Cấu trúc và tính chất của cluster VB₅⁻/⁰ tính bằng lý thuyết phiếm hàm mật độ

59
STRUCTURES AND PROPERTIES OF VB
5
−/0 CLUSTERS 
FROM DENSITY FUNCTIONAL THEORY CALCULATIONS
Tran Van Tan1, Ngo Thi Phuoc An2, Tran Thanh Tuan3, Nguyen Thi Hong Hanh1,
Nguyen Minh Thao1, Tran Quoc Tri1, and Nguyen Hoang Lin4*
1 Dong Thap University
2To Ong Vang Primary School, Dong Thap province
3Tan Hiep High School, Kien Giang province
4Mai Thanh The High School, Soc Trang province
*Corresponding author: nguyenhoanglin.c3mtt@soctrang.edu.vn
Article history
Received: 14/08/2020; Received in revised form: 14/09/2020; Accepted: 30/09/2020
Abstract
Density functional theory with the BPW91 functional and def2-TZVP basis sets was used to investigate 
the geometric structures of VB5
−/0 clusters. By using the bee colony algorithm, 300 initial structures are created 
for the studied cluster. The geometry optimizations at the BPW91/def2-SVP level result in 18 low-lying isomers 
in quartet states for the anionic cluster. The results at the BPW91/def2-TZVP level show relative energies 
and vibrational frequencies for diff erent spin states of 7 isomers of the anionic clusters and 6 isomers of the 
neutral cluster. It is found that the most stable isomers are A-VB5
−/0 with non-planar pentagonal structure. 
The adiabatic detachment energy of the anionic cluster and the ionization energy of the neutral cluster are 
1.93 and 7.36 eV. 
Keywords: BPW91 functional, electron detachment energy, geometric structure, ionization energy, 
VB5
−/0 clusters. 
----------------------------------------------------------------------------------------------------------------------
CẤU TRÚC VÀ TÍNH CHẤT CỦA CLUSTER VB
5
−/0 
TÍNH BẰNG LÝ THUYẾT PHIẾM HÀM MẬT ĐỘ
Trần Văn Tân1, Ngô Thị Phước An2, Trần Thanh Tuấn3, Nguyễn Thị Hồng Hạnh1, 
Nguyễn Minh Thảo1, Trần Quốc Trị1 và Nguyễn Hoàng Lin4*
1Trường Đại học Đồng Tháp
2Trường Tiểu học Tổ Ong Vàng, tỉnh Đồng Tháp, 
3Trường Trung học phổ thông Tân Hiệp, tỉnh Kiên Giang
4Trường Trung học phổ thông Mai Thanh Thế, tỉnh Sóc Trăng
*Tác giả liên hệ: nguyenhoanglin.c3mtt@soctrang.edu.vn
Lịch sử bài viết
Ngày nhận: 14/08/2020; Ngày nhận chỉnh sửa: 14/09/2020; Ngày duyệt đăng: 30/09/2020
Tóm tắt
Lý thuyết phiếm hàm mật độ với phiếm hàm BPW91 và bộ hàm cơ sở def2-TZVP được sử dụng để nghiên 
cứu cấu trúc hình học của cluster VB5
−/0 . Bằng cách sử dụng thuật toán đàn ong nhân tạo, 300 cấu trúc ban 
đầu được tạo ra cho cluster được nghiên cứu. Quá trình tối ưu hóa hình học bằng phiếm hàm BPW91 và bộ 
hàm cơ sở def2-SVP cho thấy cluster anion có 18 đồng phân năng lượng thấp ở trạng thái quartet. Phiếm 
hàm BPW91 và bộ hàm cơ sở def2-TZVP cũng tính được năng lượng tương đối và tần số dao động điều hòa 
ứng với trạng thái spin khác nhau của 7 đồng phân của cluster anion và 6 đồng phân của cluster trung hòa. 
Kết quả tính toán cho thấy rằng đồng phân bền nhất là A-VB5
−/0 với cấu trúc ngũ giác không phẳng. Năng 
lượng tách của cluster anion và năng lượng ion hóa của cluster trung hòa là 1,93 và 7,36 eV. 
Từ khóa: Phiếm hàm BPW91, năng lượng tách electron, cấu trúc hình học, năng lượng ion hóa, cluster VB5
−/0 .
Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67
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1. Introduction
Clusters of transition metal with boron have 
been extensively investigated because of their 
potential application in catalysis and nanomaterial 
(Demirci, U. et al., 2016; Mananghaya, M. et al., 
2016; Zhang, Z. et al., 2017). Several clusters 
of transition metals with boron such as MnB
16
− 
and RbB
18
− are highly stable and can be used as 
fundamental building-blocks for nanomaterial 
(Jian, T. et al., 2016a; Jian, T. et al., 2016b). 
On the other hand, methane has been known 
as an important resource which can be used to 
synthesize high value compounds (Guo, X. et 
al., 2014; Zhou, Y. et al., 2019). However, the σ 
C-H bond of methane is very stable with bond 
dissociation energy of 440 kJ/mol (Karakaya, C. 
and Kee R. J., 2016). Therefore, catalysts should 
be employed to activate the C-H bond of methane. 
In order to search for the effi cient catalysts, the 
reactivity of VB
n
+ (n=3-6) clusters with methane 
were investigated by mass spectroscopy (Chen, 
Q. et al., 2018). From the mass spectra, the 
products of the reactions of VB
3
+, VB
4
+, VB
5
+, 
and VB6+ clusters with methane are determined 
to be VB
3
CH
2
+ + H
2
 and B
3
CH
3
 + VH+; VB
4
CH
2
+ 
+ H
2
 and B
4
CH
4
 + V+; VB
5
CH
2
+; and VB
6
CH
2
+ 
and VB
6
CH
4
(CH
2
)
n
+ (n = 0-2). Density functional 
theory with M06L and BPW91 functionals were 
applied to establish mechanisms for the reactions 
of VB
3
+, VB
4
+, and VB
5
+ clusters with methane 
(Chen, Q. et al., 2018; Tran Thanh Hue et al., 
2020; Tran Van Tan and Tran Quoc Tri, 2019). 
It was found that the formation of products is 
thermodynamically and kinetically favorable. 
These experimental and theoretical results 
provide new insight into the designation of new 
catalysts for methane activation. 
Although the structures of the cationic VB
5
+ 
clusters and mechanism of this cluster with 
methane were studied, the geometric structures 
and energetic properties of the anionic and 
neutral VB
5
−/0 clusters have not been reported 
(Tran Thanh Hue et al., 2020). This study applied 
density functional theory to search for the low-
lying isomers of VB
5
−/0 clusters. The BPW91 
functional were employed for the studied system 
because this functional proves to be suffi cient 
to study the structures of VB
4
+ and VB
5
+ (Tran 
Thanh Hue et al., 2020; Tran Van Tan and Tran 
Quoc Tri, 2019). The geometries, spin states, 
vibrational frequencies and normal modes, 
relative energies, electron detachment energies 
of the anionic cluster, and ionization energies 
of the neutral cluster were calculated. The 
computational results gave a clear understanding 
of the geometrica ... B
5
− are positive 
and they are in the range from 200 to 1078 cm−1. 
It means that the optimized structure belongs to 
minimum on the potential energy surface. 
 764 1000 1027 1078
63
3.2. VB
5
The geometry optimization and vibrational 
frequency calculations for VB
5
 were performed on 
the basis of the optimized geometries of isomers 
of VB
5
−. The results of the geometry optimization 
and vibrational frequency calculations for VB
5
cluster are presented in Figure 3 and Table 2. It 
can be seen that there are 6 important isomers 
of VB
5
. The relative energies of the lowest 
energy states of these isomers are in the range 
from 0.00 to 0.89 eV. The most stable isomer is 
determined to be A-VB
5
 with a triplet ground 
state. The singlet and quintet of the same isomer 
are above the triplet ground state by 0.08 and 
0.46 eV. The quintet of B-VB
5
, triplet of C-VB
5
, 
and quintet of D-VB
5
 are higher in energy than 
the ground state by 0.21, 0.13, and 0.42 eV. The 
other isomers are less stable than the ground state 
by more than 0.71 eV. 
Figure 3. Geometries, spin multiplicities, and relative energies (eV) of the low-lying 
isomers of VB
5
 cluster as computed with the BPW91 functional
Table 2. The computed spin multiplicities (M), vibrational frequencies, and relative 
energies (RE) of the low-lying isomers of VB
5
 clusters
isomer M RE (eV) frequencies (cm–1)
A–VB
5
3 0.00 227, 320, 401, 490, 581, 607, 675, 782, 790, 991, 1019, 1120
A–VB
5
1 0.08 232, 310, 412, 480, 584, 609, 686, 750, 793, 965, 1033, 1140
A–VB
5
5 0.46 146, 216, 331, 360, 443, 622, 659, 786, 904, 987, 1061, 1094
B–VB
5
5 0.21 127, 278, 289, 350, 393, 541, 589, 721, 816, 994, 1133, 1223
B–VB
5
3 0.50 127, 200, 300, 323, 396, 488, 636, 712, 806, 1002, 1152, 1199
B–VB
5
1 0.67 153, 318, 329, 357, 423, 497, 612, 736, 817, 983, 1107, 1212
C–VB
5
3 0.13 309, 337, 378, 435, 500, 581, 621, 728, 825, 920, 1102, 1141
C–VB
5
1 0.39 198, 269, 367, 417, 511, 521, 638, 731, 823, 953, 1063, 1112
C–VB
5
5 0.51 143, 298, 342, 416, 478, 516, 600, 739, 900, 927, 1086, 1150
D–VB
5
5 0.42 172, 204, 242, 347, 404, 572, 610, 695, 917, 945, 1067, 1271
A–VB
5
, 3, 0.00 B–VB
5
, 5, 0.21 C–VB
5
, 3, 0.13 D–VB
5
, 5, 0.42 
E–VB
5
, 3, 0.71 F–VB
5
, 3, 0.89
Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67
64
Natural Sciences issue
D–VB
5
3 0.67 146, 195, 214, 321, 415, 594, 615, 703, 909, 967, 1080, 1265
D–VB
5
1 0.93 215, 227, 268, 376, 421, 594, 630, 713, 856, 967, 1080, 1253
E–VB
5
3 0.71 284, 298, 497, 514, 601, 603, 653, 745, 756, 884, 886, 991
F–VB
5
3 0.89 201, 229, 296, 321, 342, 509, 634, 699, 748, 1076, 1151, 1272
F–VB
5
5 1.07 95, 194, 229, 322, 332, 534, 608, 637, 714, 984, 1104, 1283
F–VB
5
1 1.11 211, 236, 276, 311, 335, 508, 625, 698, 746, 1082, 1150, 1266
Figure 4. The vibrational frequencies (cm−1) and normal modes of the triplet states of A-VB
5
as computed with the BPW91 and def2-TZVP basis set
The vibrational frequencies of the relevant 
isomers of the VB
5
 cluster are presented in 
Table 2. It can be seen that all the frequencies 
are positive. The smallest frequency is around 
100 cm−1, while the largest frequency is around 
1300 cm−1. The vibrational normal modes of 
the neutral triplet ground state are displayed in 
Figure 4. The normal modes with frequencies 
of 226, 401, 580, 675, 790, 990, and 1119 cm−1 
are symmetric modes, while the others are 
antisymmetric modes. 
 227 320 401 490
 581 607 675 782
 790 991 1019 1120
3.3. Structures and NPA charges of 
VB
5
−/0/+ clusters
In order to understand the structural 
variations of the anionic, neutral, and cationic 
clusters, the important isomers of VB
5
−/0/+ clusters 
were collected and presented in Figure 5. It 
should be noted that the computational results of 
the anionic and neutral are obtained in this work, 
while those of the cationic cluster is discussed in 
the previous work (Tran Thanh Hue et al., 2020). 
65
It can be seen that the lowest energy states are 
the doublet, triplet, and doublet of A-VB
5
−/0/+ 
isomers. From the anionic to the neutral and 
cationic cluster, the energy diff erences among 
the A, B, and C isomers get smaller and smaller. 
In particular, the relative energies of the A, B, 
and C isomers are 0.00, 0.42, and 0.49 eV for 
the anionic cluster; 0.00, 0.21, and 0.13 eV for 
the neutral cluster; and 0.00, 0.00, 0.14 eV for 
the cationic cluster.
Figure 5. The structures, spin multiplicities, and relative energies of the relevant isomers of VB
5
−/0/+ 
clusters as calculated with the BPW91 functional
A-VB
5
–, 2, 0.00 B-VB
5
–, 4, 0.42 C-VB
5
–, 4, 0.50
A-VB
5
, 3, 0.00 B-VB
5
, 5, 0.21 C-VB
5
, 3, 0.13
A-VB
5
+, 2, 0.00 B-VB
5
+, 4, 0.00 C-VB
5
+, 4, 0.14
The NPA charges of V1, B1, B2, B3, B4, and 
B5 atoms of the doublet ground state of A-VB
5
− 
are estimated to be +0.36, −0.38, −0.38, −0.24, 
−0.24, and −0.12 e−. For the neutral ground state, 
the NPA charges of V1, B1, B2, B3, B4, and B5 
atoms of the triplet of A-VB
5
 are evaluated to be 
+0.59, −0.13, −0.13, −0.06, −0.06, and −0.22 e−. 
The NPA charges of the doublet of A-VB
5
+ and 
quartet of B-VB
5
+ were reported in the previous 
work (Tran Thanh Hue et al., 2020). In particular, 
the NPA charges of V1, B1, B2, B3, B4, and 
B5 atoms of the doublet of A-VB
5
+ are +0.79, 
+0.11, +0.11, +0.12, +0.12, and −0.25 e−, while 
those of the quartet of B-VB
5
+ are +1.06, +0.00, 
−0.28, −0.26, +0.06, and +0.42 e−. It can be seen 
that from the anionic to the neutral and cationic 
ground states, the positive charges of V1 atom 
increases and increases. All boron atoms of the 
ground states of A-VB
5
−/0 have negative charges, 
while some boron atoms of the ground state of 
A-VB
5
+ and B-VB
5
+ have positive charges. In the 
case of the quartet of B-VB
5
+, the B5 atom has the 
largest positive charge (+0.42 e−). This positive 
charge is much larger than those of boron atoms 
of the A-VB
5
−/0/+. Due to the large positive charge 
of the B5 atom, the B-VB
5
+ is predicted to have 
Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67
66
Natural Sciences issue
high possibility to activate the C-H bond in CH
4
molecule (Tran Thanh Hue et al., 2020). 
3.4. Energetic properties of VB
5
−/0 clusters
Energetic properties of VB
5
−/0/+ clusters 
such as adiabatic detachment energy (ADE) and 
ionization energy (IE) were calculated with the 
BPW91 functional. Adiabatic detachment energy 
of the anionic cluster is the energy required to 
detach one electron of the anion to create the 
neutral. The adiabatic detachment energy can be 
calculated via the formula: 
ADE = E(VB
5
) − E(VB
5
−)
In this formula, ADE is adiabatic detachment 
energy, E(VB
5
) and E(VB
5
−) are the energies of 
VB
5
 and VB
5
−. Otherwise, ionization energy is 
the energy needed to eliminate one electron of 
the neutral to form the cation. Ionization energy 
is estimated by the formula: 
IE = E(VB
5
+) − E(VB
5
)
Table 3. The adiabatic electron detachment 
energies (ADEs) of the anionic cluster and the 
ionization energies (IEs) of the neutral cluster 
as calculated with the BPW91 functional
isomer
transition 
between spin 
states
ADE and IE 
(eV)
A–VB
5
−/0 2 → 3 1.93
B–VB
5
−/0 4 → 5 1.73
C–VB
5
−/0 4 → 3 1.56
A–VB
5
0/+ 3 → 2 7.36
B–VB
5
0/+ 5 → 4 7.15
C–VB
5
0/+ 3 → 4 7.23
The computed results as collected in Table 
3 show that the adiabatic detachment energies 
of the detachment of one electron of the anionic 
cluster to generate the neutral cluster are 1.93, 
1.73, and 1.56 eV for the A, B, and C isomers. 
The ionization energies of the elimination of one 
electron of the neutral cluster to form the cationic 
cluster are calculated to be 7.36, 7.15, and 7.23 
eV, respectively. It can be seen that the adiabatic 
detachment energies of the anionic cluster are 
much lower than the ionization ones of the 
neutral cluster. It means that the detachment of 
one electron of the anionic cluster is much more 
diffi cult than the elimination of one electron of 
the neutral cluster. 
4. Conclusion
The relevant geometric structures and 
vibrational frequencies of a large number of 
isomers of VB
5
−/0 clusters are reported based 
on the BPW91 functional calculations. The 
A-VB
5
−/0 are predicted to be the most stable 
isomers. These isomers have non-planar 
pentagonal structure in which the V atom 
locates at a corner of the pentagon. The ground 
state of the anionic clusters is doublet and the 
quartet is 0.10 eV above. The ground state of 
the neutral cluster is the triplet and the singlet 
is higher in energy by 0.08 eV. The vibrational 
frequencies of the A-VB
5
−/0 isomers are in the 
range between 200 cm−1 and 1120 cm−1. The B 
and C isomers are less stable than the A isomer 
by 0.42 and 0.50 eV for the anionic cluster and 
by 0.21 and 0.13 eV for the neutral cluster. The 
other isomers of VB
5
−/0 clusters are higher in 
energy than the most stable A-VB
5
−/0 by at least 
0.42 eV. The NPA charge of V1 atom is positive 
and it increases from the A-VB
5
− to A-VB
5
 and 
A-VB
5
+. The B5 atom of the quartet of B-VB
5
+ 
has the highest positive charge as compared to 
those of the A-VB
5
−, A-VB
5
, and A-VB
5
+ . And 
therefore, the B-VB
5
+ has high reactivity toward 
methane. The adiabatic detachment energies 
of the anionic A–VB
5
−, B–VB
5
−, and C–VB
5
− 
clusters are calculated to be 1.93, 1.73, and 
1.56 eV. The ionization energy of the neutral 
ground A–VB
5
, B–VB
5
, and C–VB
5
 cluster are 
estimated to be 7.36, 7.15, and 7.23 eV. 
Acknowledgement: This work was 
supported by the Ministry of Education 
and Training of Vietnam under Grant No. 
B2019-SPD-562-07.
67
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