铝团簇的结构、稳定性和电子性质的理论研究
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摘要
本文采用遗传算法(GA)与密度泛函理论(DFT)相结合的理论方法,对中等尺度的铝团簇Aln (n = 27-40)的几何结构进行了全局搜索和研究,并且结合相关的实验结果,对铝团簇Aln (n = 2-40)的稳定性和电子性质等方面进行了系统的分析,我们得出以下主要结论:
(1)中等尺度铝团簇Al27– Al40的稳定结构是具有层错的fcc堆积结构。我们的研究发现Al27– Al40都具有类似的堆积模式,这种模式的铝团簇结构是以一个(111)面为基底,分别以基底的上下两个方向以fcc模式堆积而成,我们也称之为双向fcc堆积。该堆积模式也可以看作是由两个fcc体片段组成的双向体结构。其中,Al27和Al28是共享一个基底的五层双四面体结构,Al29-Al32为三层的fcc堆积结构,当铝原子数达到Al33– Al35时,生长模式转变为四层原子的堆积,而到Al36– Al40时,又转变为五层原子的堆积。Aln (n = 33– 40)是在Al33的结构基础上衍生出来的一系列结构。并且,从Al23开始铝团簇已经呈现出了fcc的堆积趋势。
(2)对铝团簇Aln (n = 2 - 40)的相对稳定性进行了系统的分析,其中包括结合能、二次差分能、HOMO-LUMO能隙的分析研究。研究结果表明Al13、Al20、Al23和Al36与它们相邻的铝团簇相比具有更好的能量稳定性和反应稳定性。而Al7的结合能大,但能隙相对较小。表明Al7的热化学稳定性好,但化学反应活性比较大。
(3)对Aln (n = 2 - 40)团簇的解离能和解离通道进行了详细的计算研究。结果表明中性Aln团簇最主要的解离产物是一个Al原子;在Al+n团簇中,对于尺度较大的Al+n,最主要的解离产物是Al+n-1;而对于较小的Al+n,最主要的解离产物是Al+。我们计算得到的解离能和解离行为的结果与实验观测相一致。
(4)计算研究了Al2– Al40团簇的绝热电离势(IP)。研究结果表明Al6、Al8、Al13、Al17、Al20、Al28、Al34和Al36比其它相邻的铝团簇具有更高的IP值。铝团簇的电离势在尺寸较小时峰值较突出,尤其是尺寸n=3?6时,比其它尺寸铝团簇的电离势高0.5eV以上。其结果与实验观测相符合。
Recently, aluminum clusters have attracted much attention of researchers because of its special electronic structures, super light weight and unique conductive characteristics and so on. Apart from clusters of alkali metals (Na and K in particular), aluminum clusters are perhaps the most extensively studied simple metal systems. The theoretical studies have been focused on the electronic and geometric structures of Al clusters. The experimental studies include measurements of ionization potentials, dissociation energies, mobilities, electron affinities, photoelectron spectra, and polarizabilities, etc. With the development of technology, the aluminum-related materials have gradually extended to the novel electronic device, electronic industries, micro-electronics, and nanomaterials, etc. Cluster have special structures and properties which are strongly size-dependent. Among various clusters, magic clusters with special stability play important roles in the synthesis of novel materials. It is well known that the jellium model provides a good description of the electronic shell structure and stability of simple metal clusters. Photoelectron experiments suggested a set of shell closings consistent with the jellium model. And the studies of medium-sized aluminum clusters can help us to find out the cluster growth trend. The appearance of the bulk motif in Al clusters is a very interesting topic.
We use the genetic algorithm (GA) coupled with a TB potential of Al to search for low-energy candidates of Al clusters. The low-energy candidates were further optimized by all electrons Perdew-Burke-Ernzerhof (PBE) method and DND basis set of DMol3 included in Materials Studio (MS). We also performed calculations with the PBE method and plane wave (PW) basis set using VASP. In this paper, we search for stable structures of medium-sized Al clusters, and the binding energies,. HOMO-LUMO gaps, second differences in energies, the electronic affinities, ionization potentials, fragmentation energies and electron occupations have been caculated in order to analyze the stabilities and electronic structures of the clusters. The main research results are listed as follows:
(1) It is found that the medium-sized aluminum clusters at the size range of Al31-40 favor a fcc-like motif with stacking fault. We found that Al27 - Al40 are formed by up and down fcc stackings with a stacking fault in the middle (or two fcc fragments), which is called a bidirectional fcc stacking. For Al27 and Al28, the lowest-energy isomers are double-tetrahedron structures with five layers. Al29-Al32 have the structures with three layers. The motif of Al33-Al35 has been changed to four layers stacking. Form Al36-Al40, the lowest-energy isomers have the structures of five layers stacking. We note that Al29 and Al30 favor a bidirectional fcc stacking pattern at the PBE functional. However at the BLYP level the double-tetrahedron structures are lower in energy. The orders of stabilities of two types of structures are different at the PBE and BLYP functionals. They can be expected to occur with similar probabilities, due to small energy differences. From another point of view, the growth motif from Al29 to Al32, is by capping atoms on Al29, and Aln (n = 33 - 40) is a series of structures by capping atoms on Al33. From Aln (n = 2 ? 40), it is obviously that Al23 already starts to have a fcc-like stacking tendency.
(2) We have carried out a systematic study on relative stabilities of aluminum clusters Aln (n = 2 ? 40), including binding energies, second differences in energies, HOMO-LUMO gaps. Our results show that the binding energy curve can be roughly divided into four regions: n < 7 where the binding energy increases rapidly as the cluster size increases, 7 < n < 13 where the binding energy increases moderately with the cluster size, 13 < n < 23 where binding energy increases slowly, and n > 23 where binding energy increases smoothly. In particular, at Al7, Al13, Al20, Al23, Al28, and Al36, there are clear peaks, indicting that these clusters have special stabilities compared with their neighbors. The curve of the second differences in energies shows an oscillating behavior, and Al7, Al13, Al20, Al23, Al28 and Al36 correspond to local maxima on the curve. The large energy gaps are found at n= 8, 13, 18, 20, 23, 25, 27, 31, and 36. Al13, Al20, Al23 and Al36 have both higher energetic stability and reactive stability than their neighbors. Al7 has large thermostatic stability, but it’s energy gap is relatively small. This suggests that Al7, with a better thermodynamic stability, is more reactive due to the smaller energy gap.
(3) The calculated fragmentation energies and the predicted dissociation products of Aln (n = 2 ? 40) reveal that the most dominant channel of neutral Al clusters is the evaporation of an atom from the cluster, and the main products from the dissociations of aluminum cluster ions are Al+n-1 for the larger clusters but Al+ for the smaller ones. The present calculated results and analyses of fragmentations are consistent with the experimental observations. Since the clusters with larger fragmentation energies should be more stable, the relative stable isomers from our present study are found to be Al7, Al13, Al20, Al23, Al27, Al30, Al34 and Al36.
(4) We calculated adiabatic ionization potentials (IPs) for Al2– Al40. The results suggest that Al6、Al8、Al13、Al17、Al20、Al28、Al34 and Al36 have larger IPs than their neighbors. The IPs of Aln clusters increase steeply at small size, and the ionization energies for n = 3 - 6 are larger by more than 0.5 eV compared with those of other clusters studied in this work. A very large decrease from n =13 to 14 can be attributed by the special stability of Al13. The calculated general tendency of the adiabatic IPs and the oscillations of IPs agree well with the results of the photoionization spectroscopy measurements, though the calculated IPs are about 0.13～0.79 eV smaller than the experimental data. We note that the strong oscillations of the IPs in 12≤N≤23 are due to competition and coexistence of icosahedral, decahedral and fcc-based structures.
(1)中等尺度铝团簇Al27– Al40的稳定结构是具有层错的fcc堆积结构。我们的研究发现Al27– Al40都具有类似的堆积模式,这种模式的铝团簇结构是以一个(111)面为基底,分别以基底的上下两个方向以fcc模式堆积而成,我们也称之为双向fcc堆积。该堆积模式也可以看作是由两个fcc体片段组成的双向体结构。其中,Al27和Al28是共享一个基底的五层双四面体结构,Al29-Al32为三层的fcc堆积结构,当铝原子数达到Al33– Al35时,生长模式转变为四层原子的堆积,而到Al36– Al40时,又转变为五层原子的堆积。Aln (n = 33– 40)是在Al33的结构基础上衍生出来的一系列结构。并且,从Al23开始铝团簇已经呈现出了fcc的堆积趋势。
(2)对铝团簇Aln (n = 2 - 40)的相对稳定性进行了系统的分析,其中包括结合能、二次差分能、HOMO-LUMO能隙的分析研究。研究结果表明Al13、Al20、Al23和Al36与它们相邻的铝团簇相比具有更好的能量稳定性和反应稳定性。而Al7的结合能大,但能隙相对较小。表明Al7的热化学稳定性好,但化学反应活性比较大。
(3)对Aln (n = 2 - 40)团簇的解离能和解离通道进行了详细的计算研究。结果表明中性Aln团簇最主要的解离产物是一个Al原子;在Al+n团簇中,对于尺度较大的Al+n,最主要的解离产物是Al+n-1;而对于较小的Al+n,最主要的解离产物是Al+。我们计算得到的解离能和解离行为的结果与实验观测相一致。
(4)计算研究了Al2– Al40团簇的绝热电离势(IP)。研究结果表明Al6、Al8、Al13、Al17、Al20、Al28、Al34和Al36比其它相邻的铝团簇具有更高的IP值。铝团簇的电离势在尺寸较小时峰值较突出,尤其是尺寸n=3?6时,比其它尺寸铝团簇的电离势高0.5eV以上。其结果与实验观测相符合。
Recently, aluminum clusters have attracted much attention of researchers because of its special electronic structures, super light weight and unique conductive characteristics and so on. Apart from clusters of alkali metals (Na and K in particular), aluminum clusters are perhaps the most extensively studied simple metal systems. The theoretical studies have been focused on the electronic and geometric structures of Al clusters. The experimental studies include measurements of ionization potentials, dissociation energies, mobilities, electron affinities, photoelectron spectra, and polarizabilities, etc. With the development of technology, the aluminum-related materials have gradually extended to the novel electronic device, electronic industries, micro-electronics, and nanomaterials, etc. Cluster have special structures and properties which are strongly size-dependent. Among various clusters, magic clusters with special stability play important roles in the synthesis of novel materials. It is well known that the jellium model provides a good description of the electronic shell structure and stability of simple metal clusters. Photoelectron experiments suggested a set of shell closings consistent with the jellium model. And the studies of medium-sized aluminum clusters can help us to find out the cluster growth trend. The appearance of the bulk motif in Al clusters is a very interesting topic.
We use the genetic algorithm (GA) coupled with a TB potential of Al to search for low-energy candidates of Al clusters. The low-energy candidates were further optimized by all electrons Perdew-Burke-Ernzerhof (PBE) method and DND basis set of DMol3 included in Materials Studio (MS). We also performed calculations with the PBE method and plane wave (PW) basis set using VASP. In this paper, we search for stable structures of medium-sized Al clusters, and the binding energies,. HOMO-LUMO gaps, second differences in energies, the electronic affinities, ionization potentials, fragmentation energies and electron occupations have been caculated in order to analyze the stabilities and electronic structures of the clusters. The main research results are listed as follows:
(1) It is found that the medium-sized aluminum clusters at the size range of Al31-40 favor a fcc-like motif with stacking fault. We found that Al27 - Al40 are formed by up and down fcc stackings with a stacking fault in the middle (or two fcc fragments), which is called a bidirectional fcc stacking. For Al27 and Al28, the lowest-energy isomers are double-tetrahedron structures with five layers. Al29-Al32 have the structures with three layers. The motif of Al33-Al35 has been changed to four layers stacking. Form Al36-Al40, the lowest-energy isomers have the structures of five layers stacking. We note that Al29 and Al30 favor a bidirectional fcc stacking pattern at the PBE functional. However at the BLYP level the double-tetrahedron structures are lower in energy. The orders of stabilities of two types of structures are different at the PBE and BLYP functionals. They can be expected to occur with similar probabilities, due to small energy differences. From another point of view, the growth motif from Al29 to Al32, is by capping atoms on Al29, and Aln (n = 33 - 40) is a series of structures by capping atoms on Al33. From Aln (n = 2 ? 40), it is obviously that Al23 already starts to have a fcc-like stacking tendency.
(2) We have carried out a systematic study on relative stabilities of aluminum clusters Aln (n = 2 ? 40), including binding energies, second differences in energies, HOMO-LUMO gaps. Our results show that the binding energy curve can be roughly divided into four regions: n < 7 where the binding energy increases rapidly as the cluster size increases, 7 < n < 13 where the binding energy increases moderately with the cluster size, 13 < n < 23 where binding energy increases slowly, and n > 23 where binding energy increases smoothly. In particular, at Al7, Al13, Al20, Al23, Al28, and Al36, there are clear peaks, indicting that these clusters have special stabilities compared with their neighbors. The curve of the second differences in energies shows an oscillating behavior, and Al7, Al13, Al20, Al23, Al28 and Al36 correspond to local maxima on the curve. The large energy gaps are found at n= 8, 13, 18, 20, 23, 25, 27, 31, and 36. Al13, Al20, Al23 and Al36 have both higher energetic stability and reactive stability than their neighbors. Al7 has large thermostatic stability, but it’s energy gap is relatively small. This suggests that Al7, with a better thermodynamic stability, is more reactive due to the smaller energy gap.
(3) The calculated fragmentation energies and the predicted dissociation products of Aln (n = 2 ? 40) reveal that the most dominant channel of neutral Al clusters is the evaporation of an atom from the cluster, and the main products from the dissociations of aluminum cluster ions are Al+n-1 for the larger clusters but Al+ for the smaller ones. The present calculated results and analyses of fragmentations are consistent with the experimental observations. Since the clusters with larger fragmentation energies should be more stable, the relative stable isomers from our present study are found to be Al7, Al13, Al20, Al23, Al27, Al30, Al34 and Al36.
(4) We calculated adiabatic ionization potentials (IPs) for Al2– Al40. The results suggest that Al6、Al8、Al13、Al17、Al20、Al28、Al34 and Al36 have larger IPs than their neighbors. The IPs of Aln clusters increase steeply at small size, and the ionization energies for n = 3 - 6 are larger by more than 0.5 eV compared with those of other clusters studied in this work. A very large decrease from n =13 to 14 can be attributed by the special stability of Al13. The calculated general tendency of the adiabatic IPs and the oscillations of IPs agree well with the results of the photoionization spectroscopy measurements, though the calculated IPs are about 0.13～0.79 eV smaller than the experimental data. We note that the strong oscillations of the IPs in 12≤N≤23 are due to competition and coexistence of icosahedral, decahedral and fcc-based structures.
引文
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