The use of the generator coordinate method for designing basis set. Application to oxo-diperoxo molybdenum complexes

The use of the generator coordinate method for designing basis set.

Application to oxo-diperoxo molybdenum complexes

Fabrıcio R. Sensatoa,*, Rogerio Custodioa, Quezia B. Cassb, Elson Longob,Marcelo Z. Hernandesc, Ricardo L. Longoc, Juan Andresd

aInstituto de Quımica, Universidade Estadual de Campinas, CP 6154, 13083-970 Campinas, SP, BrazilbDepartamento de Quımica, Universidade Federal de Sao Carlos, C.P. 676, 13565-905 Sao Carlos, SP, BrazilcDepartamento de Quımica Fundamental, Universidade Federal de Pernambuco, 50540-760 Recife, PE, Brazil

dDepartament de Ciencies Experimentals, Universitat Jaume I, Apartat 224, 12080 Castello, Spain

Received 10 December 2001; accepted 22 April 2002

Abstract

The molecular and electronic structures of MoO(O2)2 (1), MoO(O2)2(OPy) (2) and MoO(O2)2(OPy)(H2O) (3) complexes

were investigated at the Hartree–Fock and density functional method (B3LYP) calculation levels. The generator coordinate

method (GCM) has been used to design basis sets that properly represent the electronic density on the Mo and O atoms for all

electron calculations, while a variant of the GCM method has been employed to design a valence basis set for the Mo atom for

the pseudopotential calculations. Compound 1 adopts a distorted tetragonal pyramid structure, where the four peroxo oxygen

atoms are located in the same plane, which is perpendicular to the axis defined by the Mo and oxo oxygen atoms. An analysis

based upon the geometrical and electronic parameters and the vibrational frequencies renders that 1 can be described as two

peroxide fragments bonded to the MoO moiety. 2 and 3 complexes are bipyramidal pentagonal structures, with the OPy ligand

occupying a quasi-equatorial position in the same plane as the two peroxo triangles while the H2O ligand is situated trans to the

oxo group in 3. A comparison between theoretical and experimental results for the geometry and vibrational frequencies of 3

complex shows good agreement. The relationship between the reactivity of 1, 2 and 3 complexes and their coordination number

has been established by analyzing the values of the vibrational frequencies, frontier molecular orbitals and the values of electron

affinities. q 2002 Elsevier Science B.V. All rights reserved.

Keywords: Generator coordinate method; Basis sets; Oxo-diperoxo molybdenum complexes; Oxygen transfer reaction; Electronic structure

calculations

1. Introduction

Oxo-diperoxo complexes of transition metals

are an important class of compounds used in the

oxidation of a variety of organic substrates [1–4].

In the 1960s, oxo-diperoxo transition metal

compounds with general formula MO(O2)2L1L2

(M ¼ Mo or W and donor ligands L1, L2 ¼

pyridine, dimethylformamide or hexamethylpho-

sphoric triamide), were synthesized by Mimoun [1,

2,4]. Since then, several oxo-diperoxo-molyb-

denum complexes, known as Mimoun complexes,

have been prepared [5–9] and several reviews on

this topic have been published by Jorgensen [10],

Dickman and Pope [11] and Morris [12].

0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.

PII: S0 16 6 -1 28 0 (0 2) 00 2 02 -6

Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264

www.elsevier.com/locate/theochem

* Corresponding author.

E-mail address: [email protected] (F.R. Sensato).

The complex MoO(O2)2(OPy), was first syn-

thesized and characterized via infrared spectroscopy

by Mimoun et al. [1]. The relative stability and

chemical reactivity of several diperoxo complexes

MO(O2)2L1L2 (M ¼ Mo and W, L1 ¼ amine oxide,

tertiary phosphine oxide, or tertiary arsine oxide and

L2 ¼ L1 or H2O) have been established by Westland

et al. [13]. The pyridine oxide complexes (L1 ¼ OPy)

were found to be the most unstable, exhibiting the

lowest activation energy for the loss of an oxygen

molecule. However, as far as we know, there is no

study concerning the molecular structure and the

reactivity of MoO(O2)2 (1), MoO(O2)2(OPy) (2) and

MoO(O2)2(OPy)(H2O) (3) (Fig. 1). Only recently, 3

compound has been synthesized and structurally

characterized by our research group [14].

Mononuclear molybdenum complexes containing

dioxygen ligands have been the subject of several

theoretical studies [15–24]. The catalytic properties

of oxo-bisperoxo-molybdenum complexes are depen-

dent on both number and type of ligand attached to the

Mo ion. Therefore, the knowledge of the electronic

and molecular structures of these complexes can

provide an understanding and rationalization of their

catalytic behavior.

The main concern of the present work is to

determine the electronic and molecular structures of

1, 2 and 3 complexes, using Hartree–Fock (HF) and

density functional (DFT; B3LYP) methods. The goal

is therefore to establish a relationship between their

electronic and molecular structures with their reactiv-

ity and catalytic activity.

The layout of this paper is presented as it follows.

Section 2 is devoted to the description of the

computational procedure together with a detailed

formulation of the generator coordinate method

(GCM). This method was employed to obtain accurate

all-electron basis sets in order to represent adequately

the Mo and O atoms and a valence basis set for Mo

atom adapted to be used with the effective core

potentials (ECPs). In Section 3, the results are

reported and discussed. Section 4 closes this paper.

2. Computational procedure and generator

coordinate method

All calculations were carried out with theFig. 1. Optimized molecular structure of (A) MoO(O2)2 (1); (B)

MoO(O2)2(OPy) (2) and (C) MoO(O2)2(OPy)(H2O) (3) complexes.

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264252

GAUSSIAN 98 program [25] without any symmetry

constraint. The HF and DFT with the B3LYP

functional were then selected [26–29]. The optimized

structure have been identified as energy minima by

calculation of the eigenvalues of the hessian matrices

associated with the corresponding stationary point in

the potential surface [30]. Supplementary vibrational

and spectral analyses were carried out with the

GAUSSVIEW 2.0 program [31] and the ORTEP-3

program [32] was used to visualize and to draw the

molecular structures.

Uncontracted basis sets for representing Mo

(17s11p8d) [33] and O (9s4p) [34] have been used,

while the standard 6-31G(d,p) basis sets have been

employed for the C, N and H atoms [35]. The

adequacy and necessary corrections for the basis

functions in the valence region of the Mo and O

atoms were carried out by the application of the

Fig. 2. Weight functions for the p (solid line) and d (dotted line) atomic orbitals of molybdenum obtained from all-electron calculations at the

ROHF level using (a) the preprocessed Huzinaga’s original (18s11p8d) basis set and (b) the (18s12p9d) improved basis set. Both calculations

have been performed at the equilibrium geometry of the [MoO(O2)2(OPy)(H2O)]2 species.

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264 253

GCM [36,37], which has been used to design basis

sets for atoms and molecules (see Refs. [38–46] and

references therein). The basic assumption of this

method is to describe one-electron function as an

integral transform:

cið1Þ ¼ð1

0fið1;aÞfiðaÞda; with i ¼ 1;…; n ð1Þ

where fi and fi are the generator and weight functions,

respectively, and a is the generator coordinate. The

mathematical and computational foundations of this

method are described elsewhere [47–50]. The most

significant aspect is that the use of numerical

techniques recovers the Hartree–Fock–Roothaan

equations and allows the use of conventional ab initio

molecular orbital programs. Therefore, the linear

combination of the uncontracted basis function

coefficients can be associated with discretized weight

functions. In practice, the analysis of the adequacy of

a basis function is considerably simple and requires

only a careful observation of the approximated weight

functions through the behavior of the LCAO coeffi-

cients at the SCF level with an uncontracted basis set.

A convenient way to visualize the tendency of the

approximated weight functions is to define a logar-

ithmic set of exponents, ViðkÞ ¼ lnðaiÞ; and create

plots of the LCAO coefficients with respect to the

corresponding Vi. In the relabeled space the largest V

represent the innermost primitives and negative V the

primitives in the valence region.

Fig. 2 shows, as an example, the p and d

approximated weight functions for Mo in the outer

molecular orbitals of the [MoO(O2)2(OPy)(H2O)]2

(32) anionic complex obtained with a (18s11p8d)

uncontracted geometric basis set for Mo which has

previously been preprocessed into a geometric basis

set represented by

aiðkÞ ¼ exp½V0ðkÞ þ ði 2 1ÞDVðkÞ�;

with i ¼ 1;…; nk

ð2Þ

where nk is the number of primitives in the mesh

of symmetry k, V0 and DV are the initial exponent

and a constant distance between the exponents in

the logarithmic space, respectively. The anionic

species was chosen to provide elements that

characterized the adequacy of the basis functions

because we are particularly interested in calculating

electron affinities, which are evaluated in the

present study as a difference between the total

energies of the anion radical and the neutral

compound. The need for diffuse functions in

order to adequately describe the electronic distri-

bution in the anionic system emerges naturally

from the analysis of the weight functions, which

provides a precise indication of the number of

primitives to be included in the basis set [42]. The

s weight function, not presented in Fig. 2, correctly

goes to zero at the boundaries of ln(a ), indicating

a satisfactory basis set. However, the p (solid line)

and d (dotted line) weight functions show the need

for enlargement of the respective basis sets in the

valence region (negative Vi ¼ lnðaiÞ), since both

functions present a significant gap between the last

coefficient of each symmetry and the expected zero

of the weight function for all molecular orbitals.

The improvement of the weight functions is

accomplished by enlarging the basis set in the

deficient region until they converge to zero. More

diffuse functions can be added to the basis function

preserving the geometric tendency shown in Eq. (2)

Table 1

Improved (18s12p9d1f) basis set for the Mo atom

Molybdenum basis set

s p d f

0.0305417a 0.1319095a 0.0716065a 0.5018503

0.0817269a 0.3420828a 0.1895673a

0.2186936a 0.8871281a 0.5018503a

0.5852040a 2.3006017a 1.3285717a

1.5659521a 5.9661829a 3.5171896a

4.1903435a 15.4721863a 9.3112195a

11.2129734a 40.1242390 24.6500243a

30.0048843a 104.0547550 65.2571551

80.2903073 269.8466640 172.7583000

214.8494686 699.7971604

574.9173927 1814.7938477

1538.4259995 4706.3304856

4116.6863033

11015.8734476

29477.4629092

78878.9762064

211072.8764730

564811.5800334

a Exponents that must to be used along with the Hay and Wadt

ECP.

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264254

using the equation

aiþ1ðkÞ ¼a2

i ðkÞ

ai21ðkÞð3Þ

where aiðkÞ is the lowest exponent of symmetry

species k, ai21ðkÞ is the next lowest exponent and

aiþ1ðkÞ the exponent of the diffuse function to be

added to the basis set. In this study, the weight

functions of 32 were analyzed for each basis

function symmetry in each molecular orbital for

Mo and O. Corrections of the basis set for the Mo

atom were achieved by increasing the (17s11p8d)

basis in the valence region up to a (18s12p9d)

geometric basis set and for the O atom from (9s4p)

up to (11s5p) (Tables 1 and 2).

Calculations involving transition metal are com-

putationally demanding, which can be considerably

reduced by replacing the inner (core) electrons by

ECP. All-electron basis sets should generally not be

used together with ECPs [51]. The modifications of

the basis set for Mo using pseudopotential was also

carried out using GCM and are described in detail

elsewhere [43,44,46]. Eq. (1) shows that the complete

space of the a exponent should comprise a range from

0 to 1. Although in practice the a space is limited to a

narrower region, a large number of functions must be

included either in atomic or molecular calculations to

describe appropriately the regions near the nuclei.

However, the limits of integration in Eq. (1) need to

be changed from (0,1) to (0,acut) when the core

electrons are replaced by a pseudopotential, which is

equivalent to saying that the basis set has no effect on

the wavefunction in a range between (acut,1) when

the pseudopotential starts to take effect. Mathemat-

ically the use of ECP changes Eq. (1) to

cið1Þ ¼ðacut

0fið1;aÞfiðaÞda; with i ¼ 1;…; n

ð4Þ

In order to evaluate the effect of the pseudopotential

on the wavefunction, Fig. 3 presents the Mo s weight

functions for the 5s atomic orbital calculated with the

previously improved (18s12p9d) basis set at the HF

level of theory with all electron (dashed line) and the

same basis set in conjunction with the Hay and Wadt

(HW) quasi-relativistic pseudopotential [52] (dotted

line). The two weight functions are practically

equivalent in the valence region, more specifically,

for V larger than 3.4, however, they are quite different

in the inner region. This value of V (<3.4) also

indicates where the pseudopotential starts to take

effect, i.e. the value (acut) at which the original basis

set should be terminated. This analysis suggests that

some primitive functions can be removed from the

inner region for an ECP calculation. Numerical tests

have shown that basis sets can be removed after the

first gaussian exponent where the weight function

presents essentially no change [43], i.e. for V larger

than 3.4 in Fig. 3. The Mo weight functions from Fig.

3 show that the first eight s gaussian functions must be

retained in the calculation using pseudopotential. The

cutoff in the inner region for p, d and other meshes can

be taken as the same for the s mesh. Consequently the

(18s12p9d) basis set can be drastically reduced to a

(8s6p7d) basis function when HW pseudopotential is

used. The discretization parameters (Eq. (2)) defining

the uncontracted (18s12p9d) all-electron basis set for

Mo atom are s mesh: V0 ¼ 23.489, DV ¼ 0.984,

N ¼ 18; p mesh: V0 ¼ 22.026, DV ¼ 0.953,

N ¼ 12; d mesh: V0 ¼ 22.637, DV ¼ 0.974,

N ¼ 9. The same values are used for the ECP basis

set, except that N ¼ 8; 6 and 7, for the s, p and d

meshes, respectively. The optimized geometric par-

ameters for the O atom are for s mesh, V0 ¼ 23.821,

DV ¼ 1.310, N ¼ 11 whereas for p mesh,

V0 ¼ 22.675, DV ¼ 1.388, N ¼ 5: It is important

to note that Walch et al. [53] has also presented

supplemental basis functions to the Huzinaga’s basis

set for the Mo atom, namely, two additional diffuse

Table 2

Improved (11s5p2d) basis set for the O atom

Oxygen basis set

s p d

0.0219125 0.0689206 1.1056131

0.0811708 0.2760426 0.2760462

0.3006826 1.1056131

1.1138250 4.4282302

4.1259653 17.7360626

15.2839002

56.6164738

209.7255980

776.8909554

2877.8535497

10660.4935937

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264 255

functions were required for the p mesh:

a1(p) ¼ 0.1339 (Va1(p) ¼ 22.011) and

a2(p) ¼ 0.0462 (Va2(p) ¼ 23.076) while for the d

mesh an additional exponent a1(d) ¼ 0.0562

(Va1(d) ¼ 22.80) was suggested. The value of

Va1(p) for the p mesh is very similar to the value

obtained by us, V0(p) ¼ 22.026 (Table 1) for the

most diffuse exponent. A comparison of the exponent

values for the d mesh obtained by us,

V0(d) ¼ 22.637 and Walch et al. [53],

Va1(d) ¼ 22.80, also shows good agreement.

In addition to these diffuse functions, Walch et al.

[53] also recommended a set of 4f functions for the

basis set of the Mo atom. The Hellmann–Feynman

force analysis and total energy convergence were used

as criteria to include polarization functions on Mo and

O centers. Such a procedure is based on the magnitude

of the electric field on the nuclei in the molecular

system [41,44] and suggests the need of one f valence

polarization function (0.502) for the Mo center and

two d functions (0.276 and 1.106) for the O atoms.

It is important to note that we obtained similar

exponents for our basis function to those obtained by

Walch et al. [53] who used a much more elaborate and

demanding procedure than the GMC.

Optimized exponents for each mesh of Mo and O

Fig. 3. Molybdenum s weight function for the 5s atomic orbital calculated at the HF level using the improved (18s12p9d) basis set. The dashed

line is the s weight function from all-electron calculations; the dotted line is the weight function using the same basis set and the pseudopotential

by Hay and Wadt; the solid line is the s weight function using only improved outermost primitives and pseudopotential.

Table 3

Selected computing methods (level of calculation þ basis set)

Computing methods A B C D

Level of theory HF HF DFT–B3LYP DFT–B3LYP

Mo (8s6p7d1f) þ ECP (18s12p9d1f) (8s6p7d1f) þ ECP (18s12p9d1f)

O (11s5p2d) (11s5p2d) (11s5p2d) (11s5p2d)

C, N, H 6-31G(d,p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264256

atoms are listed in Tables 1 and 2. As a result, all-

electron basis sets (18s12p9d1f) and (11s5p2d) for

Mo and O atoms, respectively, have been designed,

while a valence basis set of (8s6p7d1f) has been

designed to be used with the HW-ECP for the Mo

atom. Although it seems natural to transfer the

concept of ‘atomic core’ into Kohn-Sham density

functional calculations, there are some problems

associated with this procedure. The performance of

ECPs adjusted at the HF level is well documented but

their application in density functional calculations has

been the subject of some research [51,54]. Therefore,

we have defined four computing methods, which are

summarized in Table 3.

3. Results and discussion

Optimized molecular structures of the compounds

1, 2 and 3 with A, B, C and D computing methods are

presented in Tables 4–6, respectively. The results

show that 1 has a pyramidal arrangement with the

peroxo oxygen atoms located in the same plane (Fig.

1(a)). This plane is perpendicular to the axis formed

by the Mo and the oxo ligand, Mo–O(1), and a value

around 458 is found for the bond angles associated

with the dioxygen ligands, O(3)–Mo–O(4) and

O(5)–Mo–O(6). Tilting of peroxo ligands yields

that these groups are asymmetrically bound to the

molybdenum center. The oxygen centers of peroxo

group are not equivalent, more specifically, the Mo–

O(3) and Mo–O(5) bond distances (back-side) are

approximately 0.04 A shorter than the Mo–O(4) and

Mo–O(6) ones, for all computational methods used.

These relative differences decrease on going from 1 to

2 and 3. For the sake of comparison we have

calculated the difference in total energy between the

conformation of 1 belonging to the groups Cs and C2v

(symmetric disposal of the back-side and front-side

oxygen atoms with respect to the Mo center). Cs

conformation is proven to be more stable by about

70.0 kcal/mol than the C2v structure.

Factors controlling this asymmetry can be found by

means of an analysis of the atomic orbital contri-

butions of representative molecular orbitals. A

detailed analysis of the valence molecular orbitals

calculated at C computing method reveals that the

HOMO (28.2 eV) and HOMO-1 (28.8 eV) of 1 are

localized on the peroxo oxygen atoms and are

associated to the O–O antibonding orbital pzp(O–O)

Table 4

Calculated molecular structure for the MoO(O2)2 complex

1A 1B 1C 1D

R (A)

Mo–O(1) 1.651 1.626 1.675 1.678

Mo–O(3) 1.845 1.852 1.897 1.903

Mo–O(4) 1.886 1.897 1.932 1.943

Mo–O(5) 1.845 1.852 1.897 1.903

Mo–O(6) 1.886 1.897 1.932 1.943

O(3)–O(4) 1.410 1.400 1.443 1.434

O(5)–O(6) 1.410 1.400 1.443 1.434

d (8)

O(3)–Mo–O(5) 129.4 129.7 135.9 135.7

O(4)–Mo–O(6) 93.0 92.7 89.9 90.1

O(3)–Mo–O(4) 44.4 43.8 44.3 43.8

O(5)–Mo–O(6) 44.4 43.8 44.3 43.8

O(1)–Mo–O(3) 112.8 112.9 110.3 110.5

O(1)–Mo–O(4) 114.1 114.4 114.4 114.7

O(1)–Mo–O(5) 112.8 112.9 110.3 110.5

O(1)–Mo–O(6) 114.1 114.4 114.4 114.7

O(1)–Mo–O(4)–O(3) 298.6 298.4 294.6 294.4

O(1)–Mo–O(6)–O(5) 98.7 98.4 94.6 94.4

O(3)–O(4)–O(6)–O(5) 0.0 0.0 0.0 0.0

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264 257

(see Fig. 4(a) and (b), respectively); HOMO-2

(210.3 eV; see Fig. 4(c)) is dominated by the py

orbitals of the oxygen atoms belonging to the peroxo

group,pyp(O–O), and the dxy and dx 2 2 dy

2 orbitals of the

Mo atom. Thus, the disposal of each peroxo group with

respect to the molybdenum center is dictated by the

angle between the lobes of the dxy and dx 2 2 dy2

orbitals of molybdenum. HOMO-3 (210.8 eV) is

illustrated in Fig. 4(d) and the dominant contributions

are associated to the py orbitals of both oxo oxygen

(O1) and Mo atoms being associated to p(Mo–O1)

bond. In addition, a very strong overlap between the

py orbital of the Mo center and back-side oxygen is

observed. As a result, these features of HOMO-2 and

HOMO-3 are responsible for the asymmetry exhibited

by 1 and related complexes. HOMO-4 (210.9 eV)

has a strong contribution of dxy orbital of the Mo atom,

which overlaps with px and py orbitals of the back- and

front-side oxygen atoms, respectively. HOMO-5

(211.6 eV) is related to the bonding orbital pz(O–

O) of the peroxo groups and the bonding interaction

between the Mo and oxo oxygen atoms. Since the

HOMO-4 and HOMO-5 orbitals do not contribute to

the observed asymmetry they are not shown in Fig. 4.

Although there are no experimental data for the

bis-peroxo structure 1; it might be formed as a result

of the ligand(s) dissociation from the Mo ion of 2 or 3

during the oxidation reaction as it has been suggested

by Mimoun [2]. The introduction of a pyridine oxide

ligand (OPy) between the back-side oxygen atoms in

1 leads to 2 and causes an increase in the Mo–O(3)

and Mo–O(5) bond lengths and a smaller increase in

the Mo–O(4) and Mo–O(6) bond distances. This

leads to a smaller asymmetry of the peroxo groups of

0.02 A compared to 0.04 A of 1. However, HF and

B3LYP computing methods yielded an opposite trend

for O–O; the bond distances in the peroxo groups,

namely, the HF method predicts a small decrease

(0.01 A) in the O(3)–O(4) and O(5)–O(6) bond

distances whereas a increase of the same magnitude is

Table 5

Calculated molecular structure for the MoO(O2)2(OPy) complex

2A 2B 2C 2D

R (A)

Mo–O(1) 1.629 1.630 1.681 1.684

Mo–O(3) 1.884 1.889 1.925 1.931

Mo–O(4) 1.901 1.909 1.942 1.952

Mo–O(5) 1.884 1.889 1.925 1.931

Mo–O(6) 1.901 1.909 1.942 1.952

Mo–O(7) 2.098 2.110 2.127 2.140

O(3)–O(4) 1.400 1.394 1.453 1.447

O(5)–O(6) 1.400 1.394 1.453 1.447

O(7)–N(8) 1.326 1.326 1.337 1.336

d (8)

O(1)–Mo–O(7) 96.2 96.6 95.7 96.0

O(3)–Mo–O(5) 130.8 130.7 132.7 132.4

O(4)–Mo–O(6) 89.1 89.0 88.2 88.2

O(3)–Mo–O(4) 43.4 43.1 44.1 43.8

O(5)–Mo–O(6) 43.4 43.1 44.1 43.8

O(1)–Mo–O(3) 114.1 114.2 113.0 113.2

O(1)–Mo–O(4) 110.1 110.5 110.5 110.9

O(1)–Mo–O(5) 114.1 114.2 113.0 113.2

O(1)–Mo–O(6) 110.1 110.5 110.5 110.9

Mo–O(7)–N(8) 118.4 118.4 116.7 116.6

O(1)–Mo–O(4)–O(3) 2104.2 2103.9 2102.3 2102.2

O(1)–Mo–O(6)–O(5) 104.2 103.9 102.4 102.2

O(3)–O(4)–O(6)–O(5) 0.0 0.0 0.0 0.0

O(1)–Mo–O(7)–N(8) 180.0 180.0 180.0 179.9

Mo–O(7)–N(8)–C(9) 91.0 91.0 90.7 90.7

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264258

obtained with B3LYP. The Mo-centered bond angles

between the oxo oxygen O(1) and the back-side

oxygen atoms (O(3) and O(5)) increase approximately

38, whereas the bond angles formed with the front-side

oxygen atoms (O(4) and O(6)) decrease nearly 48. All

four computing methods show that the oxo oxygen,

the back-side oxygen and Mo atoms lie onto the same

plane, which leads to a 08 dihedral angle O(3)–Mo–

O(1)–O(5) for all 1, 2 and 3 compounds.

The most noticeable feature induced by adding a

water molecule into 2 to yield 3 is the increase of the

O(3)–Mo–O(5) bond angle from approximately 1308

to around 1408. The Mo-centered bond angles formed

between the oxo and the back- and front-side oxygen

atoms decrease 58 and 38, respectively.

The X-ray structure of 3 has recently been

determined [14], and a comparison between the

theoretical and experimental data shows a very good

agreement, except for the bond distance between the

metal ion and the oxygen atom of the water ligand,

Mo(2)–O(19), that has been calculated to be 2.80 A,

which compares poorly with the experimental data

2.30 A. A similar result was reported by Rosch et al.

[55] who have compared experimental and theoretical

results for an analogue complex ReO(O2)2(CH3)(H2-

O), namely, the experimental data is 2.25 A, whereas

the calculated is 2.48 A, whose discrepancy has been

rationalized in terms of a co-crystallized ether

molecule. More recently, upon investigating the olefin

epoxidation by peroxo complexes with structures

(NH3)(L)M(O)22n(h 2-O2)1þn (n ¼ 0, 1; L ¼ none,

NH3; M ¼ Cr, Mo, W) Rosch et al. [20] inferred that

the corresponding part of the potential energy surfaces

is rather flat so that small perturbations may cause

Table 6

Calculated and experimental molecular structure for the MoO(O2)2(OPy)(H2O) complex

3A 3B 3C 3D Exp. [14]

R (A)

Mo–O(1) 1.622 1.624 1.676 1.679 1.670

Mo–O(3) 1.899 1.904 1.940 1.946 1.955

Mo–O(4) 1.905 1.913 1.949 1.958 1.919

Mo–O(5) 1.899 1.904 1.940 1.946 1.955

Mo–O(6) 1.905 1.913 1.949 1.958 1.919

Mo–O(7) 2.090 2.102 2.117 2.130 2.076

O(3)–O(4) 1.400 1.395 1.452 1.446 1.470

O(5)–O(6) 1.400 1.395 1.452 1.446 1.470

O(7)–N(8) 1.325 1.324 1.338 1.337 1.354

Mo–O(19) 2.820 2.844 2.811 2.838 2.295

Hwat–O(3)back-side 2.522 2.523 2.489 2.491 2.718

Hwat–O(4)front-side 2.353 2.347 2.249 2.240 2.832

d (8)

O(1)–Mo–O(7) 96.8 97.2 96.3 96.7 89.2

O(3)–Mo–O(5) 141.4 140.8 143.0 142.5 156.7

O(4)–Mo–O(6) 90.2 90.2 89.5 89.6 88.9

O(3)–Mo–O(4) 43.2 42.9 43.8 43.5 44.6

O(5)–Mo–O(6) 43.2 42.9 43.8 43.5 44.6

O(1)–Mo–O(3) 109.0 109.3 108.1 108.4 101.6

O(1)–Mo–O(4) 107.7 108.0 107.9 108.3 102.8

O(1)–Mo–O(5) 109.0 109.3 108.1 108.4 101.6

O(1)–Mo–O(6) 107.7 108.0 107.9 108.3 102.8

Mo–O(7)–N(8) 120.5 120.4 118.1 117.0 123.0

O(1)–Mo–O(19) 178.3 178.1 177.8 177.6 170.8

O(1)–Mo–O(4)–O(3) 299.2 299.2 297.7 297.6 293.5

O(1)–Mo–O(6)–O(5) 99.2 99.2 97.7 97.7 93.5

O(3)–O(4)–O(6)–O(5) 0.0 0.0 0.0 0.0 0.0

O(1)–Mo–O(7)–N(8) 180.0 180.0 180.0 180.0 180.0

Mo–O(7)–N(8)–C(9) 90.7 90.7 90.4 90.4 90.8

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264 259

large structural effect. In addition, Frenking et al. [21]

have studied the equilibrium geometries of the

molybdenum oxo and peroxo compounds MoOn

(O2)32n and the related complexes [MoOn(O2)32n

(OPH3)] and [MoOn(O2)32n(OPH3)(H2O)] (n ¼ 0–3)

by DFT–B3LYP calculations and found a similar

discrepancy, which was partly attributed to inherent

solid-state effects. Thiel et al. [23] have also found

that the calculated distance between the axial ligand

and the molybdenum atom is overestimated with

respect to the corresponding distance for analogous

molybdenum peroxo complexes. It is important to

note that even in the experimental structure determi-

nation, the Mo–O(19) (2.295 A) distance is reported

to be larger than the Mo–O(7) distance (2.064 A).

The difference between the axial and equatorial bond

lengths has been reported to occur in analogue

complexes which has been supposed to be trans

influence of O(1) [6–9]. However, the considerable

discrepancy between our theoretical and experimental

results for Mo–O(19) distance cannot be regarded as

only resulting from such an effect. In addition, we

have characterized experimentally that the water

ligand forms intermolecular hydrogen bonds with

the peroxo groups of two other adjacent complexes in

the crystal [14]. Our calculation has not taken into

account these intermolecular interactions and, as a

result, a spurious and strong intramolecular inter-

action between the hydrogen atom of water ligand and

the peroxo group is favored (see Table 6 for the

calculated bond distance between the Hwat and front-

side oxygen atoms). Such an intramolecular inter-

action of the hydrogen atom towards the peroxo group

causes a displacement of the oxygen of the water in an

opposite direction leading to a very large value for the

Mo–O(19) bond. When the environment effect is

modeled by two methanol molecules that form

hydrogen bonds with the coordinated water, such a

bond distance decrease to a value of 2.3 A. A detailed

analysis along with the experimental data is presented

elsewhere [14].

An analysis of the relativistic effects can be

performed by comparing the results obtained with

the A and B, and the C and D computing methods. A

shorter Mo – oxygen bond distances have been

obtained when relativistic ECP was used (Tables

4–6). These findings have also been observed by van

Wullen for a similar analysis of the Mo(CO)6 complex

[51].

Once the molecular structure has been obtained,

the vibrational frequencies were calculated. Several

recent studies have shown that the vibrational

frequencies calculated with DFT methods agree well

with the experimental data (see Ref. [56] and

references therein). In addition, vibrational frequen-

cies for a large number of inorganic molecules have

been calculated using B3LYP functional in conjunc-

tion with the HW-ECP, which yielded a reasonable

agreement with the experiment [57]. Therefore, the C

and D methods were used and the assignments of the

more significant infrared bands are compared to

experimental results in Table 7. Calculated frequency

values are known to be overestimated by 10–15%,

partly due to the neglect of the anharmonic effects and

the inherent limitations of the theory. In order to

address this systematic difference, it has been

proposed that scaling factors be obtained by compar-

ing calculated values with large experimental data sets

[56–59]. We have determined the scaling factors for

the C and D computing methods by comparing

experimental and theoretical results for the main

vibrational modes of compound 3. Optimum scaling

factors were obtained in the same way as that

described in the literature [56–59] and the values

Fig. 4. Dominant orbital contribution for some occupied molecular

orbitals of the MoO(O2)2 complex calculated with the C method: (a)

HOMO; (b) HOMO-1; (c) HOMO-2 and (d) HOMO-3.

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264260

0.9056 and 0.9097 were obtained for the C and D

methods, respectively. The calculated vibrational

frequencies of the 1, 2 and 3 complexes after scaling

are listed in Table 7 along with the experimental

values. The corresponding vibrational modes, from i

to ix, are also presented in Table 7. An analysis of the

results points out that a good agreement between the

theoretical values calculated with 3C and 3D and

experimental data is obtained. The overall root mean

square errors for the fundamental frequencies for 3C

and 3D are 22 and 23 cm21, respectively, affording

unambiguous assignment of the observed vibrational

frequencies for the coordination polyhedron around

Mo atom.

On going from 1 to 2 for either C or D methods, the

most prominent feature is the displacement by

43 cm21 of the vibrational mode iv to a lower

frequency value caused by the introduction of the

OPy ligand which elongates the bond distance

between the Mo atom and the back-side oxygens

(see Tables 4 and 5 for corresponding bond distances).

The calculated values for the vibrational frequencies

of 1, 2 and 3 suggest that the O–O fragment is

associated with a peroxo group (e.g. for H2O2, the

distance O–O and the corresponding vibrational

frequency are 1.453 A and 882 cm21, respectively

[60]). In addition, the stretching movement associated

with the Mo–OPy and Mo–OH2 bonds of 2 and 3

complexes present very low values (around 360 and

115 cm21, respectively), characterizing the flatness of

the potential curves associated with these ligands.

The metal-mediated epoxidation of olefins mech-

anism has been subjected to a great deal of

experimental and theoretical studies. Two main

mechanisms concerning stoichiometric olefin epox-

idation by MoO(O2)2(L1,L2) have generated a long

Table 7

Selected calculated and experimental vibrational frequencies (cm21) for compounds 1, 2 and 3

1C 2C 3C 1D 2D 3D Exp. [1] Exp. [13] Exp. [14]

(i) 945 933 937 942 930 934 960 970 969

(ii) 881 880 876 892 887 883 875 873

(iii) 872 871 868 881 878 876 860 859

(iv) 638 595 594 637 594 592 580 577 582

(v) 588 578 562 585 574 558 540 537

(vi) 502 504 495 493 499 490

(vii) 515 526 505 509 519 503

(viii) Mo–OPy 361 358 359 356

(ix) Mo–OH2 116 113

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264 261

controversy, namely, Mimoun [2] proposed a coordi-

nation of the olefin at the metal and a subsequent

cycloinsertion into a metal–peroxo bond forming a

five-membered dioxymetallocycle that decomposes

into an epoxide and the corresponding monoperoxo

complex, while Sharpless [61] suggested an alterna-

tive mechanism involving transfer of one of the

peroxo oxygens to the olefin through a three-

membered ring transition state. Recently, two theor-

etical studies have corroborated the mechanism

suggested by Sharpless [20,22].

Still, an important point to consider is how the

reactivity of the oxo-peroxo complexes depends upon

the coordination around the metal atom. We have

observed experimentally that the oxo-peroxo molyb-

denum complex in its dehydrate form (compounds

related to 1 or 2) is more reactive towards olefin and

sulfide oxidation that the hydrated ones (compounds

related to 3) [62]. The question of whether either 1 or

2 is the ultimate moiety remains unanswered. The

approach of an olefin molecule towards the oxo-

peroxo complex may be able to induce the displace-

ment of the OPy ligand (substitution mode ) so that the

olefin attacks directly 1. Otherwise, the ligand may

remain bonded to metal atom during the formation of

an olefin-coordinated specie (addition mode ).

Olefin epoxidation by d0 metal–peroxo complexes

closely resemble epoxidation by purely organic

oxidants. This provides support for the conclusion

that oxygen transfer by metal catalyzed reactions

presents also an electrophilic character. Using an

NDDO approach, Filatov et al. [17] has compared the

electron affinities of MoO(O2)2L1 (L1 ¼ H2O or NH3)

and MoO(O2)2L1L2 (L1 and L2 ¼ H2O or NH3), and

inferred that the lower electron affinity exhibited by

the seven-coordinated species is the reason for these

complexes being much less reactive towards epoxida-

tion of olefins than the six-coordinated ones. In light

of this, we have calculated the electron affinities of 1,

2 and 3 complexes at the C level, which were

computed as the difference between the total energies

of the radical anion and the neutral compound by two

approaches, namely, with the former being calculated

at the geometry for the latter (vertical electron affinity,

VEA), and the anionic specie being allowed to relax

(adiabatic electron affinity, AEA). The corresponding

values of VEA and AEA are summarized in Table 8.

As expected, the calculated AEA values are larger

than the corresponding VEA ones; however, both

approaches yielded the same qualitative and quanti-

tative trend. Compound 1 is the most electrophilic

whereas 2 and 3 should exhibit similar electrophili-

city. The electrophilic properties of 1, 2 and 3 are also

reflected by the pertinent charge distribution. Table 9

presents the NBO population analysis of 1, 2 and 3

calculated with the C method. The smaller electron

affinities of 2 and 3 is caused by the electron donation

of approximately 0.3 electrons from the OPy ligand to

the MoO(O2)2 moiety. As a result, electron affinity

considerations render that compound 1 could be

expected to be the ultimate specie toward the

epoxidation of olefins.

Olefin epoxidation by a d0 metal peroxo is also

generally considered as an electrophilic attack of the

peroxo oxygen on the olefin. Based on a charge

decomposition analysis (CDA) scheme [63] on the

transition state related to the Sharpless mechanism,

Frenking et al. [22] suggested that the epoxidation

with metallo peroxides should be considered as a

nucleophilic attack of ethylene toward the sp orbital

of the O–O bond. Rosch et al. [20] have also

established a linear correlation between the energy

of the molecular orbital with dominant contribution of

sp(O–O) orbital of the complex and the height of the

activation barrier for the interaction between the

Table 8

The calculated vertical (VEA) and adiabatic (AEA) electron

affinities (eV) for compounds 1, 2 and 3 with the C method

1C 2C 3C

VEA 2.9 1.2 1.1

AEA 3.3 1.4 1.4

Table 9

Calculated atomic charges based on the NBO population analysis

for compounds 1, 2 and 3 with the C method

1C 2C 3C

O(1) 20.51 20.52 20.48

Mo 1.84 1.79 1.77

O(3), O(5) 20.35 20.41 20.41

O(4), O(6) 20.31 20.36 20.39

O(7) 20.56 20.56

N(8) 0.05 0.06

O(19) 21.02

H(20), H(21) 0.53

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264262

olefin molecule and the oxo-peroxo complex of Mo.

That is, for a fixed electron donor, the activation

barrier increases if the energy of the molecular orbital

with dominant contribution of sp(O–O) level also

increases, even if it is not the LUMO of the complex.

An analysis of the molecular orbital structure for

compound 1 calculated at C method reveals that the

energy associated to the molecular orbital with

dominant contribution of sp(O – O) level is

20.7 eV, while a value of approximately 1.0 eV

was found for compounds 2 and 3 indicating that the

compound 1 is the most reactive towards nucleophilic

attack. The calculated LUMO energy values also

support this trend. The LUMO energy of 1 is 25.1 eV

while the values of 23.1 and 22.7 eV were found for

2 and 3, respectively.

The Mo–H2O bond energy of 3 as well as the Mo–

OPy bond energy of 2 have also been calculated with

the C method, and they are 29.7 and 244.6 kcal/mol,

respectively. As a result, there might be two

competitive effects: the electrophilic properties as

well as the value of the energy associated to the

molecular orbital with dominant contribution of the

sp(O–O) level for 1, 2 and 3 favor the substitution

approach of the olefin molecule, while the Mo–OPy

bond energy supports the addition process.

4. Conclusions

The electronic and molecular structures of oxo-

diperoxo complexes: MoO(O2)2, MoO(O2)2OPy and

MoO(O2)2(OPy)(H2O), where OPy ¼ pyridine N-

oxide, have been investigated using ab initio HF and

DFT (B3LYP) methods. The GCM has been used to

design all-electrons basis sets for the oxygen and

molybdenum atoms as well as a valence basis set for

the Mo atom for pseudopotential calculations. The

GCM approach has proven to be quite versatile,

efficient, and simple to be used and implemented. The

results obtained with the designed valence basis set

for Mo atom adapted to be used with the HW-ECP

compared very well with the all-electron ones. The

atomic orbital contributions of the oxygen and Mo

atoms to the HOMO-2 and HOMO-3 molecular

orbitals are responsible for generating an asymmetric

(Cs) structure for all complexes investigated. The

MoO(O2)2 compound has proven to be the most

reactive towards oxygen transfer based upon the

energy of the sp(O–O) molecular orbital and the

values of the electron affinities of each complex

studied. The reliability of these results is strengthened

by the very good agreement between the calculated

and experimental molecular structures as well as for

the vibrational frequencies.

Acknowledgments

This work was supported by the Brazilian funding

agencies: FAPESP/CEPID and by the ‘Programa de

Cooperacao Internacional’ supported by CAPES

(Brazil) and Ministerio de Educacion y Cultura del

Gobierno Espanol (Spain). The authors also wish to

thank the computer centers CENAPAD-NAR-UFS-

Car, CENAPAD-SP, CESUP-RG (Brazil), Servei

d’Informatica de la Universitat Jaume I-Castellon-

Spain for making their computational facilities

available.

References

[1] H. Mimoun, I.S. Roch, L. Sajus, Bull. Soc. Chim. Fr. 5 (1969)

1481.

[2] H. Mimoun, I.S. Roch, L. Sajus, Tetrahedron 26 (1970) 37.

[3] S.A. Matlin, P.G. Sammes, R. Upton, J. Chem. Soc. Perkin

Trans. 1 (1979) 2481.

[4] H. Mimoun, Angew. Chem., Int. Ed. Engl. 21 (1982) 734.

[5] J.M. Le Carpentier, R. Schlupp, R. Weiss, Acta Crystallogr., B

28 (1972) 1278.

[6] E.O. Schlemper, G.N. Schrauzer, L.A. Hughes, Polyhedron 3

(1984) 377.

[7] W.P. Griffith, A.M.Z. Slawin, K.M. Thompson, D.J. Williams,

Chem. Soc. Chem. Commun. (1994) 569.

[8] P. Martın-Zarza, P. Gili, F.V. Rodrıguez-Romero, C. Ruiz-

Perez, X. Solans, Inorg. Chim. Acta 223 (1994) 173.

[9] W.R. Thiel, T. Priermeier, Angew. Chem., Int. Ed. Engl. 34

(1995) 1737.

[10] K.A. Jørgensen, Chem. Rev. 89 (1989) 431.

[11] M.H. Dickman, M.T. Pope, Chem. Rev. 94 (1994) 569.

[12] M.J. Morris, Coord. Chem. Rev. 152 (1996) 309.

[13] A.D. Westland, F. Haque, J. Bouchard, Inorg. Chem. 19

(1980) 2255.

[14] F.R. Sensato, Q.B. Cass, E. Longo, J. Zukerman-Schpector, R.

Custodio, J. Andres, M.Z. Hernandes, R.L. Longo, Inorg.

Chem. 40 (2001) 6022.

[15] K.F. Purcell, Organometallics 4 (1985) 509.

[16] K.A. Jørgensen, R. Hoffmann, Acta Chem. Scand. B 40 (1986)

411.

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264 263

[17] M.J. Filatov, K.V. Shalyaev, E.P. Talsi, J. Mol. Catal. 87

(1994) L5.

[18] L. Salles, J.-Y. Piquemal, R. Thouvenot, C. Minot, J.-M.

Bregeault, J. Mol. Catal. A 117 (1997) 375.

[19] I.V. Yudanov, C. Di Valentin, P. Gisdakis, N. Rosch, J. Mol.

Catal. A 158 (2000) 189.

[20] C. Di Valentin, P. Gisdakis, I.V. Yudanov, N. Rosch, J. Org.

Chem. 65 (2000) 2996.

[21] D.V. Deubel, J. Sundermeyer, G. Frenking, Inorg. Chem. 39

(2000) 2314.

[22] D.V. Deubel, J. Sundermeyer, G. Frenking, J. Am. Chem. Soc.

122 (2000) 10101.

[23] A. Hroch, G. Gemmecker, W.R. Thiel, Eur. J. Inorg. Chem. 5

(2000) 1107.

[24] D.V. Deubel, J. Sundermeyer, G. Frenking, Org. Lett. 3 (2001)

329.

[25] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A.

Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery,

Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam,

A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi,

V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C.

Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala,

Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck,

K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz,

B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi,

R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham,

C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe,

P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres,

C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople,

Gaussian, Inc., Pittsburgh PA, 1998.

[26] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200.

[27] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.

[28] A.D. Becke, Phys. Rev. A 38 (1988) 3098.

[29] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.

[30] J.B. Foresman, A. Frish, Exploring Chemistry with Electronic

Structure Methods, Gaussian Inc, Pittsburgh, 1993.

[31] GAUSSVIEW (2.0), Gaussian Inc., Pittsburgh, PA, 1998.

[32] L.J. Farrugia, J. Appl. Crystallogr. 30 (1997) 565.

[33] S. Huzinaga, J. Chem. Phys. 66 (1977) 4245.

[34] F.B. Duijneveldt, IBM Res. J. (1971) 945.

[35] R. Ditchfield, W.J. Hehre, J.A. Pople, J. Chem. Phys. 52

(1970) 5001.

[36] D.L. Hill, J.A. Wheeler, Phys. Rev. 89 (1953) 1102.

[37] J.J. Griffin, J.A. Wheeler, Phys. Rev. 108 (1957) 311.

[38] R.O. Vianna, R. Custodio, H. Chacham, J.R. Mohallem, Int.

J. Quantum Chem. Symp. 26 (1992) 311.

[39] R. Custodio, J.D. Goddard, J. Mol. Struct. (Theochem) 277

(1992) 263.

[40] R. Custodio, M. Giordan, N.H. Morgon, J.D. Goddard, Int.

J. Quantum Chem. 42 (1992) 411.

[41] R. Custodio, J.D. Goddard, M. Giordan, N.H. Morgon, Can.

J. Chem. 70 (1992) 580.

[42] R. Custodio, J.D. Goddard, J. Mol. Struct. (Theochem) 281

(1993) 75.

[43] R. Custodio, W.M. Davis, J.D. Goddard, J. Mol. Struct.

(Theochem) 315 (1994) 163.

[44] N.H. Morgon, R. Custodio, J.M. Riveros, Chem. Phys. Lett.

235 (1995) 436.

[45] N.H. Morgon, R. Custodio, J.G.R. Tostes, C.A. Taft, J. Mol.

Struct. (Theochem) 335 (1995) 11.

[46] M. Giordan, R. Custodio, N.H. Morgon, Chem. Phys. Lett. 279

(1997) 396.

[47] J.R. Mohallem, R.M. Dreizler, M. Trsic, Int. J. Quantum

Chem. Symp. 20 (1986) 45.

[48] J.R. Mohallem, Z. Phys. D 3 (1986) 339.

[49] J.R. Mohallem, M. Trsic, J. Chem. Phys. 86 (1987) 5043.

[50] H.F.M. Costa, M. Trsic, J.R. Mohallem, Mol. Phys. 62 (1987)

91.

[51] C.V. Wullen, Int. J. Quantum Chem. 58 (1996) 147.

[52] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 299.

[53] S.P. Walch, C.W. Bauschlicher Jr, C.J. Nelin, J. Chem. Phys.

79 (1983) 3600.

[54] T.V. Russo, R.L. Martin, P.J. Hay, J. Phys. Chem. 99 (1995)

17085.

[55] P. Gisdakis, S. Antonczak, S. Kostlmeier, W.A. Herrmann, N.

Rosch, Angew. Chem., Int. Ed. Engl. 37 (1998) 2211.

[56] M.W. Wong, Chem. Phys. Lett. 26 (1996) 391.

[57] I. Bytheway, M.W. Wong, Chem. Phys. Lett. 282 (1998) 219.

[58] J.A. Pople, H.B. Schlegel, R. Krishnan, D.J. Defrees, J.S.

Binkley, M.J. Frisch, R.A. Whiteside, R.F. Hout, W.J. Hehre,

Int. J. Quantum Chem. Symp. 15 (1981) 269.

[59] J.A. Pople, A.P. Scott, M.W. Wong, L. Radom, Isr. J. Chem.

33 (1993) 345.

[60] N.N. Greenwood, A. Earnshaw, Chemistry of the Elements,

Pergamon Press, Oxford, 1984.

[61] K.B. Sharpless, J.M. Townsend, D.R. Williams, J. Am. Chem.

Soc. 94 (1972) 295.

[62] M.Z. Hernandes, Thesis, Universidade Federal de Sao Carlos,

Sao Carlos, 1998.

[63] S. Dapprich, G. Frenking, J. Phys. Chem. 99 (1995) 9352.

F.R. Sensato et al. / Journal of Molecular Structure (Theochem) 589–590 (2002) 251–264264