Download Comparison for Bonding Situation between Tetrylone and Tetrylene

Canadian Chemical Transactions
Research Article
Year 2016 | Volume 4 | Issue 2 | Page 143-156
DOI:10.13179/canchemtrans.2016.04.02.0274
Comparison for Bonding Situation between Tetrylone and
Tetrylene Ligands of Tungsten Tetracarbonyl Complexes: A
Theoretical Study
Ai Nhung T. Nguyen1,*, Phuong Loan T. Huynh1, and Tan Hiep Dang2
1
Department of Chemistry, Hue University of Sciences, Hue University, Hue City, Vietnam
2
HCMC University of Food Industry, Tan Phu, Ho Chi Minh City, Vietnam
*Corresponding Author, Email: [email protected]
Received: January 10, 2016
Revised: February 29, 2016
Accepted: March 1, 2016
Published: March 3, 2016
Abstract: Quantum chemical calculations at the gradient-corrected (BP86) density functional
calculations with SVP, TZVPP, TZ2P+ basis sets were carried out for complexes of carbodiphosphoraneanalogues (called tetrylones) [(CO)4W-{E(PH3)2}] (W4-EP2) and N-heterocyclic carbene-analogues
(called tetrylenes) [(CO)4W-{NHEMe}] (W4-NHE) when E = C to Pb. The bond dissociations energies
(BDEs) calculated for the W-E bonds in W4-EP2 and W4-NHE systems considering dispersion
interactions showed that the effect of bulky ligands E(PH3)2 and NHEMe influenced of the intrinsic W-E
bond strength. The EDA-NOCV results suggested that the E(PH3)2 ligands in W4-EP2 are strong donors and weak -donors and the NHEMe ligands in W4-NHE were strong -donors and weak πacceptors. NOCV pairs were used in a description of the chemical bond between the W(CO) 4 fragment
and the ligands (E(PH3)2 and NHEMe) in the transition-metal complexes in which the NOCV pairs led to
very valuable description of the bonding situation of the donor-acceptor fragments in the complexes.
Keywords: Density Functional Calculation; Energy Decomposition Analysis (EDA); Natural Orbital for
Chemical Valence (NOCV), Tetrylones; Tetrylenes.
1. INTRODUCTION
Recently studies concerned with carbodiphosphorane-analogues (called tetrylones) have become
a flourishing research [1-14] in which tetrylones (carbones, silylones, germylones, stannylones,
plumbylones) EL2 possess two lone pairs at E central atom (E = C to Pb). The different E(0) compounds
EL2 have recently been theoretically investigated by Frenking et al. [1-12]. The first stable silylones and
germylones became isolated by Roesky et al. [15] and Driess et al. [16, 17]. Comparison with tetrylones,
the tetrylenes (ER2) (carbenes, silylenes, germylenes, stannylenes, plumbylenes) possess only one
electron lone pair at E central atom and have two electron-sharing bonds (ER) to E atom [1, 3, 18-21].
The different electronic structures of tetrylones compared with tetrylenes were revealed by charge- and
energy decomposition analyses and they became obvious experimentally by a distinctively different
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chemical reactivity [1, 3]. In addition, tetrylones and tetrylene compounds had a strong -donation
capacity towards Lewis acids [1, 3-5, 20, 21]. It has been noted that transition metal complexes with
carbene ligands [22-28] and heavier homologues where E = Si to Pb have been studied extensively in
recent past [29-34] since carbene ligands were found to be excellent catalysts in various chemical
reactions [35-41]. It has been proposed that carbodiphosphoranes may even be better ligand than carbene
for Grubb‟s catalysts [42], but little is known experimentally about the catalytic properties of transition
metal complexes carrying carbodiphosphoranes ligand [43]. In this paper, we wanted to focus on a
comparison for bond dissociation energy (BDEs) with and without dispersion interaction between
tetrylone complexes [(CO)4W-{E(PH3)2}] and tetrylene complexes [(CO)4W-{NHEMe}] (E = C to Pb)
(Scheme 1). Furthermore, the electronic structures would be analyzed using energy-partitioning method.
We also wanted to draw a thorough picture of electronic structures and natural of chemical bonding of the
free ligands E(PH3)2 and NHEMe as donor fragments and W(CO)4 as acceptor fragments using energy
decomposition analysis (EDA) with natural orbital for chemical valence (NOCV).
a)
c)
b)
E
C
Si
Ge
Sn
Pb
Complex
W4-CP2
W4-SiP2
W4-GeP2
W4-SnP2
W4-PbP2
Fragment
CP2
SiP2
GeP2
SnP2
PbP2
C
Si
Ge
Sn
Pb
W4-NHC
W4-NHSi
W4-NHGe
W4-NHSn
W4-NHPb
NHC
NHSi
NHGe
NHSn
NHPb
d)
Scheme 1: Overview of the complexes (a and c) and the ligands (b and d) investigated in this work
2. COMPUTATIONAL METHODS
We firstly optimized the molecules without symmetry constraints using Gaussian 03 [44] optimizer
together with Turbomole 6.0.1 [45] energies and gradients at the BP86 [46,47] /def2-SVP [48] level of
theory. Vibrational frequencies have also been calculated at the same level of theory to confirm the
minima on the potential energy surface of structures. For the heavier group-14 atoms Sn, Pb and transition
metal atom W, small-core quasi-relativistic effective core potentials (ECPs) were used [49, 50]. The level
BP86/def2-TZVPP [51] //BP86/def2-SVP was used for the calculation of the bond dissociation energies
using the NBO 3.1 program [52]. The effect of dispersion interaction on the calculated bond dissociation
energies has been estimated with the D3 dispersion correction that was suggested by Grimme [53].
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The EDA-NOCV [54,55] method was used to calculate the bond dissociation energy, De, which
was divided into the instantaneous interaction energy ΔEint and the preparation energy ΔEprep. The bond
dissociation energy was one measure of the strength in a chemical bond with:
ΔE (= -De) = ΔEint + ΔEprep
(1)
The preparation energy ΔEprep was required to promote the acceptor fragment W(CO)4 and donor
fragments E(PH3)2 and NHEMe from their equilibrium geometries in the electronic ground state to the
geometries and electronic reference state. The interaction energy ΔEint could be further divided into three
main components:
ΔEint = ΔEelstat + ΔEPauli + ΔEorb
(2)
where Eelstat was the quasiclassical electrostatic interaction energy between the fragments, calculated by
means of the frozen electron density distribution of the fragments in the geometry of the molecules.
EPauli refer to the repulsive interactions between the fragments, which were caused by the fact that two
electrons with the same spin could not occupy the same region in space, and could be calculated by
enforcing the Kohn-Sham determinant on the superimposed fragments to obey the Pauli principle by antisymmetrisation and renormalisation. The stabilising orbital interaction term Eorb was calculated in the
final step of the energy partitioning analysis when the Kohn–Sham orbital relaxed to their optimal form.
The EDA-NOCV method combined charge (NOCV) and energy (EDA) partitioning schemes to
decompose the deformation density which was associated with the bond formation, Δρ, into different
components of the chemical bond. NOCV [55,56] was defined as the eigenvector of the valence operator,
, given by Equation (3):
 ψi = υ ψi
(3)
In the EDA-NOCV scheme the orbital interaction term, ΔEorb, was given by Equation (4):
N /2
E orb 
 E
k 1
N /2
orb
k

 F
k
k 1
TS
 k, k
TS
 Fk,k

(4)
in which FTS-k,-k and FTSk,k were diagonal transition-state Kohn–Sham matrix elements corresponding to
orb
NOCVs
 with the eigenvalues –υk and υk, respectively. The Ek term of a particular type of bond were
assigned by visual inspection of the shape of the deformation density, Δρk. The EDA-NOCV scheme thus
provided information about the strength of orbital interactions in terms of both, charge (Δρorb) and energy
contributions (∆Eorb) in chemical bonds, even in molecules without symmetry.
In this study, all complexes were optimized for the energy decomposition analysis (EDA) with the
program package ADF 2009.01 [57, 58] with BP86 in conjunction with a triple-ζ-quality basis set using
uncontracted Slater-type orbitals (STOs) augmented by two sets of polarization function, with a frozencore approximation for the core electrons [59]. An auxiliary set of s, p, d, f, and g STOs were used to fit
the molecular densities and to represent the Coulomb and exchange potentials accurately in each SCF
cycle [60]. Scalar relativistic effects were incorporated by applying the zeroth-order regular
approximation (ZORA) [61, 62]. The level BP86/TZ2P+ was used for the bonding analyses in term of the
EDA [57]-NOCV [55, 56] method of C1 symmetric geometries.
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3. RESULTS AND DISCUSSION
3.1. Bond dissociation energies with and without dispersion interactions
At first, we wanted to concentrate on the calculations for the bond dissociation energies (BDEs) of
the tetrylones W4-EP2 and tetrylenes W4-NHE complexes with E = C to Pb. The fact was that we found
the same trend in structures of W(CO)4-E(PH3)2 (W4-EP2) complexes compared with the more bulky
ligands W(CO)4-E(PPh3)2 [2]. However, a different trend of theoretically predicted BDEs was found for
the complexes W4-CP2 to W4-PbP2. Table 1 shows that the BDEs of the carbone complex exhibited the
strongest W-C bond (54.1 kcal/mol) and decreased from W4-CP2 (De = 54.1 kcal/mol) to W4-GeP2 (De
= 46.1 kcal/mol) and then slightly increased from W4-GeP2 to W4-PbP2 (De = 48.5 kcal/mol). From
this, we can affirm that the trend of BDEs in tetrylone complexes W4-EP2 decreased from the lighter to
the heavier homologues accepted for a stronger donor with the trend Ge < Sn < Pb [1, 2]. In contrast, the
calculated BDEs values of W4-NHE exhibited the strongest bond W-C in carbene complex W4-NHC
(De = 55.7 kcal/mol) and significantly decreased from W4-NHC to W4-NHPb (De = 26.3 kcal/mol) with
the order was W4-NHC > W4-NHSi > W4-NHGe > W4-NHSn > W4-NHPb.
Table 1. Calculated metal-ligand bond dissociation energies, De (kcal/mol), at the BP86/def2TZVPP//BP86/def2-SVP level.
Molecule
De (kcal/mol)
W4-CP2
54.1
W4-SiP2
50.1
W4-GeP2
46.1
W4-SnP2
47.6
W4-PbP2
48.5
W4-NHC
55.7
W4-NHSi
44.5
W4-NHGe
36.5
W4-NHSn
29.7
W4-NHPb
26.3
It has been pointed out that dispersion interactions might have an influence on the theoretically
predicted BDEs [1, 53]. We also calculated the BDEs considering dispersion correction using the DFT
dispersion interaction. The complexes W4-EP2 and W4-NHE had to be considered for dispersion
interaction to affirm that these interactions might have an influence on the calculated results, especially on
the theoretically predicted BDEs. The effect of dispersion interaction on the calculated BDEs has been
estimated with the DFT-D3 dispersion correction that was suggested by Grimme [53]. Figure 1 shows the
calculated BDEs, De (kcal/mol), with and without corrections for dispersion interactions for two systems
W4-EP2 and W4-NHE, which have been calculated at the BP86/TZVPP-De (the black line) level and
BP86/TZVPP-D3 (the red line) level using BP86/SVP-optimized geometries. Firstly, we wanted to
mention about the tetrylene complexes with the calculated BDEs for the complexes W4-NHE became
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E (kcal/mol)
Year 2016 | Volume 4 | Issue 2 | Page 143-156
W4-EP2
W4-NHE
E = 11.7
E = 14.4
E = 13.5
E = 11.1
60
E = 9.7
50
E = 13.8
E = 8.9
E = 14.3
40
DFT-D3
E = 8.3
30
E = 11.2
1
C
2
Si
3 Sn
4
5
Pb
Ge
--
1'
C
2'
Si
3' Sn
4'
Ge
DFT-De
5'
Pb
Figure 1. Calculated bond dissociation energies, De (kcal/mol), with and without corrections for
dispersion interactions for W4-EP2 and W4-NHE (E = C to Pb) at the BP86/def2 TZVPP//BP86/def2SVP level.
uniformly larger for E = Si to Sn by about 9 kcal/mol when dispersion interactions were considered. The
largest dispersion correction value 11.2 kcal/mol was calculated for W4-NHPb, which was caused by the
strongly side-on-bonded ligand [2, 20]. Note that the strongly attractive force between the NHCMe
substituents and the W(CO)4 fragment when the W-C bond exhibited the shortest bond length giving the
same value of dispersion correction (11.1 kcal/mol) in the complex W4-NHC compared with the W4NHPb adduct. Although the W-E bonds became longer for the heavier systems, but the pair coefficients
employed for calculating the strength of the dispersion interactions became larger when the atoms became
heavier [1,53].
The calculated De (kcal/mol) values for W4-EP2 showed that the dispersion interactions were
slightly larger than those in W4-NHE. This can be explained that the E(PH3)2 fragment did not have
much more bulky substituent than the NHEMe moiety. The increase in the BDEs of the W-E bonds of W4EP2 when dispersion interactions were considered came from the attractive forces between the PH3
substituent and the W(CO)4 fragment, which were not related to the intrinsic W-E bond strength. The
dispersion correction for W4-EP2 stayed nearly the same from the lighter W4-SiP2 (14.4 kcal/mol) to the
heavier homologues W4-PbP2 (14.3 kcal/mol) except for the smallest value in W4-CP2 (11.7 kcal/mol).
This is because the W-E bonds were longer for heavier atoms E, this led to longer distances between the
PH3 substituent and the W(CO)4 fragment and the E(PH3)2 fragment had less bulky substituent compared
with the E(PPh3)2 moiety [1] which exhibited the different trend for BDEs when considering dispersion
interactions. The calculated data suggested that it was useful to consider dispersion interactions separately
from energies which came from covalent bonding [1, 53]. Thus, it could be asserted that the calculated
BDEs of complexes with the inclusion of dispersion interactions confirmed the conclusion that the W-E
bonds of the tetrylene ligands became weaker for the heavier homologues.
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3.2. Analysis of the bonding situation
The nature of the W-E bond was analyzed using EDA-NOCV calculations to further explain the
chemical bonding of tetrylones-W(CO)4 and tetrylenes-W(CO)4. Firstly, we considered the tetrylone
complexes W4-EP2 which the molecules were divided into the fragments E(PH3)2 and W(CO)4, and both
were in the singlet state. Table 2 shows the EDA-NOCV results for the (CO)4W-tetrylone bonds. The
preparation energies Eprep changed very little between 4.2 and 5.6 kcal/mol in W4-SiP2 and W4-CP2.
The Pauli repulsion ∆EPauli gave the largest value (146.3 kcal/mol) for W4-CP2 and decreased for the
heavier homologues. This is because the decrease in bond strength came from the π interaction. From this
it may follows that the decrease in bond strength from the lighter to the heavier species came from
stronger attraction rather than weaker repulsion [1, 2]. The electrostatic term ∆Eelstat decreased from 141.9 kcal/mol for W4-CP2 to -114.5 kcal/mol for W4-PbP2 and remained almost constant in the
heavier homologues which are -114.9 kcal/mol for W4-SiP2, -108.0 kcal/mol for W4-GeP2, and -112.6
kcal/mol for W4-SnP2. The same trend was shown for the orbital interactions, which exhibited the
decrease in the orbital interactions from -67.4 kcal/mol for W4-CP2 to -62.9 kcal/mol for W4-PbP2.
Thus, the decrease in bond strength in W4-EP2 correlated with the decrease of Eelstat and Eorb.
Table 2. EDA-NOCV results at the BP86/TZ2P+ level for compound W4-CP2 to W4-PbP2 using the
moieties [W(CO)4] and [E(PH3)2] (E = C to Pb) as interacting fragments. The complexes are analyzed
with C1 symmetry. Energy values in kcal/mol.
Compound
W4-SnP2
W4-PbP2
W(CO)4
W(CO)4
Fragment
Sn(PH3)2
Pb(PH3)2
-54.6
-55.5
Eint
120.4
121.9
EPauli
[a]
-112.6 (64.4 %) -114.5 (64.5 %)
Eelstat
[a]
-62.4 (35.6 %)
-62.9 (35.5 %)
Eorb
[b]
-49.8 (79.8 %)
-51.4 (81.7 %)
Eσ
[b]
-10.5
(16.8
%)
-9.5 (15.1 %)
Eπ
[b]
-2.1 (3.4 %)
-2.0 (3.2 %)
Erest
4.7
4.8
Eprep
[c]
-49.9 (-47.6)
-50.7 (-48.5)[c]
E (= -De)
[a]
The values in parentheses are the percentage contributions to the total attractive interaction Eelstat + Eorb.
[b]
The values in parentheses are the percentage contributions to the total orbital interaction Eorb.
[c]
W4-CP2
W(CO)4
C(PH3)2
-63.0
146.3
-141.9 (67.8 %)
-67.4 (32.2 %)
-42.9 (63.6 %)
-21.8 (32.3 %)
-2.7 (4.1 %)
5.6
-57.4 (-54.1)[c]
W4-SiP2
W(CO)4
Si(PH3)2
-54.7
122.4
-114.9 (64.9 %)
-62.2 (35.1 %)
-43.4 (69.8 %)
-16.8 (27.0 %)
-2.0 (3.2 %)
4.2
-50.5 (-50.1)[c]
W4-GeP2
W(CO)4
Ge(PH3)2
-52.8
112.5
-108.0 (65.3 %)
-57.3 (34.7 %)
-44.4 (77.5 %)
-11.2 (19.5 %)
-1.7 (3.0 %)
4.7
-48.1 (-46.1)[c]
The values in parentheses give the dissociation energy at the BP86/def2-TZVPP//BP86/def2-SVP level.
The ∆Eorb term of the EDA-NOCV results was considered to obtain more detailed information
about the nature of the bonding in the W4-CP2 to W4-PbP2 complexes. The plots of the pairs of orbitals
Ψk/Ψ-k that yield the NOCVs providing the largest contributions to the - and -orbital terms E and E
in W4-EP2 (E = C, Si) and the associated deformation densities  and stabilization energies were shown
in Figure 2. The shape of orbital pairs in W4-CP2 exhibited the head-on mode between C(PH3)2 and
W(CO)4, whereas the heavier homologues E(PH3)2 bind to W(CO)4 in W4-EP2 (E = Si to Pb) in side-on
modes.
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Ψ-1 = -0.57
W4-CP2 (σ)
Ψ1 = 0.57
∆ρ1 (∆E = -32.9) (a)
Ψ-1 = -0.70
W4-SiP2 (σ)
Ψ1 = 0.70
∆ρ1 (∆E = -39.2) (d)
Ψ-2 = -0.40
W4-CP2 (π)
Ψ2 = 0.40
∆ρ2 (∆E = -11.6) (b)
Ψ-2 = -0.36
W4-SiP2 (π)
Ψ2 = 0.36
∆ρ2 (∆E = -7.5) (e)
Ψ-3 = -0.35
W4-CP2 (π)
Ψ3 = 0.35
∆ρ3 (∆E = -7.3) (c)
Ψ-3 = -0.28
W4-SiP2 (π)
Ψ3 = 0.28
∆ρ3 (∆E = -7.5) (f)
Figure 2. Most important NOCV pairs of orbitals Ψ-k, Ψk with their eigenvalues -υk, υk given in
parentheses, and the associated deformation densities ∆ρk and orbital stabilization energies ∆E for the
complexes W4-CP2 and W4-SiP2. The charge flow in the deformation densities is from the yellow →
blue region. (a) -NOCV of W4-CP2; (b), (c) π-NOCVs of W4-CP2; (d) -NOCV W4-SiP2; (e), (f) πNOCVs of W4-SiP2. Energy values in kcal/mol.
This gave a good agreement with the optimized structures of investigated complexes [2] which are not
shown in this study. The homologues W4-GeP2 to W4-PbP2 exhibited similar shapes compared with
W4-SiP2 and therefore, they were not shown in Figure 2. Note that the green/red colors in the figures for
Ψk/Ψ-k indicated the sign of the orbitals, and the yellow/blue colors in the deformation density 
designated charge depletion, and the blue areas pointed to charge accumulation. The charge flow 
occurs in the direction from yellow to blue. Figure 2a and 2d gave the NOCV pairs Ψ1/Ψ-1 and the
deformation densities ∆ρ1 of the most important pairs of  orbitals for ∆Eσ of W4-CP2 and W4-SiP2. The
shape of the orbital pairs clearly indicated that the -orbital interactions took place between the donor
orbitals of the ligands CP2 and SiP2, which were mainly localized at the divalent carbon(0) or silicon(0)
atom, and the acceptor orbital of W(CO)4. Note that the NOCV pairs were analyzed in the tetrylone
complexes W4-EP2 because the ligands E(PH3)2 were double donors and the W atom of W(CO)4 needed
4 electrons to get 18 electrons in the metal complex, thus, there should be no significant contribution from
(CO)4W→E(PH3)2 π back-donation. Figure 2b and 2c shows two NOCV pairs Ψk/Ψ−k (k = 2 to 3) that
dominate the total stabilization ∆Eπ in W4-CP2. The shape of the NOCV pairs Ψ2/Ψ-2 and Ψ3/Ψ-3, and
particularly the deformation densities ∆ρ2 and ∆ρ3, reveal that the associated energy stabilization came
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mainly from π donation with some extent of relaxation. The NOCV pairs Ψ2/Ψ-2 and Ψ3/Ψ-3, and the
deformation densities ∆ρ2 and ∆ρ3 clearly showed that the large stabilization of -11.6 and -7.3 kcal/mol
came from (CO)4W←C(PH3)2 π donation. From this it follows that donation of the carbon π lone pair to
the acceptor fragment W(CO)4 was significant. We found that the structure in shape of W4-SiP2
exhibited the tetrylone ligands Si(PH3)2 bind to W(CO)4 mainly through the π density. Thus, inspection of
the shape of the orbitals of W4-SiP2 made it possible to identify the NOCV pairs Ψ2/Ψ-2, and Ψ3/Ψ-3 as πtype orbitals. Figure 2e and 2f shows plots of the orbital pairs, charge flows, and associated stabilization
energies. The shapes of charge flow ∆ρ2 and ∆ρ3 could be assigned to (CO)4W→Si(PH3)2 π-backdonation
where the Si-P vacant antibonding orbital serves as an acceptor, but the contribution of π-backdonation to
Si-P bond was not appreciable.
Table 3. EDA-NOCV results at the BP86/TZ2P+ level for compound W4-NHC to W4-NHPb using the
moieties [W(CO)4] and [NHEMe] (E = C to Pb) as interacting fragments. The complexes are analyzed with
C1 symmetry. Energy values in kcal/mol.
Compound W4-NHC
W4-NHSi
W4-NHGe
W4-NHSn
W4-NHPb
W(CO)4
W(CO)4
W(CO)4
W(CO)4
W(CO)4
Fragment
NHCMe
NHSiMe
NHGeMe
NHSnMe
NHPbMe
-31.9
-59.6
-48.4
-38.6
-33.3
Eint
55.0
127.2
101.7
85.4
68.1
EPauli
[a]
-132.3 (70.8%) -92.7 (61.8%) -73.0 (58.8%) -55.9 (55.1%) -46.2 (53.1%)
Eelstat
[a]
-54.5 (29.2%) -57.4 (38.2%) -51.1 (41.2%) -45.6 (44.9%) -40.7 (46.9%)
Eorb
[b]
-37.6 (69.0%) -35.2 (61.3%) -30.6 (59.9%) -27.7 (60.7%) -32.2 (79.1%)
Eσ
[b]
-13.6 (25.0%) -20.2 (35.2%) -18.9 (37.0%) -16.9 (37.1%) -6.7 (16.5%)
Eπ
[b]
-3.3 (6.0%)
-2.0 (3.5%)
-1.6 (3.1%)
1.0 (2.2%)
-1.8 (4.4%)
Erest
4.7
4.9
2.9
2.4
2.1
Eprep
[c]
[c]
[c]
[c]
-27.2 (-26.3)[c]
-45.5 (-44.5)
-36.2 (-36.5)
-31.2 (-29.7)
E (= -De) -54.7 (-55.7)
[a]
The values in parentheses are the percentage contributions to the total attractive interaction Eelstat + Eorb.
[b]
The values in parentheses are the percentage contributions to the total orbital interaction Eorb.
[c]
The values in parentheses give the dissociation energy at the BP86/def2-TZVPP//BP86/def2-SVP level.
The results of EDA-NOCV calculations for the W4-NHE complexes were shown in Table 3. Like
the W4-EP2 system, the preparation energies ∆Eprep varied very little between 2.1 kcal/mol for W4NHSn and 4.9 kcal/mol for W4-NHC. The BDEs of W4-NHE significantly decreased with the order is:
W4-NHC > W4-NHSi > W4-NHGe > W4-NHSn > W4-NHPb. The decrease of the BDEs from the
lighter to heavier adduct was determined by the intrinsic strength of the metal-ligand bonds ∆Eint. Table 3
also shows that the Pauli repulsion ∆EPauli had the largest value of 127.2 kcal/mol for W4-NHC and got
smaller from E = C to E = Pb (55.0 kcal/mol), which meant the decrease in bond strength came from the
weaker attractive interactions. In addition, the electrostatic term ∆Eelstat continuously decreased from the
W4-NHC (-132.3 kcal/mol) to W4-NHSi (-92.7 kcal/mol), and W4-NHGe (-73.0 kcal/mol), and it
became weakest in W4-NHPb (-46.2 kcal/mol). However, the orbital term ∆Eorb decreased from W4NHC (-54.5 kcal/mol) to the W4-NHPb (-40.7 kcal/mol) except for the slightly increase from W4-NHC
to W4-NHSi (-57.4 kcal/mol).
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Ψ-1 = -0.52
W4-NHC (σ)
∆ρ1 (∆E = -32.2) (a)
Ψ1 = 0.52
Ψ-1 = -0.71
Ψ-2 = -0.36
W4-NHC (π)
Ψ2 = 0.36
∆ρ2 (∆E = -8.8) (b)
Ψ-2 = -0.25
Ψ-3 = -0.21
W4-NHC (σ)
Ψ3 = 0.21
∆ρ3 (∆E = -5.4) (c)
Ψ-3 = -0.20
W4-NHPb (σ)
Ψ1 = 0.71
∆ρ1 (∆E = -31.8) (d)
W4-NHPb (π)
Ψ3= 0.25
∆ρ2 (∆E = -2.8) (e)
W4-NHPb (π)
Ψ3 = 0.20
∆ρ3 (∆E = -2.2) (f)
Figure 3. Most important NOCV pairs of orbitals Ψ-k, Ψk with their eigenvalues -υk, υk given in
parentheses, and the associated deformation densities ∆ρk and orbital stabilization energies ∆E for the
complexes W4-NHC and W4-NHPb. The charge flow in the deformation densities is from the
yellow→blue region. (a), (c) σ-NOCVs of W4-NHC; (b) π-NOCV of W4-NHC; (d) σ-NOCV W4NHPb; (e), (f) π-NOCVs of W4-NHPb. Energy values in kcal/mol.
We realized that the slightly decrease of bond strength from W4-CP2 to W4-PbP2 correlated with
the slightly decrease of the electrostatic term Eelstat and the orbital interactions Eorb. In contrast, the
trend of bond strength from W4-NHC to W4-NHPb came from the significantly decrease of Eelsta and
Eorb. The NOCV pairs of W4-NHE were considered like the tetrylone complexes. The plots of the pairs
of orbital Ψk/Ψk that yield the NOCVs providing the largest contributions to the σ- and π-orbital terms ∆Eσ
and ∆Eπ in W4-NHE (E = C, Pb) and the associated deformation densities ∆ρ and stabilization energies
were shown in Figure 3. The homologues W4-NHE (E = Si to Sn) exhibited similar shapes compared
with the lighter homologue W4-NHC and therefore, they were not shown in Figure 3. The shape of the
NOCV pairs Ψ1/Ψ-1 and the deformation density ∆ρ1 of W4-NHC exhibited typical features for
(CO)4W←NHEMe  donation. Figure 3a shows that the -type interaction was clearly from the donating
NHCMe fragment to the accepting W(CO)4 fragment while the NOCV pairs Ψ3/Ψ-3 and the deformation
density ∆ρ3 of W4-NHC exhibited the small stabilization of -5.4 kcal/mol came from (CO)4W←NHEMe 
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donation (Figure 3c). The NOCV pair Ψ2/Ψ-2 and the deformation density ∆ρ2 clearly showed that the
stabilization of -8.8 kcal/mol came from (CO)4W←NHCMe π-backdonation (Figure 3b). It followed that
donation of the carbon π lone pair to the tungsten tetracarbonyl was very weak. Figure 3d, 3e, and 3f
show significantly different EDA-NOCV results for W4-NHPb because of the surprising structure of the
plumbylene ligand, which was bonded through its π-electron density. Figure 3d clearly shows that the σtype interaction had the direction of the charge flow of (CO) 4W←NHPbMe. In this case, the significantly
different binding mode of the NHPbMe ligand exhibits strange NOCV pairs compared with the lighter
homologues. The deformation density ∆ρ1 exhibited a small area of charge donation (yellow area) at the
W(CO)4 moiety associated with the deformation density ∆ρ1 and a stabilization energy of -31.8 kcal/mol.
Figure 3e and 3f show that the very weak π-type orbital interactions in W4-NHPb came from typical πdonation (CO)4W←NHPbMe and the relaxation of the W(CO)4 fragment in which the shape of the charge
flow Ψ2/Ψ-2 and Ψ3/Ψ-3 indicated stabilization of -2.8 and -2.2 kcal/mol.
4. CONCLUSIONS
The calculated BDEs for the W-E bond in W4-EP2 and W4-NHE systems considering dispersion
interactions showed that the effect of bulky ligands E(PH3)2 and NHEMe influenced of the intrinsic W-E
bond strength. The EDA-NOCV results suggested that the BDEs trend in W4-EP2 came from the
increase in (CO)4W←E(PH3)2 donation and strong electrostatic attraction. The ligands E(PH3)2 in W4EP2 were strong -donors and very weak π-donors while the NHEMe ligands in W4-NHE were strong donors and weak π-acceptors. The results showed that the set of orbitals applied in the two fragments in
complexes allowed for a separation and quantitative assessment of the contributions to the deformation
density of donation from ligand  metal to back-donation ligand  metal electron transfer processes.
The EDA-NOCV method was especially useful in a description of bonding situation in transition metal
complexes.
ACKNOWLEDGEMENTS
This research is funded by Vietnam National Foundation for Science and Technology Development
(NAFOSTED) under grant number 104.06-2014.13 (Nguyen Thi Ai Nhung). The jobs of this study were
run via Erwin cluster which is an excellent service provided by the Hochschulrechenzentrum of the
Philipps-Universität Marburg-Germany. NTAN thanks Prof. Dr. Gernot Frenking for allowing
continuously to use her own computer accounts at Frenking‟s group. Further computer time provided by
the HLRS Stuttgart, the HHLRZ Darmstadt, and the CSC Frankfurt is also acknowledged.
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