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 北京化工大学学报(自然科学版)  2018, Vol. 45 Issue (6): 6-12   DOI: 10.13543/j.bhxbzr.2018.06.002 0

### 引用本文

YU YuTian, HU XiaoMin, LEI Ming, YANG ZuoYin. The relationship between water molecule pairs and hydrogen bond energy in cage hydration clusters[J]. Journal of Beijing University of Chemical Technology (Natural Science), 2018, 45(6): 6-12. DOI: 10.13543/j.bhxbzr.2018.06.002.

### 文章历史

The relationship between water molecule pairs and hydrogen bond energy in cage hydration clusters
YU YuTian , HU XiaoMin , LEI Ming , YANG ZuoYin
Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China
Abstract: A series of cage hydration clusters 521 512, 592 51262 and 501 435663 were randomly generated. The energy of hydrogen bonding is the difference between the energy of these cages and the loose cage. Their energies were calculated using the DFT/B97D/6-311++g(2d, 2p) method and the DFT/M052X/6-311++g(2d, 2p) method in the Gaussian09 package. The relationships between the distribution of different water molecule pairs, the energy of hydrogen bonds and the stability of the cage hydration clusters in the three cage hydration clusters are discussed. The results show that in the three cage hydration clusters, if we only considered the influence of the neighboring water molecules in the central water molecule pair, there are only four hydrogen bond types in each cage structure. When the number of one of the hydrogen bond types is fixed, the numbers of the others will also be fixed. The average energy of hydrogen bonds and single hydrogen bonds in the three cage-type hydrated clusters increase with increasing value n(1221). However for the same value of n(1221), the average energy of single hydrogen bonds is almost equal in the three different cages. When the values of n(1221) are different, the energies of the hydrogen bond network overlap for different cage hydration clusters, so there is no strict correspondence between the stability of the cage hydration clusters and the distribution of four types of hydrogen bonds.
Key words: hydration cluster isomer    distribution of hydrated clusters    hydrogen bond network type    hydrogen bond network energy    cage stability

1 模型构建与计算方法

 图 1 512、51262和435663笼形水合簇的模型 Fig.1 Model of the cage hydration clusters 512, 51262 and 435663
 图 2 笼形水合簇中水分子对的4种类型 Fig.2 The four types of water molecule pairs in cage-type hydration clusters

 ${{E}_{\text{bind}}}={{E}_{\text{cluster}}}-{{E}_{\text{loose}}}\text{ }\!\!~\!\!\text{ }$ (1)

2 结果与讨论 2.1 笼形水合簇构建的合理性

2.2 4种氢键类型之间的关系

 $n\left( 1212 \right)+n\left( 1221 \right)=10\text{ }$ (2)
 $n\left( 1212 \right)=n\left( 2121 \right)$ (3)
 $n\left( 2112 \right)=n\left( 1221 \right)+10$ (4)

 $n\left( 1212 \right)+n\left( 1221 \right)=12$ (5)
 $n\left( 1212 \right)=n\left( 2121 \right)$ (6)
 $n\left( 2112 \right)=n\left( 1221 \right)+12$ (7)

2.3 氢键类型的分布与笼形结构的稳定性

 图 3 n(1221)值不同时，3种笼形水合簇中氢键总能量的分布 Fig.3 Distribution of total energy of hydrogen bonds in three kinds of cage clusters when the values of n(1221) are different
 图 4 512、51262和435663笼形水合簇中氢键网络平均能量 Fig.4 The average energies of the total energy of the hydrogen-bonding network in cage hydration clusters 512, 51262 and 435663

3 结论

(1) 在512、51262和435663 3种笼形簇中，若只考虑近邻水分子对中心水分子对的影响，则各笼形结构中只有4种氢键类型1212、1221、2112和2121。在这4种氢键类型中只有1种变量，只要确定其中1种氢键类型的个数，其他3种氢键类型的个数也可以被确定；当n(1221)变大时，n(2112)也变大，其余的n(1212)和n(2121)都将变小；反之亦然。

(2) 对于相同的笼形水合簇，n(1221)值相等时，存在许多能量不同的异构体，即只用n(1221)的值不能区分异构体的热力学稳定性。

(3) 3种笼形水合簇中氢键的平均能量(绝对值)和单个氢键的平均能量(绝对值)都随n(1221)的增大而增加。在n(1221)相等的条件下，不同类型笼形水合簇氢键网络中单个氢键的平均能量几乎相等，当n(1221)的变化值相同时，其单个氢键平均能量的变化也几乎相等。

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