若干弱相互作用体系的结构和性质的理论研究
摘要
Brutschy和Hobza在介绍范德华分子时，指出了弱相互作用的重要性。众所周知，由于地球上所有的生命都与超分子化学物质有关，弱相互作用在化学，物理，尤其是生物学科中都扮演着重要的角色，范德华力则更为重要。发现具有异常性质的新型分子簇，以及揭示新的分子间相互作用的本质，一直以来都是化学领域中令人振奋的工作。弱相互作用对分子复合体系的结构及性质具有重要的影响，近几年来，弱相互作用已成为理论和实验工作者很感兴趣的研究方向。弱相互作用在生物分子识别，离子载体的选择性，晶体的组装，分子簇的形成等方面都起着决定性作用。
本论文中对若干具有代表性的弱相互作用体系的结构和性质进行了理论研究，得到了新的分子结构和新的分子间相互作用形式，有助于增进对生物分子识别，晶体组装，原子簇的形成等分子间相互作用本质的了解，并为设计新材料提供新思路。本论文中包括以下五个方面：
（1）CH2F2…H2O氢键体系的理论研究：二氟甲烷CH2F2中不含有氯，被太阳的紫外线照射不会放出对臭氧具有破坏力的氯原子，具有化学
的稳定性，是一种潜在的新型环保制冷剂。通过对CH2F2…H2O体系的研究，有助于我们了解其在大气层中的存在形式。通过从头计算，用较大基组6-311+G(2d,2p)，在MP2水平上计算得到CH2F2…H2O体系的优化几何构型，与实验结构一致。其中 ∠(F…H-O) = 116.5°，偏离普通氢键之键角达63.5°，为探讨产生氢键巨大弯曲的原因，采用点电荷扫描的办法，探测CH2F2…H2O体系中H2O的 O原子上的两对孤电子对的方向，发现了一个强的π型二级氢键相互作用。使用这种新的相互作用方式说明了产生氢键弯曲的原因，并且在MP4水平使用Counterpoise技术计算了π型二级氢键的稳定化能。CH2F2…H2O中π型二级氢键稳定化能是体系相互作用能的46.6%，对体系的影响很大。
（2）(HF)n (n=1~10)体系的偶极矩、极化率和第一超极化率的从头计算研究：新型非线性光学材料的研究大量出现，与之相比分子间相互作用对非线性光学性质贡献的研究是一个新的课题。因为晶体材料的性质不仅决定于分子本身的性质，还决定于分子的排列方式及分子间相互作用的效应，因此分子间相互作用体系的非线性光学性质的研究是非线性光学材料从分子设计到材料设计的桥梁。 (HF)n体系是典型的氢键体系，本论文中在MP2和B3LYP水平上, 使用aug-cc-pVDZ基组对(HF)n (n=1~10)折线型体系的几何结构进行了优化, 得出的HF分子簇的几何参数趋近于晶体结构结果. 使用MP2, B3LYP和HF方法计算了体系的静态偶极矩μ0, 极化率α0及第一超极化率β0, 并且分析了分子间相互作用对体系非线性光学性质的影响。
（3）FH…C4H4…HF体系的从头计算研究：使用高水平的从头计算方法，BSSE校正后的Counterpoise势能面方法（相互作用能最小优化方法），在MP2/aug-cc-pVDZ水平上得到了(电子氢键体系FH…C4H4…HF
的结构。在CCSD(T)/aug-cc-pVDZ水平计算出体系的分子间相互作用能是-7.8 kcal/mol。FH与子体系C4H4…HF之间的相互作用能是-3.4 kal/mol。得到FH…C4H4…HF体系的结构是（1(1）构型的。在优化出的结构中，两个HF分子在环的两边，在经过C=C键中点连线且垂直于环丁二烯的平面上，形状就象一个车轮和两边的脚踏板。在这样的结构中，发现一种反芳香性环的(电子氢键，这种氢键的质子受体是反芳香性的4电子4中心(键，给体则是两个HF分子中酸性的H原子。此外，还揭示了两种二级相互作用。第一种是HF的H原子与C4H4中与之距离较近的两个H原子间的排斥作用，第二种是F原子的孤对电子与C4H4中与之距离较远的两个H原子间的双重(型氢键作用。将分子间相互作用体系的结构特征与二级相互作用之间建立了联系。反芳香性环的(双氢键的弯曲来自与两个(型氢键。C4H4上的一对H原子的偏转是这对H原子与近端HF的H原子间静电排斥作用和它们与远端HF分子的F原子间形成了(型氢键的共同作用结果。
（4）使用弥散键函数的新方法计算(HF)2-体系的电子束缚能：采用了Aug-cc-pvtz基组，在MP2水平上对(HF)2-构型进行了优化，得出了比较理想的几何结构，计算振动频率表明此结构是稳定构型。使用弥散键函数方法，键函数[sp(0.09,0.03,0.01)，d(0.06,0.02)]放在距离端氢为1.5?处，在MP4(SDTQ)水平下得到了(HF)2-体系电子束缚能为498.23cm-1，达到实验值的98%。证明了键函数在此类体系的计算中是可行的。
（5）(HF)n- (n=2,3,4)体系的非线性光学性质的从头计算研究：在MP2的从头计算水平上发现，偶极束缚电子体系(HF)n- (n=2-4)拥有非常大的第一超极化率β0和偶极矩μ和极化率α，为了提高非线性光学性质，一个弱束缚的电子是设计非线性光学材料的新的和非常重要的设计思路。
Brutschy and Hobza have pointed out the importance of weak interactions in the introduction of their paper [Chem. Rev. 100, 3862 (2000)] It is well known that these weak interactions play an important role in chemistry, physics, and particularly in the biodisciplines. Since all life on earth may be viewed as a matter of supramolecular chemistry, with vdW forces playing a central role. Discovering novel molecular complex with unusual properties and nature of new intermolecular interactions is always an exciting paper of chemistry. A great interest has been evinced in the recent past to examine their role on the structure and properties of molecular complexes.
The theoretical studies were performed on the structures and properies of some representative systems containing weak interactions in this thesis. The results obtained on new structure and intermolecular interactions may be valuable for improving our understanding of the nature of intermolecular interaction in biological molecular recognition, crystal packing, cluster
formation, and so on.
(1)By means of ab initio calculations of MP2/6-311+G(2d,2p) method, the optimized geometry of the CH2F2…H2O complex is obtained. The structure of a subunit in the complex is similar to that of its molecule (CH2F2, H2O). It was found that the geometry structure of the complex CH2F2…H2O is close to its experimental structure. ∠(F…H-O)=116.5°is large deviation from a strictly linear H-bond. It is a result that a strong π-type secondary hydrogen bond is formed. Using a probing point charge to detect the orientations of the lone pairs at atom O of the CH2F2…H2O, we establish here aπ-type secondary H-bond interaction model because long pairs ni and CHi(i=1,2) are almost parallel and in a plane, the additional secondary H-bond between ni and CHi(i=1,2) form. The doubleπ-type H-bond is very strong. Furthermore, the stabilized energy of bending H-bond comes from π-type H-bond (= -0.0658 ev) is also calculated.
(2) The research about the new type non-linear optical materials have shown us a new field to investigate the interactions between molecules. The character of the crystal material owns not only to the molecule itself, but also to the arranged mode and the interactions between molecules. So the research about the systems with intermolecular interactions on the non-linear optical character will lead to the design on non-linear optical materials from molecule level to real materials. Many theoretical research on this filed have been carried out. By means of ab inito calculations of MP2/aug-cc-pVDZ and B3LYP/aug-cc-pVDZ methods, the optimized geometries of the (HF)n (n=1~10) are obtained. The (HF)n structure is approach to HF chain
configuration in crystal, when number of the HF molecule is large. The static dipole moments (μ0), polarizabilities (α0) and first hyperpolarizabilities (β0) of (HF)n (n=1~10) clusters are investigated by means of MP2, B3LYP and HF method with basis sets aug-cc-pVDZ.
(3) By counterpoise-correlated potential energy surface method (interaction energy optimization), the structure of the ( H–bond complex FH…C4H4…HF has been obtained at the second-order M?ller-Plesset perturbation (MP2/aug-cc-pVDZ) level. Intermolecular interaction energy of the complex is calculated to be -7.8 kcal/mol at the coupled-cluster theory with single, double substitutions and perturbatively linked triple excitations CCSD (T)/ aug-cc-pVDZ level. The optimized structure is a “wheel with a pair of pedals” shaped (1(1) structure in which both HF molecules almost lie on either vertical line passing through the middle-point of the C = C bond on either side of the horizontal plane of the C4 ring for cyclobutadiene. In the structure, an antiaromatic ring (- dihydrogen bond is found, in which the proton acceptor is antiaromatic 4 electron and 4 center (-bond and the donors are both acidic H atoms of HF molecules. In accompanying with the (- dihydrogen bond, two secondary interactions are exposed. The first is a repulsive interaction between an H
本论文中对若干具有代表性的弱相互作用体系的结构和性质进行了理论研究，得到了新的分子结构和新的分子间相互作用形式，有助于增进对生物分子识别，晶体组装，原子簇的形成等分子间相互作用本质的了解，并为设计新材料提供新思路。本论文中包括以下五个方面：
（1）CH2F2…H2O氢键体系的理论研究：二氟甲烷CH2F2中不含有氯，被太阳的紫外线照射不会放出对臭氧具有破坏力的氯原子，具有化学
的稳定性，是一种潜在的新型环保制冷剂。通过对CH2F2…H2O体系的研究，有助于我们了解其在大气层中的存在形式。通过从头计算，用较大基组6-311+G(2d,2p)，在MP2水平上计算得到CH2F2…H2O体系的优化几何构型，与实验结构一致。其中 ∠(F…H-O) = 116.5°，偏离普通氢键之键角达63.5°，为探讨产生氢键巨大弯曲的原因，采用点电荷扫描的办法，探测CH2F2…H2O体系中H2O的 O原子上的两对孤电子对的方向，发现了一个强的π型二级氢键相互作用。使用这种新的相互作用方式说明了产生氢键弯曲的原因，并且在MP4水平使用Counterpoise技术计算了π型二级氢键的稳定化能。CH2F2…H2O中π型二级氢键稳定化能是体系相互作用能的46.6%，对体系的影响很大。
（2）(HF)n (n=1~10)体系的偶极矩、极化率和第一超极化率的从头计算研究：新型非线性光学材料的研究大量出现，与之相比分子间相互作用对非线性光学性质贡献的研究是一个新的课题。因为晶体材料的性质不仅决定于分子本身的性质，还决定于分子的排列方式及分子间相互作用的效应，因此分子间相互作用体系的非线性光学性质的研究是非线性光学材料从分子设计到材料设计的桥梁。 (HF)n体系是典型的氢键体系，本论文中在MP2和B3LYP水平上, 使用aug-cc-pVDZ基组对(HF)n (n=1~10)折线型体系的几何结构进行了优化, 得出的HF分子簇的几何参数趋近于晶体结构结果. 使用MP2, B3LYP和HF方法计算了体系的静态偶极矩μ0, 极化率α0及第一超极化率β0, 并且分析了分子间相互作用对体系非线性光学性质的影响。
（3）FH…C4H4…HF体系的从头计算研究：使用高水平的从头计算方法，BSSE校正后的Counterpoise势能面方法（相互作用能最小优化方法），在MP2/aug-cc-pVDZ水平上得到了(电子氢键体系FH…C4H4…HF
的结构。在CCSD(T)/aug-cc-pVDZ水平计算出体系的分子间相互作用能是-7.8 kcal/mol。FH与子体系C4H4…HF之间的相互作用能是-3.4 kal/mol。得到FH…C4H4…HF体系的结构是（1(1）构型的。在优化出的结构中，两个HF分子在环的两边，在经过C=C键中点连线且垂直于环丁二烯的平面上，形状就象一个车轮和两边的脚踏板。在这样的结构中，发现一种反芳香性环的(电子氢键，这种氢键的质子受体是反芳香性的4电子4中心(键，给体则是两个HF分子中酸性的H原子。此外，还揭示了两种二级相互作用。第一种是HF的H原子与C4H4中与之距离较近的两个H原子间的排斥作用，第二种是F原子的孤对电子与C4H4中与之距离较远的两个H原子间的双重(型氢键作用。将分子间相互作用体系的结构特征与二级相互作用之间建立了联系。反芳香性环的(双氢键的弯曲来自与两个(型氢键。C4H4上的一对H原子的偏转是这对H原子与近端HF的H原子间静电排斥作用和它们与远端HF分子的F原子间形成了(型氢键的共同作用结果。
（4）使用弥散键函数的新方法计算(HF)2-体系的电子束缚能：采用了Aug-cc-pvtz基组，在MP2水平上对(HF)2-构型进行了优化，得出了比较理想的几何结构，计算振动频率表明此结构是稳定构型。使用弥散键函数方法，键函数[sp(0.09,0.03,0.01)，d(0.06,0.02)]放在距离端氢为1.5?处，在MP4(SDTQ)水平下得到了(HF)2-体系电子束缚能为498.23cm-1，达到实验值的98%。证明了键函数在此类体系的计算中是可行的。
（5）(HF)n- (n=2,3,4)体系的非线性光学性质的从头计算研究：在MP2的从头计算水平上发现，偶极束缚电子体系(HF)n- (n=2-4)拥有非常大的第一超极化率β0和偶极矩μ和极化率α，为了提高非线性光学性质，一个弱束缚的电子是设计非线性光学材料的新的和非常重要的设计思路。
Brutschy and Hobza have pointed out the importance of weak interactions in the introduction of their paper [Chem. Rev. 100, 3862 (2000)] It is well known that these weak interactions play an important role in chemistry, physics, and particularly in the biodisciplines. Since all life on earth may be viewed as a matter of supramolecular chemistry, with vdW forces playing a central role. Discovering novel molecular complex with unusual properties and nature of new intermolecular interactions is always an exciting paper of chemistry. A great interest has been evinced in the recent past to examine their role on the structure and properties of molecular complexes.
The theoretical studies were performed on the structures and properies of some representative systems containing weak interactions in this thesis. The results obtained on new structure and intermolecular interactions may be valuable for improving our understanding of the nature of intermolecular interaction in biological molecular recognition, crystal packing, cluster
formation, and so on.
(1)By means of ab initio calculations of MP2/6-311+G(2d,2p) method, the optimized geometry of the CH2F2…H2O complex is obtained. The structure of a subunit in the complex is similar to that of its molecule (CH2F2, H2O). It was found that the geometry structure of the complex CH2F2…H2O is close to its experimental structure. ∠(F…H-O)=116.5°is large deviation from a strictly linear H-bond. It is a result that a strong π-type secondary hydrogen bond is formed. Using a probing point charge to detect the orientations of the lone pairs at atom O of the CH2F2…H2O, we establish here aπ-type secondary H-bond interaction model because long pairs ni and CHi(i=1,2) are almost parallel and in a plane, the additional secondary H-bond between ni and CHi(i=1,2) form. The doubleπ-type H-bond is very strong. Furthermore, the stabilized energy of bending H-bond comes from π-type H-bond (= -0.0658 ev) is also calculated.
(2) The research about the new type non-linear optical materials have shown us a new field to investigate the interactions between molecules. The character of the crystal material owns not only to the molecule itself, but also to the arranged mode and the interactions between molecules. So the research about the systems with intermolecular interactions on the non-linear optical character will lead to the design on non-linear optical materials from molecule level to real materials. Many theoretical research on this filed have been carried out. By means of ab inito calculations of MP2/aug-cc-pVDZ and B3LYP/aug-cc-pVDZ methods, the optimized geometries of the (HF)n (n=1~10) are obtained. The (HF)n structure is approach to HF chain
configuration in crystal, when number of the HF molecule is large. The static dipole moments (μ0), polarizabilities (α0) and first hyperpolarizabilities (β0) of (HF)n (n=1~10) clusters are investigated by means of MP2, B3LYP and HF method with basis sets aug-cc-pVDZ.
(3) By counterpoise-correlated potential energy surface method (interaction energy optimization), the structure of the ( H–bond complex FH…C4H4…HF has been obtained at the second-order M?ller-Plesset perturbation (MP2/aug-cc-pVDZ) level. Intermolecular interaction energy of the complex is calculated to be -7.8 kcal/mol at the coupled-cluster theory with single, double substitutions and perturbatively linked triple excitations CCSD (T)/ aug-cc-pVDZ level. The optimized structure is a “wheel with a pair of pedals” shaped (1(1) structure in which both HF molecules almost lie on either vertical line passing through the middle-point of the C = C bond on either side of the horizontal plane of the C4 ring for cyclobutadiene. In the structure, an antiaromatic ring (- dihydrogen bond is found, in which the proton acceptor is antiaromatic 4 electron and 4 center (-bond and the donors are both acidic H atoms of HF molecules. In accompanying with the (- dihydrogen bond, two secondary interactions are exposed. The first is a repulsive interaction between an H
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乙硼烷离子和自由基异构体重排与体系势能面的量子化学计算研究,孙延波, 吴迪,李泽生,黄旭日,孙家锺, Chem. J. Chin. Univ.(高等学校化学学报)2002,23(9), 1727-1730
多面体碳烷的红外正则振动理论和计算分析, 杜莉萍, 吴迪, 郭纯孝,Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 185 ~ 190
键函数对ArCl-相互作用势理论计算结果的影响，孙延波,吴迪,李志儒,孙家钟，Chem. J. Chin. Univ.(高等学校化学学报)2002,23(1), 121 ~ 122
Ab Initio Study of the Interaction Hyperpolarizabilities of H-Bond Dimers between Two π-Systems，Bing-Qiang Wang, Zhi-Ru Li, Di Wu, Xi-Yun Hao, Ru-Jiao Li, and Chia-Chung Sun，J. Phys. Chem. A 2004, 108(13), 2464-2468
An ab Initio Prediction of the Extraordinary Static First Hyperpolarizability for the Electron-Solvated Cluster (FH)2{e}(HF)，Ying Li, Zhi-Ru Li, Di Wu, Rui-Yan Li, Xi-Yun Hao, and Chia-Chung Sun，J. Phys. Chem. B 2004, 108, 3145-3148
The interaction between trapped electron and water molecules in one interior structure of water tetramer anion，Xi-Yun Hao, Zhi-Ru Li, Di Wu, Ze-ShengLi, Chia-ChungSun，Chem. Phys. Lett. 2003, 370, 665–669
A theoretical prediction on intermolecular monoelectron dihydrogen bond H…e…H in the cluster anion (FH){e}(HF)2，Xi-Yun Hao, Zhi-Ru Li, Di Wu, Yi Wang, Ze-Sheng Li, and Chia-Chung Sun，J. Chem. Phys. 2003, 118(1), 83-86
The evolution of the monoelectron dihydrogen bond H…e…H in the symmetric and asymmetric cluster anions (FH)n{e}(HF)m，Xi-Yun Hao, Zhi-Ru Li, Di Wu, Ze-Sheng Li, and Chia-Chung Sun，J. Chem. Phys. 2003, 118(24), 10939-10943
Ab Initio Study of the Interaction Hyperpolarizabilities of HCN-HF and HNC-HF
Complexes, Ru-Jiao Li, Zhi-Ru Li, Di Wu, Xi-Yun Hao, Bing-Qiang Wang, and Chia-Chung Sun，J. Phys. Chem. A 2003, 107, 6306-6310
Ab initio study of the interaction hyperpolarizabilities of the van der Waals complex Ar–HF, Bing-Qiang Wang, Zhi-Ru Li, Di Wu, Chia-Chung Sun，J. Mol. Struct. (Theochem) 2003, 620, 77–86.
Density functional study of structures and interaction hyperpolarizabilities of NH3–HCl–(H2O)n (n=0–4) clusters，Ru-Jiao Li, Zhi-Ru Li, Di Wu, Xi-Yun Hao, Ying Li, Bing-Qiang Wang, Fu-Ming Tao, Chia-Chung Sun，Chem. Phys. Lett. 2003, 372, 893–898
Single-electron hydrogen bonds in the methyl radical complexes H3C…HF and H3C…HCCH: an ab initio study，Bing-Qiang Wang, Zhi-Ru Li, Di Wu, Xi-Yun Hao,Ru-Jiao Li, Chia-Chung Sun，Chem. Phys. Lett. 2003, 375, 91–95
(H2O)2和(HCl)2非线性光学性质的从头计算研究，王义，李志儒，吴迪，郝希云，张蛮，储三阳，孙家锺，Chem. J. Chin. Univ.(高等学校化学学报)2003,24(4), 675-677
Ne–HF、Ar–HF 和Ar–HCl 相互作用超极化率的从头计算研究，王炳强, 吴 迪, 张 蛮, 郝希云, 李志儒，Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 194 ~ 197
Kr-He 相互作用能从头计算与键函数的中心选取问题，张 蛮, 郑植仁, 吴 迪, 孙延波, 陶福明, 李志儒, 孙家钟，Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 212 ~ 214
一种cs-NH3-HCl-4H2O的结构和非线性光学性质的研究，李茹姣, 李志儒, 吴 迪, 郝希云, 王炳强，Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 369-371
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An ab initio theoretical prediction: An antiaromatic ring π-dihydrogen bond accompanied by two secondary interactions in a ‘‘wheel with a pair of pedals’’ shaped complex FH…C4H4…HF, Di Wu, Zhi-Ru Li, Xi-Yun Hao, A. F. Jalbout, L. Adamowicz, Ru-Jiao Li and Chia-Chung Sun, J. Chem. Phys. 2004, 120(3), 1330-1335
CH2F2…H2O中强π型二级氢键，吴迪, 李志儒, 郑植仁 ，Chem. J. Chin. Univ.(高等学校化学学报)2002,23(4), 640 ~ 643
(HF)n (n=1~10)体系的偶极矩、极化率和一阶超极化率的从头计算研究，吴 迪, 李志儒, 张 蛮，Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 356-361
Long Range π-Type Hydrogen Bond in the Dimers (HF)2, (H2O)2, and H2O-HF, Li Zhi-Ru, Wu Di, Li Ze-Sheng, Huang Xu-Ri, Fu-Ming Tao, and Sun Chia-Chung, J. Phys. Chem. A 2001, 105, 1163-1168
乙硼烷离子和自由基异构体重排与体系势能面的量子化学计算研究,孙延波, 吴迪,李泽生,黄旭日,孙家锺, Chem. J. Chin. Univ.(高等学校化学学报)2002,23(9), 1727-1730
多面体碳烷的红外正则振动理论和计算分析, 杜莉萍, 吴迪, 郭纯孝,Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 185 ~ 190
键函数对ArCl-相互作用势理论计算结果的影响，孙延波,吴迪,李志儒,孙家钟，Chem. J. Chin. Univ.(高等学校化学学报)2002,23(1), 121 ~ 122
Ab Initio Study of the Interaction Hyperpolarizabilities of H-Bond Dimers between Two π-Systems，Bing-Qiang Wang, Zhi-Ru Li, Di Wu, Xi-Yun Hao, Ru-Jiao Li, and Chia-Chung Sun，J. Phys. Chem. A 2004, 108(13), 2464-2468
An ab Initio Prediction of the Extraordinary Static First Hyperpolarizability for the Electron-Solvated Cluster (FH)2{e}(HF)，Ying Li, Zhi-Ru Li, Di Wu, Rui-Yan Li, Xi-Yun Hao, and Chia-Chung Sun，J. Phys. Chem. B 2004, 108, 3145-3148
The interaction between trapped electron and water molecules in one interior structure of water tetramer anion，Xi-Yun Hao, Zhi-Ru Li, Di Wu, Ze-ShengLi, Chia-ChungSun，Chem. Phys. Lett. 2003, 370, 665–669
A theoretical prediction on intermolecular monoelectron dihydrogen bond H…e…H in the cluster anion (FH){e}(HF)2，Xi-Yun Hao, Zhi-Ru Li, Di Wu, Yi Wang, Ze-Sheng Li, and Chia-Chung Sun，J. Chem. Phys. 2003, 118(1), 83-86
The evolution of the monoelectron dihydrogen bond H…e…H in the symmetric and asymmetric cluster anions (FH)n{e}(HF)m，Xi-Yun Hao, Zhi-Ru Li, Di Wu, Ze-Sheng Li, and Chia-Chung Sun，J. Chem. Phys. 2003, 118(24), 10939-10943
Ab Initio Study of the Interaction Hyperpolarizabilities of HCN-HF and HNC-HF
Complexes, Ru-Jiao Li, Zhi-Ru Li, Di Wu, Xi-Yun Hao, Bing-Qiang Wang, and Chia-Chung Sun，J. Phys. Chem. A 2003, 107, 6306-6310
Ab initio study of the interaction hyperpolarizabilities of the van der Waals complex Ar–HF, Bing-Qiang Wang, Zhi-Ru Li, Di Wu, Chia-Chung Sun，J. Mol. Struct. (Theochem) 2003, 620, 77–86.
Density functional study of structures and interaction hyperpolarizabilities of NH3–HCl–(H2O)n (n=0–4) clusters，Ru-Jiao Li, Zhi-Ru Li, Di Wu, Xi-Yun Hao, Ying Li, Bing-Qiang Wang, Fu-Ming Tao, Chia-Chung Sun，Chem. Phys. Lett. 2003, 372, 893–898
Single-electron hydrogen bonds in the methyl radical complexes H3C…HF and H3C…HCCH: an ab initio study，Bing-Qiang Wang, Zhi-Ru Li, Di Wu, Xi-Yun Hao,Ru-Jiao Li, Chia-Chung Sun，Chem. Phys. Lett. 2003, 375, 91–95
(H2O)2和(HCl)2非线性光学性质的从头计算研究，王义，李志儒，吴迪，郝希云，张蛮，储三阳，孙家锺，Chem. J. Chin. Univ.(高等学校化学学报)2003,24(4), 675-677
Ne–HF、Ar–HF 和Ar–HCl 相互作用超极化率的从头计算研究，王炳强, 吴 迪, 张 蛮, 郝希云, 李志儒，Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 194 ~ 197
Kr-He 相互作用能从头计算与键函数的中心选取问题，张 蛮, 郑植仁, 吴 迪, 孙延波, 陶福明, 李志儒, 孙家钟，Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 212 ~ 214
一种cs-NH3-HCl-4H2O的结构和非线性光学性质的研究，李茹姣, 李志儒, 吴 迪, 郝希云, 王炳强，Chem. J. Chin. Univ.(高等学校化学学报)2002,23 (Supplement), 369-371