Rev. B 53 (1996) 15397
[2] S. Rapsch, U. Schollwock and W. Zwerger, Density matrix renormalization group for disordered bosons in one dimension, Europhys. Lett. 46 (1999) 559
[3] S. R. White, I. Affleck and D. J. Scalapino, Local versus nonlocal order-parameter field theories for quantum phase transitions, Phys. Rev. B 65 (2002) 165122
[4] R. P. Feynman, Statistical Mechanics: A Set of Lectures, Benjamin, Reading, MA, 1972
[5] E. R. Davidson, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices, J. Comput. Phys. 17 (1975) 87
[6] P. Hennlius, Two-dimensional infinite-system density matrix renormalization group algorithm, Phys. Rev. B 60 (1999) 9561
[7] R. Bursill, Density matrix renormalization group algorithm for quantum lattice systems with a large number of states per site, Phys. Rev. B 60 (1999) 1643
[8] Yi Gao, Chun-Gen Liu and Yuan-Sheng Jiang, The Valence Bond Study for Benzenoid Hydrocarbons of Medium to Infinite Sizes, J. Phys. Chem. A 106 (2002) 2592
[1] 常建华 董绮功，波谱原理及解析，科学出版社，北京，2001年，352-378
[2] Z. Dubinsky, T. Berman, Seasonal changes in the spectral composition of down-Telling irradiance in Lake Kinneret, Limnol. Oceanogr, 24 (1979) 652
[3] L. A. Nafie, Polarization Modulation FTIR Spectroscopy, in Advances in Applied FTIR Spectroscopy, ed. M. W. Mackenzie, John Wiley and Sons, New York, 1988, 67-104
[4] 尤田耙，手性化合物的现代研究方法，中国科技大学出版社，合肥，1993年，122-218
[5] 黄量 戴立信，手性药物的化学与生物学，化学工业出版社，北京，2002年，1-5
[6] L. A. Nafie, R. K. Dukor and T. B. Freedman, Vibrational Circular Dichroism in Handbook of Vibrational Spectroscopy, John Wiley & Sons Ltd, Chichester, 2002, 731-744
[7] P. J. Stephens, F. J. Devlin, C. S. Ashvar, C. F. Chabalowski and M. J. Frisch, Theoretical calculation of vibrational circular dichroism spectra, Faraday Discuss., 1994, 99, 103-119.
[8] P. J. Stephens, Theory of Vibrational Circular Dichroism, J. Phys. Chem. 89 (1985) 748
[9] P. J. Stephens, Mechanisms of vectorial transmembrane reduction of viologens across phosphatidylcholine bilayer membranes, J. Phys. Chem. 91 (1987) 1712
[10] P. J. Stephens, K. J. Jalkanen, R. D. Amos, P. Lazzeretti and R. Zanasi, Ab initio calculations of atomic polar and axial tensors for hydrogen fluoride, water, ammonia, and methane, J. Phys. Chem. 94 (1990) 1811
[11] Stephens, P. J. ; Devlin, F. J. ; Chabalowski, C. F. ; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields, J. Phys. Chem. 1994, 98, 11623.
[12] Devlin, F. J. ; Finley, J. W. ; Stephens, P. J. ; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields: A Comparison of Local, Nonlocal, and Hybrid Density Functionals J. Phys. Chem. 1995, 99, 16883.
[13] R. Liu, D. R. Tate, J. A. Clark, P. R. Moody, A. S. Van Buren and J. A. Krauser, Density Functional Theory Study of Molecular Structures and Vibrational Spectra of 3, 4- and 2, 3-Pyridyne, J. Phys. Chem. 100 (1996) 3430
[14] S. Abdali, K. J. Jalkanen, H. Bohr, S. Suhai and R. M. Nieminen, The VA and VCD spectra of various isotopomers of -alanine in aqueous solution, Chem. Phys. 282 (2002) 219
[15] C. N. Tam, P. Bour and T. A. Keiderling, Vibrational Optical Activity of (3S, 6S)-3,6-Dimethyl-1, 4-dioxane-2, 5-dione, J. Am. Chem. Soc. 118 (1996) 10285
[16] F. J. Devlin, P. J. Stephens, C. Osterle, K. B. Wiberg, J. R. Cheeseman and M. J. Frisch, Configurational and Conformational Analysis of Chiral Molecules Using IR and VCD Spectroscopies: Spiropentylcarboxylic Acid Methyl Ester and Spiropentyl Acetate, J. Org. Chem. 67 (2002) 8090
[17] Frisch, M. J. Prediction of Vibrational Circular Dichroism Spectra Using Density Functional Theory: Camphor and Fenchone, J. Am. Chem. Soc. 118 (1996) 6327
[1] C. H. Heathcock, M. McLaughlin, J. Medina, J. L. Hubbs, G. A. Wallace, R. Scott, M. M. Claffey, C. J. Hayes, G. R. Ott, J. Am. Chem. Soc. 125 (2003) 12844.
[2] Y. Kiyotsuka, J. Igarashi, Y. Kobayashi, A study toward a total synthesis of fostriecin, Tetrahedron Lett. 43 (2002) 2725.
[3] J. Wouters, F. Moureau, G. Evrard, J. J. Koenig, S. Jegham, P. Gorge, F. Durant, A reversible monoamine oxidase a inhibitor, befloxatone: structural approach of its mechanism of action, Bioorg. Med. Chem. 7 (1999) 1683.
[4] W. Lijinsky, R. M. Kovatch, Toxicol. Ind. Health 8 (1992) 267.
[5] R. D. Irwin, S. L. Eustis, S. Stefanski, J. K. Haseman, Carcinogenicity of Glycidol in F344 Rats and B6C3F1 Mice, J. Appl. Toxicol. 16 (1996) 201.
[6] L. Ehrenberg and S. Hussian, Genetic toxicity of some important epoxides, Mutat. Res./Genetic Toxicology and Environmental Mutagenesis 86 (1981) 1.
[7] S. De Flora, P. Zanacehi, A. Camoirano, C. Bennicelli, G. S. Badolati, Genotoxic activity and potency of 135 compounds in the Ames reversion test and in a bacterial DNA-repair test, Mutat. Res./Reviews in Genetic Toxicology 133 (1984) 161.
[8] A. D. Becke, Density-functional thermochemistry. Ⅲ. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648
[9] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys. 88 (1988) 2547
[10] C. Lee, W. Yang and R. G. Parr, Development of the CoUe-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785
[11] J. P. Perdew, K. Burke and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Rev. B 54 (1996) 16533
[12] K. Burke, J. P. Perdew and Y. Wang, in Electronic Density Functional Theory: Recent Progress and New Directions, ed. J. F. Dobson, G. Vignale and M. P. Das, Plenum, New York, 1998.
[13] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople, GAUSSIAN 98 (Revision A.7), Craussian, Inc., Pittsburgh PA, 1998.
[14] J. H. Jensen, M. S. Gordon, Conformational potential energy surface of glycine: a theoretical study, J. Am. Chem. Soc. 113 (1991) 7917
[15] S. Wolfe, Gauche effect. Stereochemical consequences of adjacent electron pairs and polar bonds, Acc. Chem. Res. 5 (1972) 102
[16] C. S. Callam, S. J. Singer, T. L. Lowary and C. M. Hadad, Computational Analysis of the Potential Energy Surfaces of Glycerol in the Gas and Aqueous Phases: Effects of Level of Theory, Basis Set, and Solvation on Strongly Intramolecularly Hydrogen-Bonded Systems, J. Am. Chem. Soc. 123 (2001) 11743
[17] A. P. Mauricio, Scaling factors for the prediction of vibrational spectra. Ⅰ. Benzene molecule, Int. J. Quantum. Chem. 77 (2000) 661
[18] F. J. Devlin, P. J. Stephens, J. R. Chceseman and M. J. Frisch, Ab Initio Prediction of Vibrational Absorption and Circular Dichroism Spectra of Chiral Natural Products Using Density Functional Theory: Camphor and Fenchone, J. Phys. Chem. A, 101 (1997) 6322
[19] Y. He, X. Cao, L. A. Nafie and T. B. Freedman, Ab Initio VCD Calculation of a Transition-Metal Containing Molecule and a New Intensity Enhancement Mechanism for VCD, J. Am. Chem. Soc. 123 (2001) 11320
[20] W.-G. Han, K. J. Jalkanen, M. Elstner, S. Suhai, Theoretical Study of Aqueous N-Acetyl-L-alanine N'-Methylamide: Structures and Raman, VCD, and ROA Spectra, J. Phys. Chem. B. 102 (1998) 2587
[21] K. Monde, T. Taniguchi, N. Miura, S.-I. Nishimura, Specific Band Observed in VCD Predicts the Anomeric Configuration of Carbohydrates, J. Am. Chem. Soc. 126 (2004) 9496
[22] I. Alkorta and J. Elfuero, Discrimination of hydrogen-bonded complexes with axial chirality, J. Chem. Phys., 117 (2002) 6463
[23] J. Sadlej, J. Cz. Dobrowolski, J. E. Rode, M. H. Jamroz, DFT study of vibrational circular dichroism spectra of D-lactic acid-water complexesw, Phys. Chem. Chem. Phys. 8 (2006) 101
[24] S. F. Boys and F. Bemardi, Mol. Phys. 112 (1970) 553
[25] L. Turi and J. J. Dannenberg, Correcting for basis set superposition error in aggregates containing more than two molecules: ambiguities in the calculation of the counterpoise correction, J. Phys. Chem. 97 (1993) 2488
[1] C. H. Heatheock, M. McLaughlin, J. Medina, J. L. Hubbs, G. A. Wallace, R. Scott, M. M. Claffey, C. J. Hayes, G. R. Ott, J. Am. Chem. Soc. 125 (2003) 12844.
[2] Y. Kiyotsuka, J. Igarashi, Y.Kobayashi, Tetrahedron Lett. 43 (2002) 2725.
[3] J. Wouters, F. Moureau, G. Evrard, J. J. Koenig, S. Jegham, P. Gorge, F. Durant, Bioorg. Med. Chem. 7 (1999) 1683.
[4] W. Lijinsky, R. M. Kovateh, Toxicol. Ind. Health 8 (1992) 267.
[5] R. D. Irwin, S. L. Eustis, S. Stefanski, J. K. Haseman, J. Appl. Toxieol. 16 (1996)201.
[6] L. Ehrenberg, S. Hussian, Mutat. Res. 86 (1981) 1.
[7] S. De Flora, P. Zanacchi, A. Camoirano, C. Bennicelli, G S. Badolati, Murat. Res. 133 (1984) 161.
[8] T. B. Freedman, X. Cao, R. K. Dukor, L. A. Nafie, Chirality 15 (2003) 743.
[9] L. A. Nafie, Polarization Modulation FTIR Spectroscopy, in Advances in Applied FTIR Spectroscopy, ed. M. W. Mackenzie, John Wiley and Sons, New York, 1988, pp. 67-104.
[10] A. D. Becke, J. Chem. Phys. 98 (1993) 1372, 5648.
[11] R. Liu, D. R. Tate, J. A. Clark, P. R. Moody, A. S. Van Buren and J. A. Krauser, J. Phys. Chem., 100 (1996) 3430.
[12] S. Abdali, K. J. Jalkanen, H. Bohr, S. Suhai and R. M. Nieminen, Chem. Phys., 282 (2002) 219.
[13] F. J. Devlin, P. J. Stephens, J. R. Cheeseman and M. J. Frisch, J. Phys. Chem. A, 101 (1997)6322.
[14] (a) A. D. Becke, J. Chem. Phys., 98 (1993) 5648; (b) A. D. Becke, J. Chem. Phys., 88 (1988) 2547; (c) C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 37 (1988) 785; (d) J. P. Perdew, K. Burke and Y. Wang, Phys. Rev. B, 54 (1996) 16533.
[15] J. H. Jensen, M. S. Gordon, J.Am. Chem. Soc. 113 (1991) 7917.
[16] E. R. Joanna, Cz. D. Jan, Chem. Phys. Lett. 360 (2002) 123.
[17] (a) S. F. Boys and F. Bernardi, Mol. Phys. 112 (1970) 553; (b) L. Turi and J. J. Dannenberg, J. Phys. Chem. 97 (1993) 2488.
[18] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople, GAUSSIAN 98 (Revision A.7), Gaussian, Inc., Pittsburgh PA, 1998.
[19] S. Wolfe, Acc. Chem. Res. 5 (1972) 102.
[20] A. P. Mauricio, Int. J. Quantum. Chem. 77 (2000) 661.
[21] J. E. Rode, J. Cz. Dobrowolski, J. Mol. Struct. (THEOCHEM). 637 (2003) 81.
[22] J. Sadlej, J. Cz. Dobrowolski, J. E. Rode, M. H. Jamroz, Phys. Chem. Chem. Phys. 8 (2006) 101.
[23] T. Steiner, Angew. Chem. Int. Ed. 41 (2002) 48.
[1] F. Remize, L. Bamavon, S. Dequin, Metabol. Eng. 3 (2001) 301.
[2] O. Bastiansen, Acta Chem. Scand. 3 (1949)415.
[3] R. Chelli, F. L. Gervasio, C. Gellini, P. Procacci, G. Cardini, V. Schettino, J. Phys. Chem. A 104 (2000) 5351.
[4] C. S. Callam, S. J. Singer, T. L. Lowary, C. M. Hadad, J. Am. Chem. Soc. 123 (2001) 11743.
[5] C. H. Heathcock, M. McLaughlin, J. Medina, J. L. Hubbs, G. A. Wallace, R. Scott, M. M. Claffey, C. J. Hayes, G. R. Ott, J. Am. Chem. Soc. 125 (2003) 12844.
[6] Y. Kiyotsuka, J. Igarashi, Y. Kobayashi, Tetrahedron Lett. 43 (2002) 2725.
[7] J. Wouters, F. Moureau, G. Evrard, J. J. Koenig, S.Jegham, P.Gorge, F. Durant, Bioorg. Med. Chem. 7 (1999) 1683.
[8] L. Ehrenberg, S. Hussian, Mutat. Res. 86 (1981) 1.
[9] S. De Flora, P. Zanacchi, A. Camoirano, C. Bennicelli, G. S. Badolati, Mutat. Res. 133 (1984) 161.
[10] W. Lijinsky, R. M. Kovatch, Toxicol. Ind. Health 8 (1992) 267.
[11] R. D. Irwin, S. L. Eustis, S. Stefanski, J. K. Haseman, J. Appl. Toxicol. 16 (1996) 201.
[12] H. Landin, E. Tareke, P. Rydberg, U. Olsson, M. Tornqvist, Food Chem. Toxicol. 38 (2000) 963.
[13] M. J. Frisch, G. W. Trucks, H.B. Schlegel, G. E. Scuseria, M. A. Robb, J.R. Cheeseman, J. A. Montgomery, Jr. T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomclli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewsld, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Forcsman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chcn, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision B.01, (Gaussian, Inc., Pittsburgh PA, 2003.).
[14] R. Hauschid, J. Petit, Bulletin de la Societe Chimique de France, Memoires (1956) 878.