Structures and properties of VB₅ clusters from density functional theory calculations

Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67

STRUCTURES AND PROPERTIES OF VB₅^−/0CLUSTERS

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 Lin^4*

¹Dong 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^−/0clusters. 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 diﬀerent 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^−/0with 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^−/0clusters.

----------------------------------------------------------------------------------------------------------------------

−/0

CẤU TRÚC VÀ TÍNH CHẤT CỦA CLUSTER VB₅

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 Trị¹và Nguyễn Hoàng Lin^4*

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^−/0với 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

.

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Natural Sciences issue

−/0

1. Introduction

lying isomers of VB₅clusters. The BPW91

functional were employed for the studied system

because this functional proves to be suﬃcient

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

+

to study the structures of VB₄and VB₅⁺(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 geometrical structures of VB₅^−/0clusters.

−

of transition metals with boron such as MnB₁₆

and RbB₁₈⁻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 eﬃcient 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

2. Computational Methods

Density functional theory was carried out

−/0

to investigate the geometric structures of VB₅

clusters. The BPW91 functional was chosen for

these studied systems because this functional

0/+

proves to be appropriate to study the VB₄

clusters (Tran Van Tan and Tran Quoc Tri, 2019).

All the density functional theory calculations were

executed with NWCHEM 6.8 package (Valiev,

M. et al., 2010). The geometry optimization

and vibrational frequency calculations were

performed for all the possible spin states to

search for the relevant isomers. To search for the

important structures of the studied clusters, the

artiﬁcial bee colony algorithm as implemented

in ABCluster package was utilized (Zhang, J.

and Dolg M., 2015). The initial 300 structures as

generated with the artiﬁcial bee colony algorithm

were optimized with the BPW91 functional

(Becke, A. D., 1988) and def2-SVP basis sets

(Weigend, F. and Ahlrichs R., 2005). Then, the

geometry optimization and vibrational frequency

calculations were performed with def2-TZVP

basis sets (Weigend, F. and Ahlrichs R., 2005)

to improve the energies. The atomic charges of

the relevant isomers were calculated by doing

natural population analysis (NPA) with JANPA

package (Nikolaienko, T. Y. et al., 2014).

+

products of the reactions of VB₃, VB₄, VB₅,

and VB6+ clusters with methane are determined

to be VB₃CH₂⁺+ H₂and B₃CH₃+ VH⁺; VB₄CH₂⁺

+ H₂and B₄CH₄+ V⁺; VB₅CH₂⁺; and VB₆CH₂⁺

and VB₆CH₄(CH₂)_n⁺(n = 0-2). Density functional

theory with M06L and BPW91 functionals were

applied to establish mechanisms for the reactions

of VB₃⁺, VB₄⁺, and VB₅⁺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 VB₅

clusters and mechanism of this cluster with

methane were studied, the geometric structures

and energetic properties of the anionic and

3. Results and Discussion

3.1. VB₅⁻

−/0

neutral VB₅clusters have not been reported

(Tran Thanh Hue et al., 2020). This study applied

density functional theory to search for the low-

The geometry optimizations of 300

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Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67

structures created by the bee colony algorithm all the vibrational frequencies are positive. The

−

with the BPW91 functional and def2-SVP most stable isomer is A-VB₅with a non-planar

−

basis sets for the quartet states of VB₅cluster pentagonal structure in which the V atom locates

resulted in 18 structures with relative energies at a corner of the pentagon. The ground state of

from 0.00 to around 2.00 eV. Based on these A-VB₅⁻is the doublet; the quartet is just 0.10 eV

18 initial structures, geometry optimizations above; and the sextet is 0.69 eV less stable. The

and vibrational frequency calculations were second isomer is labeled as B-VB₅⁻with relative

performed for the doublet, quartet, and sextet energies of the quartet, sextet, and doublet states

states. The structures, spin multiplicities, relative of 0.42, 0.46, and 0.51 eV. This isomer has planar

energies, and vibrational frequency of the structure in which the V atom directly binds to

doublet, quartet, and sextet states of 7 important two boron atoms of a trapezoidal B₅moiety.

isomers of VB₅⁻as computed at the BPW91/def2- The C-VB₅⁻in quartet state is higher in energy

TZVP level are presented in Figure 1 and Table than the anionic ground state by 0.50 eV. The

1. The results show that all the structures belong remaining 4 isomers are less stable than the ﬁrst

to the minima on the potential surface because isomer by at least 0.60 eV.

A–VB₅^–, 2, 0.00

B–VB₅^–, 4, 0.42

C–VB₅^–, 4, 0.50

D–VB₅^–, 4, 0.60

E–VB₅^–, 6, 0.63

F–VB₅^–, 4, 0.76

G–VB₅^–, 4, 0.82

Figure 1. Geometries, spin multiplicities, and relative energies (eV) of the low-lying isomers

of VB₅^–cluster as computed at the BPW91/def2-TZVP level

Table 1. The computed spin multiplicities (M), relative energies (RE), and vibrational frequencies

of the low-lying isomers of VB₅^–clusters

isomer

A–VB₅^–

B–VB₅^–

C–VB₅^–

M

2

RE (eV)

0.00

frequencies (cm^–1)

200, 317, 357, 464, 576, 626, 693, 716, 764, 1000, 1027, 1078

227, 288, 387, 429, 494, 619, 627, 792, 796, 997, 1022, 1063

164, 178, 295, 352, 463, 596, 606, 760, 855, 957, 1035, 1062

117, 225, 283, 356, 382, 566, 599, 741, 843, 975, 1082, 1215

114, 265, 282, 363, 371, 569, 636, 702, 763, 933, 1118, 1172

134, 306, 336, 353, 404, 502, 658, 727, 846, 964, 1079, 1197

211, 246, 328, 404, 470, 557, 590, 701, 785, 953, 1092, 1162

4

0.26

6

0.69

4

0.42

6

0.46

2

0.51

4

0.50

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Natural Sciences issue

D–VB₅^–

E–VB₅^–

F–VB₅^–

G–VB₅^–

4

2

6

4

2

4

6

2

4

2

0.60

0.66

0.63

0.73

0.77

0.76

0.93

0.82

0.99

130, 221, 326, 372, 375, 466, 514, 537, 785, 982, 1196, 1401

108, 227, 232, 377, 380, 444, 465, 508, 790, 956, 1203, 1367

142, 181, 237, 320, 361, 584, 625, 714, 929, 965, 1093, 1197

105, 189, 216, 363, 379, 594, 604, 724, 843, 951, 1094, 1204

168, 203, 271, 375, 411, 570, 635, 720, 833, 981, 1088, 1217

136, 219, 270, 296, 329, 563, 610, 650, 748, 997, 1155, 1233

152, 211, 272, 286, 326, 546, 586, 650, 741, 1009, 1138, 1226

141, 201, 305, 362, 368, 463, 614, 685, 780, 1015, 1142, 1248

157, 194, 317, 386, 394, 433, 524, 631, 680, 1002, 1113, 1276

126, 183, 312, 368, 409, 442, 499, 631, 721, 987, 1122, 1299

The vibrational frequencies and normal (3N−6 = 3×6−6 = 12). The ﬁgure shows that all

−

modes of the doublet ground state of A-VB₅

the vibrational frequencies ofA-VB₅⁻are positive

as computed at the BPW91/def2-TZVP are and they are in the range from 200 to 1078 cm⁻¹.

displayed in Figure 2. Because there are 6 atoms It means that the optimized structure belongs to

in VB₅⁻, this cluster exhibits 12 vibrational modes minimum on the potential energy surface.

200

317

357

693

464

716

576

626

764

1000

1027

1078

Figure 2. The vibrational frequencies (cm⁻¹) and normal modes of the doublet of A-VB₅⁻

as computed with the BPW91 and def2-TZVP basis set

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Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67

3.2. VB₅

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-VB₅with 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-VB₅, triplet of C-VB₅,

and quintet of D-VB₅are 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.

The geometry optimization and vibrational

frequencycalculationsforVB₅wereperformedon

the basis of the optimized geometries of isomers

of VB₅⁻. The results of the geometry optimization

and vibrational frequency calculations for VB₅

cluster are presented in Figure 3 and Table 2. It

can be seen that there are 6 important isomers

of VB₅. The relative energies of the lowest

A–VB₅, 3, 0.00

B–VB₅, 5, 0.21

C–VB₅, 3, 0.13

D–VB₅, 5, 0.42

E–VB₅, 3, 0.71

F–VB₅, 3, 0.89

Figure 3. Geometries, spin multiplicities, and relative energies (eV) of the low-lying

isomers of VB₅cluster 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 VB₅clusters

isomer

A–VB₅

B–VB₅

C–VB₅

D–VB₅

M

3

1

5

3

1

3

1

5

RE (eV)

0.00

0.08

0.46

0.21

0.50

0.67

0.13

0.39

0.51

0.42

frequencies (cm^–1)

227, 320, 401, 490, 581, 607, 675, 782, 790, 991, 1019, 1120

232, 310, 412, 480, 584, 609, 686, 750, 793, 965, 1033, 1140

146, 216, 331, 360, 443, 622, 659, 786, 904, 987, 1061, 1094

127, 278, 289, 350, 393, 541, 589, 721, 816, 994, 1133, 1223

127, 200, 300, 323, 396, 488, 636, 712, 806, 1002, 1152, 1199

153, 318, 329, 357, 423, 497, 612, 736, 817, 983, 1107, 1212

309, 337, 378, 435, 500, 581, 621, 728, 825, 920, 1102, 1141

198, 269, 367, 417, 511, 521, 638, 731, 823, 953, 1063, 1112

143, 298, 342, 416, 478, 516, 600, 739, 900, 927, 1086, 1150

172, 204, 242, 347, 404, 572, 610, 695, 917, 945, 1067, 1271

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Natural Sciences issue

D–VB₅

E–VB₅

F–VB₅

3

1

3

5

1

0.67

0.93

0.71

0.89

1.07

1.11

146, 195, 214, 321, 415, 594, 615, 703, 909, 967, 1080, 1265

215, 227, 268, 376, 421, 594, 630, 713, 856, 967, 1080, 1253

284, 298, 497, 514, 601, 603, 653, 745, 756, 884, 886, 991

201, 229, 296, 321, 342, 509, 634, 699, 748, 1076, 1151, 1272

95, 194, 229, 322, 332, 534, 608, 637, 714, 984, 1104, 1283

211, 236, 276, 311, 335, 508, 625, 698, 746, 1082, 1150, 1266

The vibrational frequencies of the relevant the neutral triplet ground state are displayed in

isomers of the VB₅cluster are presented in Figure 4. The normal modes with frequencies

Table 2. It can be seen that all the frequencies of 226, 401, 580, 675, 790, 990, and 1119 cm⁻¹

are positive. The smallest frequency is around are symmetric modes, while the others are

100 cm⁻¹, while the largest frequency is around antisymmetric modes.

1300 cm⁻¹. The vibrational normal modes of

227

320

607

991

401

490

581

675

782

790

1019

1120

Figure 4. The vibrational frequencies (cm⁻¹) and normal modes of the triplet states of A-VB₅

as computed with the BPW91 and def2-TZVP basis set

3.3. Structures and NPA charges of

VB₅^−/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).

In order to understand the structural

variations of the anionic, neutral, and cationic

clusters, the important isomers of VB₅^−/0/+clusters

64

Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67

It can be seen that the lowest energy states are In particular, the relative energies of the A, B,

−/0/+

the doublet, triplet, and doublet of A-VB₅

and C isomers are 0.00, 0.42, and 0.49 eV for

isomers. From the anionic to the neutral and the anionic cluster; 0.00, 0.21, and 0.13 eV for

cationic cluster, the energy diﬀerences among the neutral cluster; and 0.00, 0.00, 0.14 eV for

the A, B, and C isomers get smaller and smaller. the cationic cluster.

A-VB₅^–, 2, 0.00

B-VB₅^–, 4, 0.42

C-VB₅^–, 4, 0.50

A-VB₅, 3, 0.00

B-VB₅, 5, 0.21

C-VB₅, 3, 0.13

A-VB₅⁺, 2, 0.00

B-VB₅⁺, 4, 0.00

C-VB₅⁺, 4, 0.14

−/0/+

Figure 5. The structures, spin multiplicities, and relative energies of the relevant isomers of VB₅

clusters as calculated with the BPW91 functional

The NPAcharges of V1, B1, B2, B3, B4, and those of the quartet of B-VB₅⁺are +1.06, +0.00,

B5 atoms of the doublet ground state of A-VB₅⁻−0.28, −0.26, +0.06, and +0.42 e⁻. It can be seen

are estimated to be +0.36, −0.38, −0.38, −0.24, that from the anionic to the neutral and cationic

−0.24, and −0.12 e⁻. For the neutral ground state, ground states, the positive charges of V1 atom

the NPA charges of V1, B1, B2, B3, B4, and B5 increases and increases. All boron atoms of the

atoms of the triplet of A-VB₅are evaluated to be ground states ofA-VB₅^−/0have negative charges,

+0.59, −0.13, −0.13, −0.06, −0.06, and −0.22 e⁻. while some boron atoms of the ground state of

+

The NPA charges of the doublet of A-VB₅and A-VB₅⁺and B-VB₅⁺have positive charges. In the

quartet of B-VB₅⁺were reported in the previous case of the quartet of B-VB₅⁺, the B5 atom has the

work (Tran Thanh Hue et al., 2020). In particular, largest positive charge (+0.42 e⁻). This positive

the NPA charges of V1, B1, B2, B3, B4, and charge is much larger than those of boron atoms

+

B5 atoms of the doublet of A-VB₅are +0.79, of theA-VB₅^−/0/+. Due to the large positive charge

+0.11, +0.11, +0.12, +0.12, and −0.25 e⁻, while of the B5 atom, the B-VB₅⁺is predicted to have

65

Natural Sciences issue

high possibility to activate the C-H bond in CH₄detachment energies of the anionic cluster are

molecule (Tran Thanh Hue et al., 2020).

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

diﬃcult than the elimination of one electron of

the neutral cluster.

3.4. Energetic properties of VB₅^−/0clusters

−/0/+

Energetic properties of VB₅

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:

4. Conclusion

The relevant geometric structures and

vibrational frequencies of a large number of

−/0

isomers of VB₅clusters are reported based

on the BPW91 functional calculations. The

ADE = E(VB₅) − E(VB₅⁻)

−/0

A-VB₅are 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

In this formula,ADE is adiabatic detachment

energy, E(VB₅) and E(VB₅⁻) are the energies of

VB₅and VB₅⁻. 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(VB₅⁺) − E(VB₅)

−/0

frequencies of the A-VB₅isomers are in the

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

range between 200 cm⁻¹and 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

transition

between spin

states

−/0

ADE and IE

other isomers of VB₅clusters are higher in

isomer

energy than the most stable A-VB₅^−/0by at least

0.42 eV. The NPA charge of V1 atom is positive

(eV)

A–VB₅^−/0

B–VB₅^−/0

C–VB₅^−/0

A–VB₅^0/+

B–VB₅^0/+

C–VB₅^0/+

2 → 3

4 → 5

4 → 3

3 → 2

5 → 4

3 → 4

1.93

1.73

1.56

7.36

7.15

7.23

−

and it increases from the A-VB₅to A-VB₅and

+

A-VB₅. The B5 atom of the quartet of B-VB₅

has the highest positive charge as compared to

−

+

those of the A-VB₅, A-VB₅, and A-VB₅. And

therefore, the B-VB₅⁺has high reactivity toward

methane. The adiabatic detachment energies

−

of the anionic A–VB₅, B–VB₅, and C–VB₅

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

clusters are calculated to be 1.93, 1.73, and

1.56 eV. The ionization energy of the neutral

ground A–VB₅, B–VB₅, and C–VB₅cluster 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.

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Dong Thap University Journal of Science, Vol. 9, No. 5, 2020, 59-67

Mananghaya, M., Yu, D., Santos, G. (2016).

Hydrogen adsorption on boron nitride

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