叠氮类分子簇结构和性质的量子化学研究
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摘要
本论文运用量子化学理论方法研究叠氮类分子簇的结构和性质，分两大部分。
第一部分主要研究简单叠氮化合物多聚体的分子间相互作用。目的是开拓叠氮高能体系分子间弱相互作用的研究，并为叠氮类混合炸药的配方设计提供信息，利于推进含能材料学科的发展。
对超分子模型体系叠氮化氢多聚体[(HN_3)_n，(n=2-4)]，采用密度泛函理论(DFT)B3LYP方法，在不同基组下进行计算研究。首次求得它们的全优化几何构型，二聚体为环状和链状结构，而三聚体和四聚体均为环状结构。随着聚合度(由2到4)的增加，其结构参数和电荷也随之变化。对同类构型，随着聚合度(由2到4)的增加，构型中N…H间的Mulliken集居数逐渐增加。由三聚体形成四聚体比由二聚体形成三聚体的分子间相互作用能变化大。对三聚体和四聚体，我们还重点考察了协同效应对分子间相互作用能的贡献，发现同类结构中四聚体的协同效应比三聚体的强。对所有多聚体分子间相互作用能的计算，进行基组叠加误差(BSSE)和零点能(ZPE)校正都是必要的。与单体相比，多聚体中所有N-H伸缩振动频率均发生了较明显的红移，且随聚合度(由2到4)的增加，红移数值亦增加，四聚体的红移数值高达200cm~(-1)以上。同时讨论了在不同温度下由单体形成多聚体的热力学性质变化。通过比较6-311G~(**)和6.311++G~(**)以及cc-pVTZ基组下的计算结果，说明选用较节省的6-311G~(**)基组研究(HN_3)_(1-4)体系是合适的。
在HF／6-311++G~(**)水平上分别首次求得叠氮甲烷二聚体(CH_3N_3)_2的五种稳定构型以及叠氮乙烷二聚体(CH_3CH_2N_3)_2和叠氮乙烯二聚体(CH_2CHN_3)_2的各三种稳定构型。超分子体系的几何构型和电荷与单体的相差不大，表明分子间相互作用对该类体系的构型和电荷影响很小。在MP2／6-311++G~(**)／／HF／6-311++G~(**)水平上计算(CH_3N_3)_2、(CH_3CH_2N_3)_2和(CH_2CHN_3)_2的最大分子间相互作用能分别为-10.78、-10.45和-8.66kJ·mol~(-1)，预示有机叠氮化物二聚体分子间相互作用均较弱。叠氮乙烷的最大分子间相互作用能与叠氮甲烷的几乎一样，说明甲基和乙基对体系分子间相互作用能几乎没有影响。对所有二聚体分子间相互作用能的计算，电子相关校正和BSSE校正都是必要的，相比之下，ZPE校正则较为次要。为了进一步揭示相互作用的本质，我们还对这三种二聚体进行了自然键轨道分析。基于振动分析和统计热力学，求得它们单体和二聚体在不同温度下的热力学函数。
摘要
博士论文
第二部分研究第111主族金属叠氮无机和有机分子簇的结构一性能关系。该类簇合
物具有重要应用背景，基础研究利于指导其设计和合成，同时拓展了成键和结构理论。
首先用DFT一B3LYP方法，在不同的基组水平上研究了叠氮二氢铝体系
(HZAIN3)l一4，获得(HZAIN3)2-4多聚体的全优化几何构型均为环状构型。若单体连接方
式为HZAI一Na一p一丫，则多聚体通过一子体系叠氮基的a书和另一子体系的Al原子
相连，即取Al-N一Al结合方式。三聚体拥有船式和椅式两种构象且结合能接近，四
种四聚体的结合能也只有微小差别。同时找到由单体形成二聚体的过渡态(活化能为
65.39 kJ.mol一’)，通过内察反应坐标(I RC)进一步确认了过渡态是反应物络合物(CR)
和产物(R)的直接连接。热力学计算可知，求得298.2K下最稳定二聚体、三聚体和四
聚体的浓度比为1.0:12.23:0.63。从而表明叠氮二氢铝体系是二聚体、三聚体和四
聚体的平衡共存体，且以三聚体为主要成分。比较6一31卜G*和6一31卜+G**以及
aug一cc一pVTZ基组下的计算结果，表明以较节省的6一3 11+G*基组计算该类体系是合适
的。通过简谐振动分析获得(HZAIN3)，一的IR谱。
其次，用类似的方法研究了叠氮二氢嫁(HZGaN级、多聚体的全优化几何构型、电
子结构、结合能、IR谱以及由单体形成多聚体的热力学性质变化。多聚体同样为
Ga-N一Ga连接方式。三聚体拥有船式和椅式两种构象且结合能接近，四个四聚体的
结合能也只有微小差别。与叠氮二氢铝体系相比，叠氮二氢嫁多聚体的结合能较高。
本工作进一步证明，6一31卜G*基组对研究该类体系是恰当的。通过热力学计算可知，
298.2K下最稳定二聚体、三聚体和四聚体的浓度比为1 .00:213.36:9.26，可见三聚体
为主要成分。与叠氮二氢铝体系各组分的比例数值相比较，不难看出，在叠氮二氢嫁
体系中，以三聚体所占比例更大。
接着对(MeZMN3)1一3(M=AI，Ga)进行DFT一B3LYP/snD计算研究并作比较。
(MeZMN级一3(M二Al，Ga)的各种优化构型均为环状构型，多聚体仍然取Al--N一Al或
Ga一N一Ga连接方式。讨论了聚合前后的结构和电荷变化。经零点能校正后，叠氮二
甲基铝的两个三聚体结合能接近，同样叠氮二甲基嫁的两个三聚体结合能也接近。叠
氮二甲基铝二聚体和三聚体的结合能均低于叠氮二甲基嫁的相应多聚体。对叠氮二甲
基铝和叠氮二甲基嫁多聚体的IR谱进行了归属。热力学计算发现，298.2K下叠氮二
甲基铝的最稳定二聚体与三聚体的浓度比为128630:1，叠氮二甲基稼的相应结果为
11671:1，可见叠氮二甲基铝和嫁体系以二聚体的形式存在，前者二聚体所占的比例
较后者更大。
博士
The dissertation is about quantum chemical calculations on the molecular clusters of azides. There are two parts:
In the first part, we present our systematical studies on intermolecular interactions for the simple azides clusters. The aim is to provide a pioneer model for the study of intermolecular weak interaction in the high energetic materials of the azides compounds. It not only provides important information for the design of mixed explosives, but also plays a promotive role in the development of energetic materials.
DFT theory at B3LYP level with different basis sets is performed to calculate the supermolecular systems consisting of up to four hydrazoic acid molecules (HN3)n (n=2-4). The fully optimized geometries have been obtained for the first time. The dimers are found to exhibit cyclic and chain structures. The trimers and tetramers both possess cyclic structures. Both the structural changes of submolecules and charge transfers increase in the cluster processing. The Mulliken populations on intermolecular N...H increase in the sequence of dimer, trimer and tetramer for the same shape. The transition from the trimer to the tetramer involves larger stabilization than that from the dimer to the trimer. As for the trimer and tetramer, the contribution of cooperative effect to the interaction energy is mainly investigated. It is found that cooperative effect increases from the trimer to the tetramer. The basis set superposition error (BSSE) and zero point energies (ZPE) corrections are absolutely necessary for the inter
action energies of the clusters. Compared to the monomer, the N-H stretching vibrational frequencies show a marked red shift, as the size of the cluster growths, the shifts increase, reaching more than 200 cm-1 in the tetramer. The changes of thermodynamic properties from the monomer to the (HN3)2-4 clusters at different temperature have been also discussed. The results with the 6-311G**, 6-311++G** and cc-pVTZ basis sets show it is suitable to choose the economic 6-311G** basis set to study the system of (HN3)1_4.
Five optimized geometries of (CH3N3)2 dimers and three optimized geometries of (CH3CH2N3)2 and (CH2CHN3)2 supersystems are obtained respectively at the HF/6-311++G** level for the first time. Both the structural changes and charge transfers of
each cluster are slight compared to the monomer, which implies that the influence of interaction on the geometry and charge is very weak. The corrected interaction energies of the most stable (CH3N3)2, (CH3CH2N3)2 and (CH2CHN3)2 dimers are predicted to be-10.78, -10.45 and -8.66 kJ mol-1 respectively at the MP2/6-311++G*V/HF/6-311++G** level, which shows that the intermolecular interaction of the organic azides molecules is weak. The similar corrected interaction energies of the most stable (CH3N3)2 and (CH3CH2N3)2 indicate that the methyl and ethyl group have little influence on the intermolecular interaction. The electron correlation energies and BSSE correction are absolutely necessary for the interaction energies of the dimers. The ZPE corrections are much less than the electron correlation energies and BSSE correction for the interaction energies. Natural bond orbital (NBO) analysis is performed to reveal the origin of the interaction. On the basis of vibrational analysis and statistical thermodynamic, thermodynamic properties for the monomer and the dimers at different temperature have been obtained.
In the second part, we discuss the relationship between the structures and properties of the Group IIIA inorganometallic and organometallic azide clusters. The clusters have been applied widely. The basic studied results not only provide useful information for the design and synthesis of them, but also develop the bonding and structural theory.
Firstly, the DFT/B3LYP method with different basis sets used to calculate the (H2AlN3)1-4 clusters predicts that the (H2AlN3)2-4 clusters all possess cyclic-like structures. (H2AlN3)2-4 clusters are formed by Al atoms bridged by the a-nitrogen of the azide groups (connectivity: H2A1-Na-NB-Nr)
第一部分主要研究简单叠氮化合物多聚体的分子间相互作用。目的是开拓叠氮高能体系分子间弱相互作用的研究，并为叠氮类混合炸药的配方设计提供信息，利于推进含能材料学科的发展。
对超分子模型体系叠氮化氢多聚体[(HN_3)_n，(n=2-4)]，采用密度泛函理论(DFT)B3LYP方法，在不同基组下进行计算研究。首次求得它们的全优化几何构型，二聚体为环状和链状结构，而三聚体和四聚体均为环状结构。随着聚合度(由2到4)的增加，其结构参数和电荷也随之变化。对同类构型，随着聚合度(由2到4)的增加，构型中N…H间的Mulliken集居数逐渐增加。由三聚体形成四聚体比由二聚体形成三聚体的分子间相互作用能变化大。对三聚体和四聚体，我们还重点考察了协同效应对分子间相互作用能的贡献，发现同类结构中四聚体的协同效应比三聚体的强。对所有多聚体分子间相互作用能的计算，进行基组叠加误差(BSSE)和零点能(ZPE)校正都是必要的。与单体相比，多聚体中所有N-H伸缩振动频率均发生了较明显的红移，且随聚合度(由2到4)的增加，红移数值亦增加，四聚体的红移数值高达200cm~(-1)以上。同时讨论了在不同温度下由单体形成多聚体的热力学性质变化。通过比较6-311G~(**)和6.311++G~(**)以及cc-pVTZ基组下的计算结果，说明选用较节省的6-311G~(**)基组研究(HN_3)_(1-4)体系是合适的。
在HF／6-311++G~(**)水平上分别首次求得叠氮甲烷二聚体(CH_3N_3)_2的五种稳定构型以及叠氮乙烷二聚体(CH_3CH_2N_3)_2和叠氮乙烯二聚体(CH_2CHN_3)_2的各三种稳定构型。超分子体系的几何构型和电荷与单体的相差不大，表明分子间相互作用对该类体系的构型和电荷影响很小。在MP2／6-311++G~(**)／／HF／6-311++G~(**)水平上计算(CH_3N_3)_2、(CH_3CH_2N_3)_2和(CH_2CHN_3)_2的最大分子间相互作用能分别为-10.78、-10.45和-8.66kJ·mol~(-1)，预示有机叠氮化物二聚体分子间相互作用均较弱。叠氮乙烷的最大分子间相互作用能与叠氮甲烷的几乎一样，说明甲基和乙基对体系分子间相互作用能几乎没有影响。对所有二聚体分子间相互作用能的计算，电子相关校正和BSSE校正都是必要的，相比之下，ZPE校正则较为次要。为了进一步揭示相互作用的本质，我们还对这三种二聚体进行了自然键轨道分析。基于振动分析和统计热力学，求得它们单体和二聚体在不同温度下的热力学函数。
摘要
博士论文
第二部分研究第111主族金属叠氮无机和有机分子簇的结构一性能关系。该类簇合
物具有重要应用背景，基础研究利于指导其设计和合成，同时拓展了成键和结构理论。
首先用DFT一B3LYP方法，在不同的基组水平上研究了叠氮二氢铝体系
(HZAIN3)l一4，获得(HZAIN3)2-4多聚体的全优化几何构型均为环状构型。若单体连接方
式为HZAI一Na一p一丫，则多聚体通过一子体系叠氮基的a书和另一子体系的Al原子
相连，即取Al-N一Al结合方式。三聚体拥有船式和椅式两种构象且结合能接近，四
种四聚体的结合能也只有微小差别。同时找到由单体形成二聚体的过渡态(活化能为
65.39 kJ.mol一’)，通过内察反应坐标(I RC)进一步确认了过渡态是反应物络合物(CR)
和产物(R)的直接连接。热力学计算可知，求得298.2K下最稳定二聚体、三聚体和四
聚体的浓度比为1.0:12.23:0.63。从而表明叠氮二氢铝体系是二聚体、三聚体和四
聚体的平衡共存体，且以三聚体为主要成分。比较6一31卜G*和6一31卜+G**以及
aug一cc一pVTZ基组下的计算结果，表明以较节省的6一3 11+G*基组计算该类体系是合适
的。通过简谐振动分析获得(HZAIN3)，一的IR谱。
其次，用类似的方法研究了叠氮二氢嫁(HZGaN级、多聚体的全优化几何构型、电
子结构、结合能、IR谱以及由单体形成多聚体的热力学性质变化。多聚体同样为
Ga-N一Ga连接方式。三聚体拥有船式和椅式两种构象且结合能接近，四个四聚体的
结合能也只有微小差别。与叠氮二氢铝体系相比，叠氮二氢嫁多聚体的结合能较高。
本工作进一步证明，6一31卜G*基组对研究该类体系是恰当的。通过热力学计算可知，
298.2K下最稳定二聚体、三聚体和四聚体的浓度比为1 .00:213.36:9.26，可见三聚体
为主要成分。与叠氮二氢铝体系各组分的比例数值相比较，不难看出，在叠氮二氢嫁
体系中，以三聚体所占比例更大。
接着对(MeZMN3)1一3(M=AI，Ga)进行DFT一B3LYP/snD计算研究并作比较。
(MeZMN级一3(M二Al，Ga)的各种优化构型均为环状构型，多聚体仍然取Al--N一Al或
Ga一N一Ga连接方式。讨论了聚合前后的结构和电荷变化。经零点能校正后，叠氮二
甲基铝的两个三聚体结合能接近，同样叠氮二甲基嫁的两个三聚体结合能也接近。叠
氮二甲基铝二聚体和三聚体的结合能均低于叠氮二甲基嫁的相应多聚体。对叠氮二甲
基铝和叠氮二甲基嫁多聚体的IR谱进行了归属。热力学计算发现，298.2K下叠氮二
甲基铝的最稳定二聚体与三聚体的浓度比为128630:1，叠氮二甲基稼的相应结果为
11671:1，可见叠氮二甲基铝和嫁体系以二聚体的形式存在，前者二聚体所占的比例
较后者更大。
博士
The dissertation is about quantum chemical calculations on the molecular clusters of azides. There are two parts:
In the first part, we present our systematical studies on intermolecular interactions for the simple azides clusters. The aim is to provide a pioneer model for the study of intermolecular weak interaction in the high energetic materials of the azides compounds. It not only provides important information for the design of mixed explosives, but also plays a promotive role in the development of energetic materials.
DFT theory at B3LYP level with different basis sets is performed to calculate the supermolecular systems consisting of up to four hydrazoic acid molecules (HN3)n (n=2-4). The fully optimized geometries have been obtained for the first time. The dimers are found to exhibit cyclic and chain structures. The trimers and tetramers both possess cyclic structures. Both the structural changes of submolecules and charge transfers increase in the cluster processing. The Mulliken populations on intermolecular N...H increase in the sequence of dimer, trimer and tetramer for the same shape. The transition from the trimer to the tetramer involves larger stabilization than that from the dimer to the trimer. As for the trimer and tetramer, the contribution of cooperative effect to the interaction energy is mainly investigated. It is found that cooperative effect increases from the trimer to the tetramer. The basis set superposition error (BSSE) and zero point energies (ZPE) corrections are absolutely necessary for the inter
action energies of the clusters. Compared to the monomer, the N-H stretching vibrational frequencies show a marked red shift, as the size of the cluster growths, the shifts increase, reaching more than 200 cm-1 in the tetramer. The changes of thermodynamic properties from the monomer to the (HN3)2-4 clusters at different temperature have been also discussed. The results with the 6-311G**, 6-311++G** and cc-pVTZ basis sets show it is suitable to choose the economic 6-311G** basis set to study the system of (HN3)1_4.
Five optimized geometries of (CH3N3)2 dimers and three optimized geometries of (CH3CH2N3)2 and (CH2CHN3)2 supersystems are obtained respectively at the HF/6-311++G** level for the first time. Both the structural changes and charge transfers of
each cluster are slight compared to the monomer, which implies that the influence of interaction on the geometry and charge is very weak. The corrected interaction energies of the most stable (CH3N3)2, (CH3CH2N3)2 and (CH2CHN3)2 dimers are predicted to be-10.78, -10.45 and -8.66 kJ mol-1 respectively at the MP2/6-311++G*V/HF/6-311++G** level, which shows that the intermolecular interaction of the organic azides molecules is weak. The similar corrected interaction energies of the most stable (CH3N3)2 and (CH3CH2N3)2 indicate that the methyl and ethyl group have little influence on the intermolecular interaction. The electron correlation energies and BSSE correction are absolutely necessary for the interaction energies of the dimers. The ZPE corrections are much less than the electron correlation energies and BSSE correction for the interaction energies. Natural bond orbital (NBO) analysis is performed to reveal the origin of the interaction. On the basis of vibrational analysis and statistical thermodynamic, thermodynamic properties for the monomer and the dimers at different temperature have been obtained.
In the second part, we discuss the relationship between the structures and properties of the Group IIIA inorganometallic and organometallic azide clusters. The clusters have been applied widely. The basic studied results not only provide useful information for the design and synthesis of them, but also develop the bonding and structural theory.
Firstly, the DFT/B3LYP method with different basis sets used to calculate the (H2AlN3)1-4 clusters predicts that the (H2AlN3)2-4 clusters all possess cyclic-like structures. (H2AlN3)2-4 clusters are formed by Al atoms bridged by the a-nitrogen of the azide groups (connectivity: H2A1-Na-NB-Nr)
引文
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