Theoretical study of N28 molecule using semiempirical MO methods

THEO CHEM Journal of Molecular Structure (Theochem) 362 (1996) 181-186

Theoretical study of N2s molecule using semiempirical MO methods Cheng Chen*, Kuang-Chung

Sun

Department of Applied Chemistry. Chung-Cheng Institute qf Technology, Tu-Hsi, Taoyuan 33509. Taiwan

Received 27 June 1995; accepted 19 September 1995

Abstract The N2s cluster type molecule with Td point group has been studied for the first time. Two reliable semiempirical methods, PM3 and AMl, were applied in this theoretical study. Geometrical optimization, vibrational frequencies and thermal chemical calculations are reported and all the results indicate that N2s is a stable molecule. Three kinds of nitrogen atom and three types of N-N bond are identified in this Td structure. A comparison of the optimized bond distances, first ionization potentials and the average bond energies between Nzs and Nzo showed that the structural behavior of these two cluster type molecules is quite similar. Both belong to the category of stable high energy compounds. Keywords: AM 1; Cluster molecule; Nzs; PM3

1. Introduction In our recent ab initio and semiempirical molecular orbital (MO) study of the NzO molecule, which belong to the I, symmetry group [l-4], most results calculated by the reliable ab initio and semiempirical methods are very close to each other. In these former studies, the PM3 and AM1 MNDO type semiempirical MO methods [5,6] showed their excellent reliability in the theoretical study of the NzO cluster. In order to treat another nitrogen cluster type molecule, N2s, both PM3 and AM1 methods are selected for our theoretical study in this work. The Nz8 structure as shown in Fig. 1 is constructed with 12 five-membered and four nonplanar six-membered rings. With these less angular strain rings [7-lo], the Td structure is established. The atom situated at the top of the C3 axis is * Corresponding author.

defined as NV. The nitrogen belonging to three pairs of atoms which bridge the six-membered rings is defined to be Na. The third kind of N is one of twelve nitrogens which directly connect to one of the four NV atoms. In this structure there are four NV, 12 NB and 12 N atoms forming three types of bonds, among which there are 12 NV-N, 24 N-Na and six NB-NB bonds and the total number of bonds is 42. Within these bonds, NNa bonds are members of six-membered rings and all the other bonds are members of fivemembered rings, as shown in the two illustrations in Fig. 1.

2. Calculations Much selected methods

0166-1280/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDZ 0166-1280(95)04404-3

and results

as in our former work on N2,, [l-4], we the two reliable semiempirical MO PM3 and AM1 in the GAUSSIANX package

C. Chen, K.-C. Sun/Journal of Molecular Structure (Theochem)

182

Table 1 The optimized molecule

(a)

r

Fig. 1.The Td structure of the Nzs molecule. (a) The view along the C, axis; the four nitrogens at the center of the triplet of pentagons in tetrahedral vertices; (b) the view along the C2 (and Sq) axis at the middle of the bridge nitrogens.

[l l] to study the Td type N2s molecular cluster system. Both the geometrical optimizations and the frequency calculations were successfully completed. The optimized geometry and charge densities obtained by both methods are listed in Table 1. The results shows that the bond length of the six-membered ring r(Nn-N) is the shortest among the three bond distances and that the bond angles of the non-planar six-membered rings are very close to 120”. The dihedral angles (w within the six-membered ring are not large, < 7”. Most of the results show that significant delocalization is

362 (1996) 181-186

geometries

and

charge

density

of the

Nzs

Parametd

PM3

AM1

Density

PM3

AM1

0-N) r(NmN,) ~(NB-NE) R(X-NV)~ /NNVN /NVNNB ! NNBNB iNNBN / N,NNB /J

1.4847 1.4785 1.4930 2.5694 109.1246 107.0605 108.2550 120.5244 119.2502 i6.684

1.4765 1.4622 1.4984 2.5331 109.5226 106.9204 108.2032 119.8698 119.9641 f5.739

pN, pi pNB

0.023065 0.023688 po.031377

0.033535 0.0042 13 -0.015391

d Length in A; angles in degrees. Three symmetry-inequivalent equilibrium bond lengths and five symmetry-inequivalent equilibrium angle degrees are labeled in Fig. 1. ’ R(X-NV) is the distance from the central point of the Nzs molecule to each of the four tetrahedral vertices. X is a dummy atom representing the central point of the Nzs molecule. ’ LW represents the dihedral angle between the NaNNa and NNaN planes in each of the six-membered rings.

present in the four six-membered rings. There are three kinds of charge density, PNV,pN and &. The formal charge of only m\r, is less than zero. The absolute values of these densities are all less than 0.034, and we believe that covalent character is more important than the charge transfer behavior in the bonds of this molecular cluster. The self-consistent molecular orbitals were obtained. The occupied MOs PoMo and virtual MOs PVMo of the two methods are separately tabulated in Tables 2 and 3. Although there is some alternation of order of MOs, the number and the symmetry type of MOs in both PoMo and PvMo for both PM3 and AM1 are the same, viz. r0MO=6A1+A2+6E+6T1+llT2

(1)

rVMO=2A1+A2+3E+5T1+6T2

(4

Adding these two parts for the all valence electron type semiempirical method PAvMo gives: PAvMo = PoMo -t PvMo = 8Ar + 2A2 + 9E +llT,

+ 17T2

(3)

which is identical with the symmetry adapted MOs predicated by group theory. The highest occupied MO (HOMO) from PM3 and AM 1 is not the same.

C. Chen, K.-C. Sun/Journal Table 2 The occupied

MOs of the valence electron

Occupied MOsa

of Molecular

Structure (Theochem) 362 (1996) 181-186

part for Nzs (in a.u.)

Methods

E4.q E6tz f3e c7ti f311

Eat, %a, Qc

Occupied MOs”

PM3

AMI

-1.46800 -1.38423 -1.25807 -1.22898 -1.10845 - 1.08636 -1.05828 lo.97590

-1.66075 -1.59476 -1.48009 -1.45867 -1.33897 - 1.30643 -1.27921

69t,

%a, %I, Clot*

% ;t = -e(HOMO)

a The order of occupied

MOs is arranged

according

Virtual

orbitals

orbitals

of the N2s molecule

of PM3 -0.16007 -0.15773

c181>

-0.14789

ElOa,

-0.14776 -0.1272L -0.09134 -0.08187 -0.07151 -0.06834 -0.05076 -0.14835 -0.03237 0.00116 0.00630 0.03097 0.04473 0.05485 8.62 eV

69, f191* E201>

Cl,a, ElOI, floe ElII*

cllt, f1211

Clle 6221, f13t1

lZa* WELUMO

-
AMI

tlltz

-0.76029

-0.78721

cdl,

-0.73333

-0.73503’

-0.72924 -0.69765 -0.66841 -0.62146 -0.61190 -0.56608 -0.55413 -0.55305 -0.50279 -0.50168 -0.49792 -0.48430 -0.47700

-0.72915* -0.74942* -0.70358 -0.62952 -0.62287* -0.55425’ -0.59732* -0.62888* -0.47692* -0.53110* -0.53669* -0.53476* -0.50141*

fIZl> t7e t13t* f71, e141* t8,,

6% E9a, t15t* E16t> c81,

to PM3.

from the viewpoint of transfer, we also calculate the energy gap between HOMO and LUMO in each case AC =

ELUMO -

cHOMO

orbitals

of AM 1

691, c9e

E17L2 f181, ElOa, E19t2 E20LI flO1,

Ella, floe E2lt>

El 11, E12t,

clle E2212

El31, E2a1 M~LUMO

(4)

and these AC vaIues are listed at the end of Table 2.

(in a.u.) Virtual

t171>

f91[

PM3

f7a,

The HOMO from PM3 is 8t, but the HOMO from AM1 is an Se orbital. However, if one applies Koopman’s theorem to predict the first ionization potential in the two methods, Zlst = -~oMo, the calculated Zkstvalue is 12.98 eV from both PM3 and AMI MO methods. By determining the stability Table 3 The virtual

Methods

e6e

-1.18259 -1.11507 -1.07710 - 1.00393 -0.88232a -0.94902a -0.79835 -0.79610 12.98 eV

-0.94719 -0.91911 -0.88119 -0.83057 -0.82565 -0.78325 -0.77372 12.98 eV

641,

183

-EHOMO)

-0.13792 -0.12607 -0.12220 -0.09641 -0.09433 -0.07826 -0.06269 -0.05185 -0.05083 -0.02694 -0.02184 0.01027 0.05243 0.05666 0.08649 0.10149 0.11172 9.22 eV

C. Chen, K.-C. Sun/Journal

184

ofMolecularStructure

Table 4

The calculated

vibrational

Normal mode?

lE IT2

lT1 2E 2T2

3T2 2Ti ~AI 3Ti 3E 2Ai IA2

4T, 4T2 ~AI 5T2 6T2

frequencies

Wavenumber/ cm-’

Normal modes

PM3

AM1

287 296 305 307 418 439 444 473 494 494 517 541 561 567 572 620 636

374 371 424 421 562 686 571 579 697 698 744 685 841 817 864 873 902

a The order of normal results of PM3. b IR Activities.

of the Nzs molecule

modes

4E 7T2 4Ai 5Tl 8T2 6Tl 9T2 5E 2.42

7T, 6E 10T2 8TI llTzb 5Ai 7E

are arranged

Wavenumber/ cm-’ PM3

AMI

667 668 715 733 763 780 782 782 799 906 908 922 957 978 993 1000

873 920 945 913 990 996 1002 948 967 1150 1149 1142 1198 1230 1235 1251

according

to the

The calculated results for the vibrational frequencies from both PM3 and AM1 are listed together in Table 4. All the calculated normal modes I’vib matched the theoretical predication resulting from group theory: I’vib = 5Ai + 2A2 + 7E + 8Ti + 1lT2

(5)

As shown in Table 4, all the vibrational frequencies are positive values between 280 and 1300 cm-‘. Thermodynamic quantities may be calculated from these frequencies. In addition, we have selected the enthalpy of formation AH, and the enthalpy of atomization (or the negative value of binding energy) AH, directly from the computational output and combined the AH and AS values Table 5 Thermochemical

362 ji996)

381-186

to calculate Gibbs energies of formation and atomization AGr and A: for the spontaneous processes between N2s(g) and 14N2(g) and between N2s(g) and 28N(g). (The S value of Nzs is taken directly ffrom the output of the GAUSSIANQ computation. The S values of the N atom and N2 molecules are the observed experimental values.) N2s(g) = 14N2(g)

(6)

N2s(g) = 28N(g)

(7)

Within the N2s molecular cluster, the average bond energy (B.E.) was calculated to show the strength of the 42 N-N bonds in the system. The method used was similar to that used in our former work on N20 [l], as follows B.E. = AH,/42

(8)

All the calculated thermochemical data are listed in Table 5.

3. Discussion and conclusion The large positive frequencies of all vibrational modes in both PM3 and AM1 calculation indicate that the minimum point of N2s in the potential surface of the T, structure is very deep, and that N2s is a stable molecule. In addition, the large LUMO-HOMO energy gap Ae in Table 3 is further evidence for the stability of this cluster structure. Although different electronic configurations are obtained owing to the fact that HOMO in PM3 is a three-fold degenerate 8t, and HOMO in AM1 is a two-fold degenerate 8e, the ground state of both PM3 and AM1 is the ‘Ai state with closed shell electron configuration. Moreover, the predicted Ii,, values from of the different methods are identical (and equal to 12.98 eV). With the full optimized SCF results, both the calculated

results for N,, (in kJ mol-‘)

Method

PM3 AM1

(Theo&em)

4941.97 6284.38

5600.62 6966.74

AH,

A%

B.E. = AH,/42 (kJ per bond)

8296.20 6953.79

7157.69 579 1.47

197.52 165.57

C. Chen, K.-C. Sun/Journal of Molecular Structure (Theochem)

362 (1996) 181-186

185

Table 6 Comparison of the calculated results for Nzs and Nzs Results of

Molecule

Bond distances (A)

NZ8

Average bond energy (kJ per bond)

PM3

rr N-N) rz(N-Na) rs(Na-Na) Nzo TN-N Ref. single bond length AH,/42 AH,/30 Ref. single bond energy

N2a N20

1.485 1.419 1.493 1.491 [4] 197.5 201.5 [4]

Ae

N28

8.62

N20

9.63

EHOMO)

Range of vibrational frequencies (cm-‘)

N2s N20

MOs PAvMo and the vibrational modes Pet,, shown in Tables 2, 3 and 4, are exactly those irreducible representations of the Td group which were predicted by group theory. These findings providde strong evidence to justify the conclusion that the stable structure of the ground state of N2s has Td symmetry. The results of thermochemical calculations given in Table 5 show positive values for all AH,, AGr, AH, and AG, which are quite similar to their counterparts for N2,-, in our former work [l-4]. This fact shows that both N2s and N2s belong to the category of stable high energy compounds. A closer comparison of the calculated results for N2s and N2,, was conducted, and a significant portion of the calculated results for these two molecules is listed in Table 6 for comparison. Calculated N-N distances of N2s and Nzs are close to each other, and both are slightly larger than the ordinary N-N single bond distance of 1.45 A [12]. The average bond energy of N2s is very close to the bond energy of NzO in both the PM3 and the AM1 method. Also, all the bonds are stronger than the ordinary single bond [13] owing to the existence of some delocalization in the clusters. The calculated Zlst, Ae and range of vibrational frequencies of Nzs and N2,, are all very close to each other. As a result, we conclude that the unknown molecular clusters

165.5 162.4 [l] 154.8 [13]

N28

cELIJMO -

1.471 1.462 1.498 1.483 [I] 1.45 [12]

First ionization potential (ev)

N20

AM1

12.98 13.17 [4]

287 < v < 1000 356 < v < 947 [4]

12.98 13.71 [l] 9.22 11.28 374 < v < 1251 350 < v < 835 [l]

N2s and N2s are both stable high energy compounds. Essentially as concluded in refs. [7] and [14], in addition to Ns in Oh symmetry, both N2s in Td symmetry, from this work, and N2s in Zh symmetry [1,4] are the most likely candidates as propellants or explosives if they can be synthesized in the future.

References [l] C. Chen, L-H. Lu and Y.W. Yang, J. Mol. Struct. (Theochem), 253 (1992) 1. [2] C. Chen, L-H. Lu and Y.W. Yang, J. Chung-Cheng Inst. Technol., 20(2) (1992) 133. [3] C. Chen, K-C. Sun and L-H. Lu, J. Chin. Chem. Sot. (Taipei), 40 (1993) 199. [4] C. Chen and K-C. Sun, J. Mol. Struct. (Theochem), 340 (1995) 143. [5] J.J.P. Stewart, J. Comput. Chem., 11 (1990) 543. [6] M.J.S. Dewar and E.G. Zoebisch, J. Mol. Struct. (Theochem), 49 (1988) 1. [7] W.J. Lauderdale, J.F. Stanton and R.J. Bartlett, J. Phys. Chem., 96 (1992) 1173. [8] M.J. Nguyen, J. Phys. Chem., 94 (1990) 6923. [9] R. Engelke, J. Phys. Chem., 94 (1990) 6924. [lo] R. Engelke, J. Phys. Chem., 93 (1989) 5722. [l l] M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres,

186

C. Chen, K.-C. Sun/Journal of Molecular Structure (Theochem)

K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92, Revision E.3, Gaussian, Inc., Pittsburgh, PA, 1992. [12] J.A. Pople and D.L. Beveridge, Approximate Molecular

362 (1996) 181-186

Orbital Theory, McGraw-Hill Book Co., New York, 1970. p. 111. [13] K.S. Pitzer, Quantum Chemistry, Prentice-Hall, Englewood Cliffs, NJ, 1953, p. 170. [14] R. Engelke and J.R. Stine, J. Phys. Chem., 94 (1990) 5689.