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The role of valence interaction in some cation-molecule complexes
Journal of Molecular Structure (Theochem), 301(1994) 99- 105 0166-1280/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved
99
The role of valence interaction in some cation-molecule complexes PK. Nandi, A.B. Sannigrahi* Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India (Received 25 August 1993; accepted 19 September 1993) Abstract The role of valence interaction in the 1 : 1 and 1 : 2 complexes between Li+, Na+, Be*+, Mg*+ and CO and N2 was qualitatively assessed using charge-density-related quantities such as charge transfer, the bond index of the cation-donor atom bond, the valency of interaction and the change in molecular valency calculated at the HF/63 lG*//3-21G level. It has been observed that the relative stability of the complexes can be rationalised on the basis of valence interaction. The molecular hardness parameters have also been calculated. The maximum hardness principle is found to be satisfied in the case of (MCO)“+-(MOC)“+ pairs, and the interaction between (MXY)“+ and XY follows the qualitative prediction from the HSAB principle, where M ‘+ is the metal ion and XY is the base.
Introduction In view of its importance in a wide variety of fields such as molecular spectroscopy, surface and colloid chemistry, molecular biology, thermodynamics, molecular beam experiments and polymer science, the study of intermolecular interactions has been a very active area of research [l-5] over the past two decades or so. The interaction between two closed-shell species is of special interest, particularly from the viewpoint of chemical bonding, because the energy of such interactions varies over a very wide range - from a few tenths of a kilocalorie per mole (in a typical van der Waals complex) to a few hundreds of kilocalories per mole (in many cation-dipole complexes). Several attempts have been made [6-151 to understand the origin of intermolecular interaction by decomposing the interaction energy into various components. Although there is no unique scheme * Corresponding
author.
SSDZ0166-1280(93)03576-S
of decomposition, it is generally recognised that the stability of an intermolecular complex stems from electrostatic (ES), polarisation (PL), exchange repulsion (EX), charge transfer (CT) and dispersion interactions. With the exception of the last, contributions from all other components can be estimated at the Hartree-Fock (HF) level as has been done in the Kitaura-Morokuma (KM) scheme [6]. The KM scheme has been applied [16-211 to a number of intermolecular interactions. Inclusion of electron correlation is essential to account for the dispersion interaction. The latter contribution can also be estimated using London’s equation [22]. For a given cation the strength of an ionmolecule interaction generally increases with increasing polarity of the molecule. In such complexes the ES interaction predominates over other components. The non-electrostatic or valence and dispersion interactions are, however, expected to play an increasingly important role with decreasing polarity of the molecule. The aim of the present
P.K. Nandi and A.B. SannigrahijJ. Mol. Struct. (Theochem)
100
study was to assess qualitatively the role of valence interaction in the stability of some cation-molecule complexes. We selected four cations (Li+, Naf, Be2+ and Mg2+) and one non-polar (N,) and one extremely weakly polar molecule (CO) and studied the nature of their interaction in terms of charge transfer, bond index and valency, as obtained from HF wavefunctions. In this context a new index of covalent bonding between the interacting species, namely, the valency of interaction, has been proposed and successfully applied. A number of ab initio quantum mechanical calculations [2336] have been reported on these systems. As any ion-molecule interaction falls in the broad category of an acid-base interaction, we also calculated the hardness parameters for all the species, with the objective of testing the HSAB principle [37,38] and the maximum hardness (MH) principle [39,40]. Of late there has been an upsurge of interest in this field and numerical calculations [41-471 in support of these principles have started to appear.
Method of calculation
All the species considered here are closedshell systems for which the atomic charge (qA), bond index (I,& and valency (V,) are given by [48]:
qA =
IAB =
zA
-
2 B
VA =
c
&p’%a a
~(p’%b(ps)ba b
(1)
(2)
IAB
B#A
where ZA is the atomic number of A, P = 2Cc (where C is the coefficient matrix of the doubly occupied MOs) and S is the A0 overlap matrix. of interaction between two The valency monomers R and S in the supermolecule RS is
307 (1994) 99-105
given by: R
T/id =
2
r.
2 A
(4)
IAB B
This quantity has a formal analogy with the group-group bond index defined by Giambiagi et al. [49]. The change in molecular valency [50] is given by: 2
EVA-cVA-eVA A
A
(5)
A
Equation (5) differs from Eq. (4) by a factor of 0.5 and includes all possible bond indices in both the diatomic monomer and the supermolecule. The molecular hardness (n) is calculated using the expression [5 11: rl=
(“LUMO
-
EHOMO)
2
(6)
where E is the orbital energy. All calculations were done at the HF level using the 6-31G* basis set at the 3-21G optimised geometry of the monomers [52] and the complexes [ 16,271. The pertinent geometrical parameters are given in Fig. 1. Results and discussion
The calculated values of the energy (AZ?) of interaction, the bond index (ZMx,y) of the new bond formed between the cation (M”+) and the atom X or Y of the base (XY), the amount of charge transfer (qCT), the valency of interaction (Vi”,) and the change in molecular valency (A VM) in the formation of the ion-molecule complexes are presented in Table 1. All the complexes considered here were predicted [16,27] to have a linear equilibrium structure. The BSSE [53] correction was not included in the calculation of AE because it has been found [54] to be negligibly small (0.1-0.6 kcal mol-i) in several ion-molecule complexes at the HF/6-3 1+G* level. The energy of interaction between metal ions with a molecule of either CO or N2 varies in the
P.K. Nandi and A.B. Sannigrahi/J. Mol. Strut. 1.128
1.083
C-------o 2.!3!3@
2.2¶2.
307 (1994) 99-105
1.116
l.llQ
2.180
1.143
1.187
1.6s3
l.QQ6
l.Qel -I-
1.116
2.Ql3
Fig. 1. Equilibrium
1.081
2.247
2.207
structural parameters
1.081
l.lQQ
1.806 Be-4
1.103
l.QQ3 1.171 MQ-----o----c
1.146 l.Q!B c-i-----o-----c
l.llQ 2.!371 o"----Nn~~c~~----o-----c
1.142
(bond lengths in gngstr8ms) of the monomers
Be2+ > Mg2+ > Li+ > Na’. The charge ionic-radius ratio of the metal ions, i.e. the ionic potential, also varies in the same order, implying that these ion-molecule interactions are essentially electrostatic in nature. There will, however, always be a certain amount of charge transfer upon complex formation. We used this quantity (qCT) along with IMxIy, F’i,t and AV, as indices to assess qualitatively the degree of valence interaction. For the sake of simplicity the total energy of interaction was assumed to be approximately equal to the sum of the contributions from the ES and valence interactions. The interaction between a metal ion and a CO molecule leads to the formation of two possible isomers, (MCO)“+ and (MOC)“+. In analogy to the nomenclature isocyanide, isothiocyanate, etc., we tentatively call the (MOC)“+ species ‘isocarbonyls’. The relative stability of the carbonyl and isocarbonyl isomers depends [16,27] on the level of calculation employed. At the HF level, the formation of (MOC)n+ is favoured (by about 1.O-2.0 kcal mol-‘) over (MCO)“+. This is partly order,
%.Oo!s
LA-
MQ~-----o
0-----c~~--d----Q
Ml-
1.118
Na-
Be-
2.0453 1.083
1.835
2.321
Na-----o------c
Bed----c
101
L~-----o-----c
L~----c-----o
N+
w-----c----o 1.518
(Theochem)
2.lQL
and complexes.
due to the orientation of the CO dipole (C6+O”-) with regard to the cation which facilitates ES interaction. It may be noted that in (MOC)“+ A Vhl is generally negative and the CO bond is somewhat stretched with respect to that in an isolated CO molecule (Fig. 1). Thus the higher stability of the isocarbonyls at the HF level should be due to stronger ES interaction. In contrast, as indicated by the qCT, ZMXIY, L’i”t and AJfM values the valence interaction is far more pronounced in the carbonyl isomers. It has been observed by Sannigrahi et al. [54] in a different context that inclusion of electron correlation enhances qtr. The vector direction (C6-06+) of the dipole moment of CO is also reproduced correctly [52] when configuration interaction calculations are carried out including the singly excited configurations. Thus at the correlated level (MCO)“+ should be more stable than (MOC)“+, which is in agreement with the results of ab initio MP3 calculations [16]. To summarise, at the HF level the valence interaction is stronger and the ES interaction is weaker in the carbonyls. The reverse
102
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307 (1994) 99-105
Table 1 Calculated interaction energies (AE), bond indices (I ~x,v),
amount of charge transfer (PC.). valency of interaction (Vi,t) and
change in molecular valency (A V,) -AE
Species
qCT
V,nt
AVM
(kcalmol-‘) Li+ . ..co Li+ OC
14.5 15.6 12.0
0.307 0.114
0.177 0.077
0.326 0.153
0.459 -0.071
0.111
9.4 10.3
0.206 0.076
0.065 0.117
0.128 0.226
0.028 0.315
0.059
0.115
7.3
0.054
Be’+ . . CO Be’+ . . OC Be’+ . N Mg2+ . ..&
93.2 95.9
0.194 0.772
0.037 0.562
0.072 0.818
0.134 1.056
85.1 60.3
0.172 0.565
0.512 0.526
0.854 0.810
0.194 0.489
0.361
Mg2+ . ..oc Mg2+ . . N2
62.3
0.219
0.598 0.268
0.781 -0.178
OC . . . (LiCO)+
54.7 13.9
0.213 0.348
CC.
28.4 14.8 30.4 11.5 23.5
Li+
. . . N2
Na+...CO Na+ . ..oc Na+ . N2
Li+ . . CO
CO. CO.
. (LiOC)+
. . Li+ . . OC N2 . ( LiN2)+ N2 . . . Li+ N2 OC .
(NaCO)+
OC...Na+...CO CO. . . (NaOC)+ CO...Na+...OC N2 N2
. . . (NaN2)+ Na+ . . N2 OC . . (BeCO)*+
CC.
. Be’+ .
CO
9.2 18.7 10.0 20.3 6.1 14.0 11.5
0.240
0.278
0.348
0.204 0.408
0.367 0.734
0.498 0.957
0.110 0.110
0.079 0.158
0.183 0.183
0.108 0.215
0.158 0.316 0.207
-0.025 -0.096 0.298
0.120 0.239
0.412 0.229
0.506
0.209 0.209 0.073 0.073 0.066 0.066 0.124 0.724
CO.. . (BeOC)‘+ C0...Be2+...0C
170.7 18.5 174.4
N2.. (B;+N2)‘+ N2 . . . Be . . . N2
71.3 156.5
0.703 0.703
(M&O)‘+ Mg2+ . . CO
39.5 99.8
(MgOC)2+ . Mg2’ . OC
62.3 103.7
OC OC
CO.. CO.
.
N2.. . (MgN2)2+ N2 . ..Mg2+...N2
34.5 89.1
0.137 0.124
-0.054
0.059 0.119 0.045 0.089 0.496 0.993 0.465 0.931
0.459 0.117
0.301 0.616 -0.027
0.234 0.087
-0.08 1 0.119
0.174 0.786 1.530
0.253 0.890 1.946 0.227 0.387
0.475
0.796 1.567 0.741
0.583 0.583
0.951 0.387 0.714
1.414 0.621 1.235
0.191 0.191 0.271
0.125 0.249 0.162
0.242 0.484
1.545 0.155 -0.333
0.271
0.325
0.302 0.603
0.333 0.611
0.695 0.695
is true in the isocarbonyls and this accounts for their higher stability. At the correlated level both ES and valence interactions become stronger in the carbonyls than in isocarbonyls as a result of which the former isomers are more stable. We now turn our attention to the relative stability of the (MCO)“+ and (MN2)“+ complexes. In all cases the carbonyls are found to be more stable than their N2 counterparts, and the differ-
0.394 0.883 0.164
ence in their AE valves varies in the order Naf < Lif < Mg2+ < Be2+. Ikuta [16] carried out Morokuma’s energy decomposition analysis in order to rationalise the difference in the binding energy of Li+ and Naf complexes on the one hand and of CO and N2 complexes on the other. He observed that for a given base the stabilisation due to ES, PL and CT interactions is smaller in Na+ due to its higher ionic size. Our calculated
P.K. Nandi and A.B. SannigrahijJ.
Mol. Strut.
(Theochem)
307 (1994) 99-105
values of qcr, Zt,.rx,v, I’i”t and AV, also indicate that valence interaction should be weaker in the Na+ complexes. Thus both ES and valence interactions are stronger in Li+ complexes which account for their higher stability. The energy decomposition analysis of Ikuta does not adequately account for the difference in the binding energy of N2 and CO complexes with a given cation. Moreover, due to the use of a smaller basis set (3-21G) (MN2)+ is wrongly predicted to be more stable than (MCO)+. As higher order terms in the multipole expansion of charge density are more important in the ES interaction between a cation and a neutral molecule, it is not possible to infer from classical considerations whether its contribution will be greater in N2 or in CO complexes. The calculated values of qcr and other related quantities indicate that the valence interaction is far more pronounced in the carbonyls. Therefore it appears that, the stabilisation due to ES being comparable in carbonyls and the dinitrogen complexes, the valence interaction plays a more decisive role in accounting for their relative stability. The binding energy of Be2+ and Mg2+ complexes is considerably higher than that of Li+ or Na+ complexes. The ES interaction could possibly account for this large difference. However, due to the smaller M2+-X/Y distance the CT interaction should be also appreciable in these complexes. This is borne out by our calculated values of qcr and other quantities. The valence interaction is capable of distinguishing between the stability of (MgN2)2+ and (MgCO)*+. However, in the case of Be’+, the valence interaction with CO and N2 is almost equally strong. Therefore the large difference in their AE values should be mainly due to ES interaction. The formation of dicarbonyls, diisocarbonyls and tetranitrogen complexes can be described either by a one-step or a two-step reaction: M”’ + 2XY-(YXMXY)“+
or (XYMYX)“+ (7)
M”+ + XY-(MXY)“+
or (MYX)“+
(8a)
103
(MXY)“+ or (MYX)“+ + XY-(YXMXY)“+ or (XYMYX)“+
(8b) As can be seen from Fig. 1, the linear structure of 1:1 adducts is retained in the 1:2 adducts. At the HF level the stability of the 1:2 adducts is predicted [27] to follow the order OC > CO > N2. The relative stability order of the CO complexes is, however, reverted at the post-HF level. Thus the trend in AE of 1:2 adducts is identical to that in the 1:1 adducts. In the following we confine our attention to dicarbonyls and tetranitrogen complexes. It can be seen from Table 1 that all the three reactions described by reactions (7), (8a) and (8b) are exothermic. As expected, the same value of AE is obtained for reaction (7) and for the sum of reactions (8a) and (8b). In the case of Li+ and Naf, the AE, (JcT and I’i,t of reaction (7) are almost twice the corresponding values associated with reaction (8a). The same is not true for the Be2+ and Mg2+ complexes. Now AE for the onestep process is considerably higher than twice the corresponding value for the first step of the twostep process. However, qcT and I’i,t follow the same trend as in the monocation complexes. Addition of one more molecule of base to the 1:1 adduct decreases AE in all cases and enhances ZMxIy, qm and P’intvalues in all but Be2+ complexes. The AV, values do not follow any pattern in this regard. The decrease in AE is only marginal in the case of Li+ and Na’, but quite substantial in the dication complexes. Thus in the formation of 1:2 adducts from the 1:1 adducts the valence interaction becomes stronger for all the cations except Be2+. Then the decrease in AE must be caused by the ES interaction which is most prominent in the Be2+ complexes. We now consider the acid-base reactions (8a) and (8b) in terms of the hardness parameters (77) summarised in Table 2. All the cations considered here are very hard acids, their hardness varying in the order Be2+ > Li+ > Mg2+ > Na+. In contrast, both CO and N2 are soft bases. According to the HSAB principle, hard prefers hard and soft prefers
104
P.K. Nandi and A.B. Sannigrahi/J. Mol. Struct. (Theochem)
Table 2 Calculated values of hardness parameters
(7)
Species
77 (eV)
Species
17 (eV)
Li+ Be’+
35.3 68.0 10.8
Na+ Mg2+ co
22.1 33.6 9.6
N2
(MgCO)‘+ (BeCO)*+ (NaCO)+ (LiCO)+
1.8 7.9 8.3 8.7
(MgCzO,)*+ (BeC,Os)*+ (NaC,O# (LiC202)+
8.8 8.9 8.7 9.0
(MgOC)*+ (BeOC)*+ (NaOC)’ (LiOC)+
6.6 6.8 7.8 8.1
(MgO&)*+ 2t (BeOzC2) (NaO&# (Li02C2)+
1.6 8.5 8.2 8.7
(MgN2)*+ 2t (BeN2) (NaN2)’ (LiN2)+
7.9 8.1 8.9 9.2
(MgNd)*+ 2t (BeN4) (NaN.# (LiN4)+
8.9 9.3 9.3 9.7
soft. There is no such generalisation when interaction takes place between a hard acid and a soft base, or vice-versa. Thus it is not expected that the HSAB principle will be satisfied in reaction (8a). Still, some interesting features are discernible from the r] values. In all cases the hardest species is formed when the base is NZ. This is consistent with the fact that q(Nz) > r](CO). The carbonyls are always harder than the corresponding isocarbonyls. This is gratifying indeed from the viewpoint of the MH principle. For a given base the interaction energy generally follows the hardness order of the cations (Mg*+ is an exception). In contrast to reaction @a), reaction (8b) takes place between a soft acid and a soft base and should therefore be a favourable process according to the HSAB principle. It can be seen from Table 2 that in all cases 77[(MX2Y2)n+]> n[(MXY)“+] which means that the product is harder than at least one of the reactants. Concluding remarks
The results of the present investigation indicate that the relative stability of both monocarbonyls
307 (1994) 99-105
and dicarbonyls, isocarbonyls and N2 complexes of Li+, Na+, Be*+ and Mg*+ can be rationalised on the basis of valence interaction, the strength of which has been assumed to be roughly proportional to the charge-density-related quantities Vi", and A VM. The binding such as @T,zMX/Y, energy of the Be*+ complexes is the highest in the series, due to the fact that both ES and valence interactions are exceptionally strong in this case. The newly proposed index, Vint, is observed to follow a more systematic trend than A VM. All four quantities also account for the higher stability of carbonyls compared with that of isocarbonyls and N2 complexes. The MH principle can be used to explain the relative stability of carbonyls and isocarbonyls. Although the cations are very hard acids, the corresponding 1:1 adducts are rather soft and their interaction with the soft bases CO and N2 obeys the HSAB principle qualitatively. Acknowledgements
P.K.N. thanks the Council of Scientific and Industrial Research (CSIR) for financial assistance. The time and services made available by the Computer Centre, IIT, Kharagpur, are gratefully acknowledged. References (a) P. Kebarle, Annu. Rev. Phys. Chem., 28 (1977) 445. (b) D.H. Aue and M.T. Bowers, in M.T. Bowers (Ed.), Gas Phase Ion Chemistry, Vol. 2, Academic Press, New York, 1979. (c) P. Hobza and R. Zahradnik, Weak Intermolecular Interactions in Chemistry and Biology, Elsevier, Amsterdan, 1980. (d) P. Arringhini, Intermolecular Forces and Their Evaluation by Perturbation Theory, Springer, Berlin, 1981. (e) B. Jeziorski and W. Kolos, in H. Ratajczak and W.J. Orville-Thomas (Eds.), Molecular Interactions, Vol. 3, Wiley, New York, 1982. R. Walder and J.L. Franklin, Int. J. Mass. Spectrom. Ion. Phys., 36 (1980) 85. (a) I.G. Kaplan, Theory of Molecular Interactions, North-Holland, Amsterdam, 1986. (b) M. Rigby, E.B. Smith, W.A. Wakenham and
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99
The role of valence interaction in some cation-molecule complexes PK. Nandi, A.B. Sannigrahi* Department of Chemistry, Indian Institute of Technology, Kharagpur 721 302, India (Received 25 August 1993; accepted 19 September 1993) Abstract The role of valence interaction in the 1 : 1 and 1 : 2 complexes between Li+, Na+, Be*+, Mg*+ and CO and N2 was qualitatively assessed using charge-density-related quantities such as charge transfer, the bond index of the cation-donor atom bond, the valency of interaction and the change in molecular valency calculated at the HF/63 lG*//3-21G level. It has been observed that the relative stability of the complexes can be rationalised on the basis of valence interaction. The molecular hardness parameters have also been calculated. The maximum hardness principle is found to be satisfied in the case of (MCO)“+-(MOC)“+ pairs, and the interaction between (MXY)“+ and XY follows the qualitative prediction from the HSAB principle, where M ‘+ is the metal ion and XY is the base.
Introduction In view of its importance in a wide variety of fields such as molecular spectroscopy, surface and colloid chemistry, molecular biology, thermodynamics, molecular beam experiments and polymer science, the study of intermolecular interactions has been a very active area of research [l-5] over the past two decades or so. The interaction between two closed-shell species is of special interest, particularly from the viewpoint of chemical bonding, because the energy of such interactions varies over a very wide range - from a few tenths of a kilocalorie per mole (in a typical van der Waals complex) to a few hundreds of kilocalories per mole (in many cation-dipole complexes). Several attempts have been made [6-151 to understand the origin of intermolecular interaction by decomposing the interaction energy into various components. Although there is no unique scheme * Corresponding
author.
SSDZ0166-1280(93)03576-S
of decomposition, it is generally recognised that the stability of an intermolecular complex stems from electrostatic (ES), polarisation (PL), exchange repulsion (EX), charge transfer (CT) and dispersion interactions. With the exception of the last, contributions from all other components can be estimated at the Hartree-Fock (HF) level as has been done in the Kitaura-Morokuma (KM) scheme [6]. The KM scheme has been applied [16-211 to a number of intermolecular interactions. Inclusion of electron correlation is essential to account for the dispersion interaction. The latter contribution can also be estimated using London’s equation [22]. For a given cation the strength of an ionmolecule interaction generally increases with increasing polarity of the molecule. In such complexes the ES interaction predominates over other components. The non-electrostatic or valence and dispersion interactions are, however, expected to play an increasingly important role with decreasing polarity of the molecule. The aim of the present
P.K. Nandi and A.B. SannigrahijJ. Mol. Struct. (Theochem)
100
study was to assess qualitatively the role of valence interaction in the stability of some cation-molecule complexes. We selected four cations (Li+, Naf, Be2+ and Mg2+) and one non-polar (N,) and one extremely weakly polar molecule (CO) and studied the nature of their interaction in terms of charge transfer, bond index and valency, as obtained from HF wavefunctions. In this context a new index of covalent bonding between the interacting species, namely, the valency of interaction, has been proposed and successfully applied. A number of ab initio quantum mechanical calculations [2336] have been reported on these systems. As any ion-molecule interaction falls in the broad category of an acid-base interaction, we also calculated the hardness parameters for all the species, with the objective of testing the HSAB principle [37,38] and the maximum hardness (MH) principle [39,40]. Of late there has been an upsurge of interest in this field and numerical calculations [41-471 in support of these principles have started to appear.
Method of calculation
All the species considered here are closedshell systems for which the atomic charge (qA), bond index (I,& and valency (V,) are given by [48]:
qA =
IAB =
zA
-
2 B
VA =
c
&p’%a a
~(p’%b(ps)ba b
(1)
(2)
IAB
B#A
where ZA is the atomic number of A, P = 2Cc (where C is the coefficient matrix of the doubly occupied MOs) and S is the A0 overlap matrix. of interaction between two The valency monomers R and S in the supermolecule RS is
307 (1994) 99-105
given by: R
T/id =
2
r.
2 A
(4)
IAB B
This quantity has a formal analogy with the group-group bond index defined by Giambiagi et al. [49]. The change in molecular valency [50] is given by: 2
EVA-cVA-eVA A
A
(5)
A
Equation (5) differs from Eq. (4) by a factor of 0.5 and includes all possible bond indices in both the diatomic monomer and the supermolecule. The molecular hardness (n) is calculated using the expression [5 11: rl=
(“LUMO
-
EHOMO)
2
(6)
where E is the orbital energy. All calculations were done at the HF level using the 6-31G* basis set at the 3-21G optimised geometry of the monomers [52] and the complexes [ 16,271. The pertinent geometrical parameters are given in Fig. 1. Results and discussion
The calculated values of the energy (AZ?) of interaction, the bond index (ZMx,y) of the new bond formed between the cation (M”+) and the atom X or Y of the base (XY), the amount of charge transfer (qCT), the valency of interaction (Vi”,) and the change in molecular valency (A VM) in the formation of the ion-molecule complexes are presented in Table 1. All the complexes considered here were predicted [16,27] to have a linear equilibrium structure. The BSSE [53] correction was not included in the calculation of AE because it has been found [54] to be negligibly small (0.1-0.6 kcal mol-i) in several ion-molecule complexes at the HF/6-3 1+G* level. The energy of interaction between metal ions with a molecule of either CO or N2 varies in the
P.K. Nandi and A.B. Sannigrahi/J. Mol. Strut. 1.128
1.083
C-------o 2.!3!3@
2.2¶2.
307 (1994) 99-105
1.116
l.llQ
2.180
1.143
1.187
1.6s3
l.QQ6
l.Qel -I-
1.116
2.Ql3
Fig. 1. Equilibrium
1.081
2.247
2.207
structural parameters
1.081
l.lQQ
1.806 Be-4
1.103
l.QQ3 1.171 MQ-----o----c
1.146 l.Q!B c-i-----o-----c
l.llQ 2.!371 o"----Nn~~c~~----o-----c
1.142
(bond lengths in gngstr8ms) of the monomers
Be2+ > Mg2+ > Li+ > Na’. The charge ionic-radius ratio of the metal ions, i.e. the ionic potential, also varies in the same order, implying that these ion-molecule interactions are essentially electrostatic in nature. There will, however, always be a certain amount of charge transfer upon complex formation. We used this quantity (qCT) along with IMxIy, F’i,t and AV, as indices to assess qualitatively the degree of valence interaction. For the sake of simplicity the total energy of interaction was assumed to be approximately equal to the sum of the contributions from the ES and valence interactions. The interaction between a metal ion and a CO molecule leads to the formation of two possible isomers, (MCO)“+ and (MOC)“+. In analogy to the nomenclature isocyanide, isothiocyanate, etc., we tentatively call the (MOC)“+ species ‘isocarbonyls’. The relative stability of the carbonyl and isocarbonyl isomers depends [16,27] on the level of calculation employed. At the HF level, the formation of (MOC)n+ is favoured (by about 1.O-2.0 kcal mol-‘) over (MCO)“+. This is partly order,
%.Oo!s
LA-
MQ~-----o
0-----c~~--d----Q
Ml-
1.118
Na-
Be-
2.0453 1.083
1.835
2.321
Na-----o------c
Bed----c
101
L~-----o-----c
L~----c-----o
N+
w-----c----o 1.518
(Theochem)
2.lQL
and complexes.
due to the orientation of the CO dipole (C6+O”-) with regard to the cation which facilitates ES interaction. It may be noted that in (MOC)“+ A Vhl is generally negative and the CO bond is somewhat stretched with respect to that in an isolated CO molecule (Fig. 1). Thus the higher stability of the isocarbonyls at the HF level should be due to stronger ES interaction. In contrast, as indicated by the qCT, ZMXIY, L’i”t and AJfM values the valence interaction is far more pronounced in the carbonyl isomers. It has been observed by Sannigrahi et al. [54] in a different context that inclusion of electron correlation enhances qtr. The vector direction (C6-06+) of the dipole moment of CO is also reproduced correctly [52] when configuration interaction calculations are carried out including the singly excited configurations. Thus at the correlated level (MCO)“+ should be more stable than (MOC)“+, which is in agreement with the results of ab initio MP3 calculations [16]. To summarise, at the HF level the valence interaction is stronger and the ES interaction is weaker in the carbonyls. The reverse
102
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307 (1994) 99-105
Table 1 Calculated interaction energies (AE), bond indices (I ~x,v),
amount of charge transfer (PC.). valency of interaction (Vi,t) and
change in molecular valency (A V,) -AE
Species
qCT
V,nt
AVM
(kcalmol-‘) Li+ . ..co Li+ OC
14.5 15.6 12.0
0.307 0.114
0.177 0.077
0.326 0.153
0.459 -0.071
0.111
9.4 10.3
0.206 0.076
0.065 0.117
0.128 0.226
0.028 0.315
0.059
0.115
7.3
0.054
Be’+ . . CO Be’+ . . OC Be’+ . N Mg2+ . ..&
93.2 95.9
0.194 0.772
0.037 0.562
0.072 0.818
0.134 1.056
85.1 60.3
0.172 0.565
0.512 0.526
0.854 0.810
0.194 0.489
0.361
Mg2+ . ..oc Mg2+ . . N2
62.3
0.219
0.598 0.268
0.781 -0.178
OC . . . (LiCO)+
54.7 13.9
0.213 0.348
CC.
28.4 14.8 30.4 11.5 23.5
Li+
. . . N2
Na+...CO Na+ . ..oc Na+ . N2
Li+ . . CO
CO. CO.
. (LiOC)+
. . Li+ . . OC N2 . ( LiN2)+ N2 . . . Li+ N2 OC .
(NaCO)+
OC...Na+...CO CO. . . (NaOC)+ CO...Na+...OC N2 N2
. . . (NaN2)+ Na+ . . N2 OC . . (BeCO)*+
CC.
. Be’+ .
CO
9.2 18.7 10.0 20.3 6.1 14.0 11.5
0.240
0.278
0.348
0.204 0.408
0.367 0.734
0.498 0.957
0.110 0.110
0.079 0.158
0.183 0.183
0.108 0.215
0.158 0.316 0.207
-0.025 -0.096 0.298
0.120 0.239
0.412 0.229
0.506
0.209 0.209 0.073 0.073 0.066 0.066 0.124 0.724
CO.. . (BeOC)‘+ C0...Be2+...0C
170.7 18.5 174.4
N2.. (B;+N2)‘+ N2 . . . Be . . . N2
71.3 156.5
0.703 0.703
(M&O)‘+ Mg2+ . . CO
39.5 99.8
(MgOC)2+ . Mg2’ . OC
62.3 103.7
OC OC
CO.. CO.
.
N2.. . (MgN2)2+ N2 . ..Mg2+...N2
34.5 89.1
0.137 0.124
-0.054
0.059 0.119 0.045 0.089 0.496 0.993 0.465 0.931
0.459 0.117
0.301 0.616 -0.027
0.234 0.087
-0.08 1 0.119
0.174 0.786 1.530
0.253 0.890 1.946 0.227 0.387
0.475
0.796 1.567 0.741
0.583 0.583
0.951 0.387 0.714
1.414 0.621 1.235
0.191 0.191 0.271
0.125 0.249 0.162
0.242 0.484
1.545 0.155 -0.333
0.271
0.325
0.302 0.603
0.333 0.611
0.695 0.695
is true in the isocarbonyls and this accounts for their higher stability. At the correlated level both ES and valence interactions become stronger in the carbonyls than in isocarbonyls as a result of which the former isomers are more stable. We now turn our attention to the relative stability of the (MCO)“+ and (MN2)“+ complexes. In all cases the carbonyls are found to be more stable than their N2 counterparts, and the differ-
0.394 0.883 0.164
ence in their AE valves varies in the order Naf < Lif < Mg2+ < Be2+. Ikuta [16] carried out Morokuma’s energy decomposition analysis in order to rationalise the difference in the binding energy of Li+ and Naf complexes on the one hand and of CO and N2 complexes on the other. He observed that for a given base the stabilisation due to ES, PL and CT interactions is smaller in Na+ due to its higher ionic size. Our calculated
P.K. Nandi and A.B. SannigrahijJ.
Mol. Strut.
(Theochem)
307 (1994) 99-105
values of qcr, Zt,.rx,v, I’i”t and AV, also indicate that valence interaction should be weaker in the Na+ complexes. Thus both ES and valence interactions are stronger in Li+ complexes which account for their higher stability. The energy decomposition analysis of Ikuta does not adequately account for the difference in the binding energy of N2 and CO complexes with a given cation. Moreover, due to the use of a smaller basis set (3-21G) (MN2)+ is wrongly predicted to be more stable than (MCO)+. As higher order terms in the multipole expansion of charge density are more important in the ES interaction between a cation and a neutral molecule, it is not possible to infer from classical considerations whether its contribution will be greater in N2 or in CO complexes. The calculated values of qcr and other related quantities indicate that the valence interaction is far more pronounced in the carbonyls. Therefore it appears that, the stabilisation due to ES being comparable in carbonyls and the dinitrogen complexes, the valence interaction plays a more decisive role in accounting for their relative stability. The binding energy of Be2+ and Mg2+ complexes is considerably higher than that of Li+ or Na+ complexes. The ES interaction could possibly account for this large difference. However, due to the smaller M2+-X/Y distance the CT interaction should be also appreciable in these complexes. This is borne out by our calculated values of qcr and other quantities. The valence interaction is capable of distinguishing between the stability of (MgN2)2+ and (MgCO)*+. However, in the case of Be’+, the valence interaction with CO and N2 is almost equally strong. Therefore the large difference in their AE values should be mainly due to ES interaction. The formation of dicarbonyls, diisocarbonyls and tetranitrogen complexes can be described either by a one-step or a two-step reaction: M”’ + 2XY-(YXMXY)“+
or (XYMYX)“+ (7)
M”+ + XY-(MXY)“+
or (MYX)“+
(8a)
103
(MXY)“+ or (MYX)“+ + XY-(YXMXY)“+ or (XYMYX)“+
(8b) As can be seen from Fig. 1, the linear structure of 1:1 adducts is retained in the 1:2 adducts. At the HF level the stability of the 1:2 adducts is predicted [27] to follow the order OC > CO > N2. The relative stability order of the CO complexes is, however, reverted at the post-HF level. Thus the trend in AE of 1:2 adducts is identical to that in the 1:1 adducts. In the following we confine our attention to dicarbonyls and tetranitrogen complexes. It can be seen from Table 1 that all the three reactions described by reactions (7), (8a) and (8b) are exothermic. As expected, the same value of AE is obtained for reaction (7) and for the sum of reactions (8a) and (8b). In the case of Li+ and Naf, the AE, (JcT and I’i,t of reaction (7) are almost twice the corresponding values associated with reaction (8a). The same is not true for the Be2+ and Mg2+ complexes. Now AE for the onestep process is considerably higher than twice the corresponding value for the first step of the twostep process. However, qcT and I’i,t follow the same trend as in the monocation complexes. Addition of one more molecule of base to the 1:1 adduct decreases AE in all cases and enhances ZMxIy, qm and P’intvalues in all but Be2+ complexes. The AV, values do not follow any pattern in this regard. The decrease in AE is only marginal in the case of Li+ and Na’, but quite substantial in the dication complexes. Thus in the formation of 1:2 adducts from the 1:1 adducts the valence interaction becomes stronger for all the cations except Be2+. Then the decrease in AE must be caused by the ES interaction which is most prominent in the Be2+ complexes. We now consider the acid-base reactions (8a) and (8b) in terms of the hardness parameters (77) summarised in Table 2. All the cations considered here are very hard acids, their hardness varying in the order Be2+ > Li+ > Mg2+ > Na+. In contrast, both CO and N2 are soft bases. According to the HSAB principle, hard prefers hard and soft prefers
104
P.K. Nandi and A.B. Sannigrahi/J. Mol. Struct. (Theochem)
Table 2 Calculated values of hardness parameters
(7)
Species
77 (eV)
Species
17 (eV)
Li+ Be’+
35.3 68.0 10.8
Na+ Mg2+ co
22.1 33.6 9.6
N2
(MgCO)‘+ (BeCO)*+ (NaCO)+ (LiCO)+
1.8 7.9 8.3 8.7
(MgCzO,)*+ (BeC,Os)*+ (NaC,O# (LiC202)+
8.8 8.9 8.7 9.0
(MgOC)*+ (BeOC)*+ (NaOC)’ (LiOC)+
6.6 6.8 7.8 8.1
(MgO&)*+ 2t (BeOzC2) (NaO&# (Li02C2)+
1.6 8.5 8.2 8.7
(MgN2)*+ 2t (BeN2) (NaN2)’ (LiN2)+
7.9 8.1 8.9 9.2
(MgNd)*+ 2t (BeN4) (NaN.# (LiN4)+
8.9 9.3 9.3 9.7
soft. There is no such generalisation when interaction takes place between a hard acid and a soft base, or vice-versa. Thus it is not expected that the HSAB principle will be satisfied in reaction (8a). Still, some interesting features are discernible from the r] values. In all cases the hardest species is formed when the base is NZ. This is consistent with the fact that q(Nz) > r](CO). The carbonyls are always harder than the corresponding isocarbonyls. This is gratifying indeed from the viewpoint of the MH principle. For a given base the interaction energy generally follows the hardness order of the cations (Mg*+ is an exception). In contrast to reaction @a), reaction (8b) takes place between a soft acid and a soft base and should therefore be a favourable process according to the HSAB principle. It can be seen from Table 2 that in all cases 77[(MX2Y2)n+]> n[(MXY)“+] which means that the product is harder than at least one of the reactants. Concluding remarks
The results of the present investigation indicate that the relative stability of both monocarbonyls
307 (1994) 99-105
and dicarbonyls, isocarbonyls and N2 complexes of Li+, Na+, Be*+ and Mg*+ can be rationalised on the basis of valence interaction, the strength of which has been assumed to be roughly proportional to the charge-density-related quantities Vi", and A VM. The binding such as @T,zMX/Y, energy of the Be*+ complexes is the highest in the series, due to the fact that both ES and valence interactions are exceptionally strong in this case. The newly proposed index, Vint, is observed to follow a more systematic trend than A VM. All four quantities also account for the higher stability of carbonyls compared with that of isocarbonyls and N2 complexes. The MH principle can be used to explain the relative stability of carbonyls and isocarbonyls. Although the cations are very hard acids, the corresponding 1:1 adducts are rather soft and their interaction with the soft bases CO and N2 obeys the HSAB principle qualitatively. Acknowledgements
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