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The geometric structure and stability of the NO+·CH4 cationic complex
Chemical Physics ELSEVIER
Chemical Physics 224 (1997) 191-199
The geometric structure and stability of the NO + . complex Edmond
P.F.
CH 4
cationic
Lee *, Paul Mack, Timothy G. Wright *
Department of Chemistry, Universit3,of Southampton, Highfield, Southampton, S017 1BJ, UK
Received 30 July 1997
Abstract Ab initio calculations have been performed, mainly at the MP2 level of theory, using a variety of basis sets, to elucidate the structure of the NO +- CH 4 cationic complex. The complex has an equilibrium geometry of C s symmetry, in which the NO + moiety eclipses a C - H bond of the methane molecule. The geometry is compared to those of related complexes. Harmonic vibrational frequencies are also calculated, together with the interaction energy and some thermodynamic quantities for the complex formation, employing a number of the theoretical methods. In particular, the interaction energy was calculated at the CCSD(T) level of theory. The implications of these results on the resonance-enhanced multiphoton ionization (REMPI) spectroscopy of the NO - CH 4 complex are briefly discussed. © 1997 Elsevier Science B.V.
1. Introduction The NO +. CH 4 molecular complex is interesting as it consists of a closed core cation interacting with a molecular species. Recently, some effort has been put into the calculation of the geometry and vibrational frequencies of the Ar • NO + cationic complex [1-5], in which the closed shell NO + cation is interacting with a closed-shell atom. In the case of the molecular partner, CH4, there clearly arises the difficulty of deciding where the NO + moiety is positioned relative to the methane molecule. On first sight, it might be expected that the NO + fragment would be positioned to create the complex with the highest symmetry, viz, along a C 3 axis, either with the O or N atom pointing towards a H atom, or along
* Corresponding authors. Fax: +44-1703-593781; e-mail: [email protected], [email protected],uk
a C 3 axis which passes through the centre of a CH 3 face, with the latter seeming the more likely, since the hydrogens will be 6 + and the carbon will be 6-. (The latter geometry is that adopted by the CH 4 • HC1 complex [6].) In both cases, it is not obvious whether the structure with the N or O atom pointing towards CH 4 (see Fig. 1) would be the preferred one, because in the cation both the O and N atoms are positively charged [1] and hence both could be considered as electrophilic and therefore the binding atom. In addition to these possibilities, and by comparison with the predicted geometry of the A r - N O + complex [1,4], the CH 4 group could be positioned in a pseudo-T-shaped configuration. Consequently, the strategy that needs to be adopted is to determine which of the configurations are minima, and then which is the global minimum (should more than one minimum exist). The geometry o f the complex has added interest
0301-0104/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PI1 S030 I-01 04(97)00293-0
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E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
H
0
N
H,,,,,Itl C
H
i
H
[]
H
N
0
O
N
H ,,,H C
!
H.
H
I
Cl,,,,'"' H
H
[]
N
O
H
I
.Clll,,,,-'H
H Fig. 1. Stationary points of the NO+'CH4 cationic complex, under the restraint of C3v Symmetry, as calculated at the MP2(full)/6-31G * level of theory. These are all transition states, as indicated by the presence of imaginary frequencies, see text for details.
since recently, Akiike et al. [7] measured the (1 + 1) resonance-enhanced multiphoton ionization (REMPI) spectrum of NO • CH 4 via the A state (the A state of NO is formed when the 7r* electron on NO is excited to the 3s Rydberg orbital). The structure that was recorded therein was interpreted in terms of internal rotation of the C H 4 group, and a geometry of C3v symmetry was deduced by comparison with the work of Ohshima and Endo on CH 4 • HC1 (which was found to have C3v symmetry from the rotational spectrum) [6]. The interesting point about the A state of NO • C H 4 is that the radius of the Rydberg electron orbit of the A state of NO is expected to be similar to the diameter of CH 4, and so there is a competition as to whether the C H 4 group is inside the Rydberg orbit (giving essentially a Rydberg state, with a relatively strongly bonded N O + . C H 4 core), or outside (in which case the C H 4 moiety is bound only by dispersive forces). In order to decide this, it is necessary to have a good idea of the dissociation energy of the cation and its vibrational frequencies, in order to compare them to those of the A state. (If the A state is Rydberg in character, then the dissociation energy and vibrational frequencies should resemble those of the cation.) Comparison may also be made with the REMPI spectrum of the (~ state of N O . C H 4 (corresponding to a 3pTr ~ 7r* excitation on NO), which has been studied by Miller [8]. At this point it is worth noting that Bush et al. [9] in their work on the A state of Kr. NO, deduced that the krypton atom was outside the Rydberg electron orbit (on average), and that a similar conclusion held for the ~, state of A r . NO [10]. If this is the case for N O . C H 4 , then it is expected that the properties of the cation would be different from those of the A. and (~ state. In this work, the aim was to determine the geometry, vibrational frequencies and interaction energy of the ground electronic state of the NO +. C H 4 cationic complex.
2. C o m p u t a t i o n a l
details
All calculations were performed with Gaussian94 [11] using standard split-valence 6-31G and 6-311G basis sets, which were augmented with various standard diffuse and polarization functions. In addition,
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
the augmented correlation-consistent polarized triple zeta valence (aug-cc-pVTZ) basis set of Dunning and coworkers [12a,12b,12c] was also employed. Geometry optimization and hamaonic vibrational frequency calculations were carried out using M011erPlesset perturbation theory to second order (MP2) [13], with additional single point calculations performed at the CCSD(T) level [ 14a, 14b, 14c] in order to obtain more reliable interaction energies. (All calculations employ the frozen core approximation, unless explicitly noted otherwise.) Full geometry optimization calculations were carried out using analytic gradient methods, within the specified symmetry constraints. Whether the geometries obtained were minima or not was determined by the number of imaginary vibrational frequencies obtained in the analytic second derivative (frequency) calculations. One important point to be noted here is that the shallowness of the surface can lead to small imaginary frequencies if the optimization has not been forced to a tight convergence. In the work here, tight convergence thresholds were set, instead of the default values in the optimization procedure, if the lowest unprojected frequencies were found to be larger than 10i c m - J : for a perfect convergence, all vibrational frequencies should have real values, with six zero frequencies for a non-linear molecule, corresponding to rotation and translation. In some cases, if a tight optimization was not used, then the lowest unprojected frequencies were found to have values larger than 10i cm -~, and were found to affect the magnitude of the projected vibrational frequencies of the lowest intermolecular vibrational modes significantly. Interaction energies for the cation-molecule complex formation were initially calculated from the difference in the total electronic energies of the complex and the monomers with their respective basis sets. Counterpoise corrected interaction energies were obtained employing the full counterpoise correction (CP) of Boys and Bernardi [15], in order to correct for basis set superposition error (BSSE). Only one minimum was found in this study, but there were a number of transition states. All energies for the transition states found were counterpoise corrected for BSSE at the MP2(full)/6-311 + + G(2df,2p) level of theory. In addition, for the minimum geometry, as well as the 6-311 + + G(2df,2p)
193
basis set, the aug-cc-pVTZ basis set was also used at the MP2 level. In order to examine higher-order correlation effects on the interaction energy, single point CCSD(T)/aug-cc-pVTZ energy calculations were also performed at the MP2/aug-cc-pVTZ geometry. Finally, thermodynamic data were calculated under the rigid-rotor, simple harmonic oscillator (RRHO) approximation. (It should be noted that the MP2/aug-cc-pVTZ frequency calculation on the complex was not completed, owing to insufficient computing resources being available; the M P 2 / 6 3 1 1 + + G(2df,2p) frequencies were used in the evaluation of the thermodynamic data with the MP2/aug-cc-pVTZ interaction energies.)
3. Results Initial survey optimizations were performed at the MP2(full)/6-31G * level under C 3v symmetry. There are four possible isomers, as illustrated in Fig. 1. None of these structures were found to be minima, with the structures shown in Fig. l a and b both having two imaginary frequencies, and those in Fig. lc and d having four imaginary frequencies. Consequently, it appears that there is no minimum of C3v symmetry. Thus a minimum energy geometry was sought by reference to the previous calculations on A r - N O + (vide supra). These suggested a structure in which the methane is bonded off of the NO + axis, although the relative orientations of the two moieties is not immediately clear. By optimizing the likely structures of C S symmetry, two stationary points were found, which differed only in the orientation of the NO + moiety relative to CH4: These are shown in Fig. 2. The structure shown in Fig, 2a is a minimum on the potential energy surface, whereas that shown in Fig. 2b is a saddle point, i Next all of the six geometries (the four in Fig. 1, and the two in Fig. 2) were reoptimized at the MP2(full)/6-311 +
J There was one imaginary frequency (63.8i cm -~, of a" symmetry) even at the MP2/6-311 + + G(2dL2p) level; however, it should be noted that at the MP2/aug-cc-pVTZ level, this structure was found to be only 0.25 kcal m o l - I higher in energy than the minimum.
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E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
Side View
Front View
©
N
H3
H~
N
H2
~.
Fig. 2. Stationary points of the NO+.CH4 complex under C~ symmetry, and using various levels of theory. (a) Optimized geometry of the minimum energy structure, see text for details. (b) Saddle point (one imaginary frequency), see text for further details.
+ G(2df,2p) level of theory, and corrected for BSSE by a full CP correction, the results are shown in Table 1. As may be seen, with the rather large basis set used, the BSSE is quite small, and does not change the relative energy ordering, at least at this level of theory. Having noted this, any experiment will almost certainly detect an average geometry which samples both the minimum and the C s saddle point (see Fig. 2a and b), since the low-frequency vibrations imply that the molecule will be undergoing large amplitude motions, even with only the zero-point vibrational energy present. A series of calculations were then performed on the structure shown in Fig. 2a, the only minimum. The results of these calculations are summarized in Table 2. As may be seen, a reasonably thorough study o f the effects of diffuse and polarization functions, as well as the underlying valence basis set, has been made to ascertain whether the calculated geometry was reasonably stable with respect to variations in the overall basis set. It is clear that the calculated structure is very similar in all cases, and all levels of calculation carried out confirm that this structure is a minimum on the potential energy surface, as evinced by the all real computed vibrational frequencies presented in Table 3. Nevertheless, the intermolecular
bond distance, as measured between the C and N atoms (rcr~), is very sensitive to the basis set employed. Some trends appear in the computed values. First, the addition of a set of diffuse functions on all atoms ( + + ) seems to destabilize the intermolecular bond slightly, as inferred from the increase in the intermolecular bond length, when using the 6-31G * and 6-31 + + G * basis sets; however, this effect is smaller on going from 6-311G * * to 6-311 + + G * * than it is from 6-31G * to 6-31 + + G *, suggesting that the larger increase in rcN for the latter is possibly due to an inadequacy of the underlying 6-31G basis set. [The apparently more stable complex predicted here (shorter rcN) with the basis sets without diffuse functions may be considered as having a similar origin as that of the basis set superposition error.] Secondly, there is a minimal effect on going from M P 2 / 6 - 3 1 G * to M P 2 ( f u l l ) / 6 - 3 1 G * , suggesting, as might have been expected, that the combined c o r e - c o r e and c o r e - v a l e n c e correlation have minimal effects on the computed quantities considered here. Thirdly, it is clear that the polarization functions, in all cases, are having a strong influence on the description of the intermolecular bonding region, appearing to stabilize the bond. In summary, all of these trends appear to suggest that there is a subtle balance in the way that the basis set describes the complex. Clearly, both the valence and intermolecular regions of the system need to be described adequately with an underlying basis of at least triple-zeta quality; in addition, polarization functions are extremely important in stabilizing the complex. It should be noted that the total numbers of basis functions (nbasis) for the complex with the two
Table 1 Interaction energies for the six stationary points found at the MP2(full)/6-311 + + G(2df,2p) level of theory Structure Energy/E h
Interaction energy (no CP)/ kcal mol- i
Interaction energy(+CP)/ kcal mol - t
Fig. la Fig. lb Fig. lc Fig. ld Fig. 2a Fig. 2b
2.89 3.44 1.20 1.55 5.56 5.34
2.41 2.70 0.90 1.03 4.93 4.71
-
169.833676 169.834554 169.830973 169.831540 169.837935 169.837574
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
195
Table 2 Optimized geometric parameters for the C~ minimum energy structure of the NO +. C H 4 cationic complex Level of theory
MP2/ 6-31G"
MP2(full)/ 6-31G*
MP2/ 6-31 + + G *
MP2/ 6-311G* ~
MP2/ 6-311+ + G * ~
MP2/ 6-311+ + G(2df,2p)
MP2/ aug-cc-pVTZ
rCN/A
2.799
2.792
2.851
2.824
2.846
2.735
2.718
rNO///k
rcH ~/~,
1.105 1.092
1.104 1.092
1.105 1.093
1.087 1.093
1.087 1.093
1.083 1.088
1.084 1.089
rCH2/A
1.091
1.090
1.091
1.090
1.090
1.085
1.086
1.095 88.5 101.8 108.3 111.2 ±62.9
1.094 88.1 102.0 108.3 111.2 +62.9
1.094 87.5 99.3 108.2 111.2 +62.8
1.094 87.6 99.3 108.3 111.1 ±62.6
1,094 87.0 96.9 108.3 111.0 +62.6
1.090 87.3 99.9 108.5 111.1 ±62.6
1.092 86.0 99.7 108.4 111.1 -t-62.5
rcH 3, rcR4/A Z. NCH/° /ONC/° / HCH/° /_HICH3.4/° AOHJCH3.4/°a
a Where A represents a dihedral angle.
largest b a s i s sets e m p l o y e d , n a m e l y the 6-311 + + G ( 2 d f , 2 p ) and a u g - c c - p V T Z bases, are 142 a n d 230, r e s p e c t i v e l y , e v e n t h o u g h t h e s e t w o b a s e s m a y be c o n s i d e r e d to be o f s i m i l a r overall quality. A l t h o u g h
S i n c e the N O +. C H 4 c o m p l e x c o n s i s t s o f a dia t o m i c b o n d e d to a p o l y a t o m i c , there are five interm o l e c u l a r m o d e s : T h e r e are t h r e e o f a' s y m m e t r y a n d t w o o f a" s y m m e t r y . It is c l e a r f r o m the vj
rcN s e e m s to c o n t i n u e d e c r e a s i n g w i t h the i n c r e a s e o f b a s i s size, it s e e m s likely that f u r t h e r d e c r e a s e s
m o d e (the l o w e s t v i b r a t i o n o f a' s y m m e t r y ) , see T a b l e 3, that this i n t e r m o l e c u l a r vibrational fre-
w o u l d b e small, as the i n c r e a s e in n b a s i s f r o m the
q u e n c y is d e m o n s t r a t i n g a s t r o n g d e p e n d e n c e on the
6-311 + + G ( 2 d f , 2 p ) to a u g - c c - p V T Z b a s e s is v e r y c o n s i d e r a b l e already.
level o f theory: To a l e s s e r extent, this is true o f the o t h e r i n t e r m o l e c u l a r v i b r a t i o n s as well. In o r d e r to
Table 3 Harmonic vibrational frequencies for the C s minimum energy structure of the NO +. C H 4 cationic complex a'b Vibrational mode
MP2/ 6-31G*
MP2(full)/ 6-31G*
MP2/ 6-31 + + G *
MP2/ 6-311G* *
MP2/ 6-311 + + G * *
MP2/ 6-3ll + + G(2df,2p)
1 (a') I 2 (a') 1 3 (a') 1 4 (a') t 2 5 (a') t 2 6 (a') e 7 (a') NO 8 (a') a I 9 (a') t 2 10 (a') t 2 11 (a") 1 12 (a") 1 13 (a") t 2 14 (a") e 15 (a") t 2
113.9 152.2 166.2 1349.2 1421.8 1603.6 2101.4 3071.9 3218.5 3244.8 80.9 199.6 1433.6 1617.0 3192.5
114.3 154.8 168.8 1349.0 1422.5 1604.2 2106.2 3073.0 3219.9 3245.5 81.2 201.1 1434.0 1617.9 3194.6
102.5 (99.5) 144.4 (120.8) 167.7(137.4) 1345.9 (1016.4) 1414.1 (1068.1) 1583.5 (1120.3) 2102.6 (2102.1) 3064.8 (2169.4) 3203.1 (2371.9) 3233.4 (2391.2) 54.0 (42.9) 158.4 (114.6) 1422.9 (1073.0) 1581.3 (1118.7) 3187.1 (2361.7)
113.1 157.0 172.8 1313.9 1374.8 1563.9 2156.6 3042.8 3185.8 3213.7 67.9 197.7 1384.0 1573.3 3169.9
103.5 148.5 182.3 1313.6 1371.6 1563.1 2151.9 3039.4 3178.7 3211.4 52.7 161.1 1379.5 1560.3 3167.5
130.3 (126.0) 171.6 (136.8) 192.8 (166.3) 1308.5 (988.9) 1362.2 (1029.3) 1565.8 (1107.8) 2149.3 (2144.1) 3042.2 (2158.3) 3184.4 (2356.3) 3213.0 (2376.4) 77.3 (61.9) 215.4 (155.2) 1372.8 (1035.2) 1577.3 (1115.9) 3163.5 (2342.8)
a The symmetry symbols in the first column identify to which vibration of the isolated C H 4 moiety the vibrations belong; the 1 indicates an intermolecular vibration; the NO implies the vibration is the NO + stretch. b Frequencies given in parentheses are those corresponding to the fully-deuterated species, NO +. CD4.
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
196
Table 4 C a l c u l a t e d i n t e r a c t i o n e n e r g i e s , e n t h a l p i e s , e n t r o p i e s , G i b b s free e n e r g i e s a n d e q u i l i b r i u m c o n s t a n t s f o r the r e a c t i o n : N O + +
CH 4
NO + .
CH 4 Quantity AEJkcal
MP2/6-311 mol
i
A Ee + CP/kcal
mol
i
A H 0 =- D 0 / k c a l
mol - i
A/q298 ( C P ) / k c a l m o l - i AS298/cal mol- t K i AG298 ( C P ) / k c a l K v29s
+ + G(2df,2p)
-5.50
-6.19
- 4.94
- 5.63
- 3.81
-- 5,46 b
- 4.50"
- 4.33 ~ - 4.72 ~ - 17.8 ~'
+ 1.11
+ 0.43"
+ 0.58"
0.15
0.49"
a W h e r e the v i b r a t i o n a l c o n t r i b u t i o n h a s b e e n c a l c u l a t e d u s i n g the M P 2 / 6 - 3 1 1 C a l c u l a t e d at the M P 2 / a u g - c c - p V T Z
CCSD(T)/aug-cc-pVTZ
- 4.89 ~ - 17.8"
- 4.20 -- 17.8
moli
MP2/aug-cc-pVTZ
0.38 ~
+ + G(2df,2p) vibrational frequencies.
geometry.
gain a better insight into the nature of the vibrational modes, the normal coordinates were examined, and also the vibrational frequencies of the fully deuterated species were calculated in a couple of selected cases: MP2/6-31 + + G* and MP2/6-311 + + G(2df,2p), values included in parentheses in Table 3. Neither of these lines of attack yielded an unambiguous assignment of the modes; in particular, the intermolecular stretch was not obviously identifiable. It seems clear that the latter will have a' symmetry; however, the two most likely candidates, from the normal modes (v 2 and v3), seem to be a mixture of stretching and bending. From the normal mode analysis, the ~'2 vibrational motion appears to have a stronger contribution from the intermolecular stretch, and so is tentatively assigned to be such. It is not obvious how the intermolecular stretch would be~ have upon deuteration, but comparison with the deuteration shifts obtained by Hobza et al. [16] in their work on the phenol-water cation appears to suggest that the intermolecular stretch should decrease slightly upon deuteration, although the effect may be larger here, on percentage mass considerations. This is at least consistent with the observed behaviour here (Table 3). By following the usual convention for naming the intermolecular vibrations, the following tentative assignments can be made: t,~ (in-plane bend); v 2 (stretch); v 3 (in-plane wag); ~'ll (torsion); and ~'t2 (out-of-plane wag); where in-plane implies the C~ symmetry is retained, and out-of-plane implies that it is lost. The intramolecular vibrational frequencies change very little upon complexation (uncomplexed values not given here), as expected, owing to the weak interaction. Of significance, how-
ever, is that the degenerate vibrations of methane do change noticeably, with the t 2 vibrations splitting into two vibrations of a' symmetry and one of a" symmetry, with the e vibration splitting into a vibration of a' symmetry and one of a" symmetry (Table 3). Table 4 shows the calculated interaction energies at the three highest levels of theory (excluding the values of Table 1), together with calculated thermochemical quantities. It may be seen that the computed BSSE is quite small (ca. 0.6 kcal tool l), which reflects the size of the basis sets used, and demonstrates that they are close to being complete. The computed A E c at the CCSD(T)/aug-ccp T V Z / / M P 2 / a u g - c c - p V T Z level, including the CP correction for BSSE is - 5 . 4 6 kcal tool 1. The fact that this value obtained from the higher-order correlated CCSD(T) calculations is only slightly less negative than the MP2 counterpart, suggests that the high-order correlation effects on the computed relative energies are small, and that the CCSD(T) optimized geometry would probably be very close to the MP2 geometry reported here.
4. Discussion
Considering first the geometry of the complex, it is clear that the C H 4 moiety is not bonding through any of its CH o- bonds, as has been observed in recent work on ylides [17]. If the C H 4 moiety is considered as a sphere, then the Jacobi angle may be calculated to be 69.8 °, with the Jacobi bond length of 2.863 A, at the MP2/aug-cc-pVTZ level of theory.
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
It is remarkable how similar this geometry is to that of both A r . NO + (Ref. [4]) and A r . CO~-, (studied recently by Gellene [18]); there are also large similarities with the structures of N O + - X ( X = H 2 0 , CO 2 and N 2) [19]. Of interest, is that the geometry of the A r . HCO ÷ complex (isoelectronic with A t . NO ÷) is linear, as determined from ab initio [20] and microwave [21] studies. It is clear that the explanation of the geometries of these complexes is not straightforward. One picture that has been put forward is that of the H O M O - L U M O interaction [22a,22b], where the orientations of the H O M O on the electron donor ( C H 4 here) and the L U M O on the electron acceptor (NO ÷ here) determine the geometry. The L U M O here would be the ~ * orbital on NO, with the H O M O being an sp 3 hybrid orbital on methane [23], this would indicate that, subject to steric interactions, the NO + molecule would attempt to overlap one of its lobes with the sp 3 orbital, which has density on and between the H atoms of a pair of CH bonds. Indeed the minimum energy geometry (Fig. 2a) does appear to suggest that this picture works here, and is also consistent for A r . NO÷: this is despite the fact that the NO ÷ moiety carries + 0.98 e at the MP2 level, employing Mulliken population analysis, implying that almost no transfer of electronic charge occurs. It would appear that this geometry must also have a maximized combination of charge-induced dipole and dispersion interactions. (It should be noted that Mulliken charge densities are very basis set dependent, but the overall positive charge computed on NO ÷ is over + 0 . 9 2 e in all cases.) Of course, this explanation does not appear to hold for the linearity of the A r . HCO ÷ complex. The intermolecular vibrational frequencies are of a magnitude comparable to those in the hydrogenbonded phenol-water complex [16], indicating that the interaction is reasonably strong. The interaction energy for NO ÷. CH 4 is ca. 5.5 kcal mo1-1, which is equivalent to 2100 cm -~ (0.26 eV); this may be compared to the binding energies of the phenol-water complex (4600 cm 1) [24], the phenol-methanol complex (5400 c m - i ) [25] and A r . NO + (950 c m - 1) [l,26,27a,27b], showing that the interaction is considerable. The value of -/¢298 (Table 4) indicates that a -p significant concentration of the cation-molecule complex should be present when there are reasonable
197
quantities of NO + and C H 4 : At low temperatures, the formation of the complex should be even more favourable. The detection of NO +. CH 4 by mass spectrometric means would be difficult, owing to the similarity of the mass with that of NO + , and the deuterated analogue may be a better choice. Finally it is noted that, at the M P 2 / a u g - c c - p V T Z level of theory, the dipole moment of the complex (with respect to the centre-of-mass) is 4.05 Debye, indicating that it could be observed by microwave spectroscopy; the calculated rotational constants are 46.5, 5.4 and 5.0 GHz. This would be a very challenging experiment, as there appear only to have been two gas-phase microwave studies of cationic molecular complexes to date: A r . H + (Refs. 3 [28a,28b]) and A t . HCO + (Ref. [21]).
4.1. Discussion of multiphoton ionization spectra As noted in the introduction, there have been two studies of the N O . C H 4 using multiphoton ionization spectroscopy. In each case the electronic transition involved excites the NO 7r * electron to a NO Rydberg orbital, the 3 s orbital for the ,g, state (studied by Akiike et al. [7]), and the 3pTr orbital for the (~ state (as studied by Miller [8]). Vibrational frequencies were observed in both studies: For the A state there appeared to be a progression with two spacings of 27 and 43 cm -t whilst for the (~ state one progression was assigned, with a spacing of 96 c m - 1 initially, falling to 71 cm i to higher wavenumber. Assuming these progressions to be the intermolecular stretch (this assumption is based on the fact that the excitation of the ~-* electron to a Rydberg orbital on NO must change the electron distribution dramatically; additionally, if the CH 4 moiety were inside the orbit of the Rydberg electron, the intermolecular distance would be expected to change dramatically, as a charge-induced dipole effect would be present) then it may be seen that both of these are much lower than the value of ca. 172 cm-1 [the value of t, 2 at the M P 2 / 6 - 3 1 1 + + G(2df,2p) level of theory]. Obviously, it is likely that anharmonic effects are going to be important for a weakly-bonded complex; however, it is unlikely that they will lead to such a lowering of the frequency to the values seen in the MPI spectra, based on the observed lowering as seen in the studies on A r . NO + (Refs.
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E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
[1,5]). Also, the dissociation energies of the A and (~ states are ca. 216 and ca. 890 cm -~ (the latter value arises from the work of Miller (Ref. [8]), combined with the D'~ value of 121 cm 1 obtained in the work of Akiike et al. [7]). It is clear that the intermolecular vibrational frequencies are vastly different from those of the cation; additionally, so is the D O value, which may be calculated from the energy differences in Table 1, combined with the intermolecular vibrational frequencies (Table 3), yielding a value of ca. 3.8 kcal mol -~ (1330 cm 1), and this indicates that the bonding of the A and (2 states are much weaker than that of the cation. Consequently, the conclusion must be that as for A r . NO and K r . NO, the CH 4 molecule is mainly outside of the Rydberg orbital in both the A and the (~ states. Finally, with regard to the geometry, Akiike et al. [7] have concluded that the geometry of the ~, state is of C3v symmetry; the geometry of the cation, calculated here, is of Cs symmetry. Thus, assuming the geometry of Akiike et al. is correct, this is further evidence that the interaction of the NO and CH 4 in the A state is not the same as that of the cation, with dispersion effects dominating in the long-range interaction of the ,g, state, but c h a r g e - d i p o l e effects being dominant in the cation.
5. Conclusions The NO +. CH 4 complex has been studied using MP2 calculations, and relatively large basis sets. The geometry has been found to be a C s structure, in which the NO + is situated eclipsing one CH bond, and bisecting two others. The harmonic vibrational frequencies have been calculated both for the fully protonated and the fully deuterated forms; the normal modes, and isotopic shifts lead to the conclusion that the intermolecular vibrational modes are heavily mixed. The interaction energy was calculated, and it was shown that the NO +. CH 4 complex is relatively strongly bonded. Calculated thermochemical quantities indicate that the complex ought to be relatively easy to form; the calculated dipole moment and rotational constants indicate that the microwave spectrum should be quite strong. Consideration of vibrational frequencies and dissociation energies for the A and (~ excited electronic states of N O . CH 4
show that these are mainly dispersion bound complexes, with the CH 4 moiety outside of the Rydberg orbit.
Acknowledgements The authors are grateful to the EPSRC for the provision of computer time, both at ULCC and at the Rutherford Appleton Laboratories. Prof. J.M. Dyke is thanked for useful discussions. PM is grateful to the EPSRC and the M O D (Porton Down) for a C A S E studentship. E P F L is grateful to the M O D (Porton Down) for funding. T G W is grateful to the EPSRC for an Advanced Fellowship.
References [1] T.G. Wright, P. Hobza, V. Spirko, J. Chem. Phys. 100 (I 994) 5403. [2] I. Fourr& M. Raoult, Chem. Phys. 198 (1995) 1. [3] J.-M. Robbe, M, Bencheikh, J.-P. Flament, Chem. Phys. Lett. 210 (1993) 170. [4] T.G. Wright, J. Chem. Phys. 105 (1996) 7579. [5] A.M. Bush, T.G. Wright, V. Spirko, M. Jurek, J. Chem. Phys. 106 (1997) 4531. [6] Y. Ohshima, Y. Endo, J. Chem. Phys. 93 (1990) 6256. [7] M. Akiike, K. Tsuji, K, Shibuya, K. Obi, Chem. Phys. Lett. 243 (1995) 89. [8] J.C. Miller, J. Chem. Phys. 86 (1987) 3166. [9] A.M. Bush, J.M. Dyke, P. Mack, D.M. Smith, T.G. Wright, J. Chem. Phys. 105 (1996) 9804. [10] A.M. Bush, J.M. Dyke, P. Mack, D.M. Smith, T.G. Wright, J. Chem. Phys., in press. [11] Gaussian 94 (Revision C.3), M.J. Frisch, G~W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheesemans, T.A. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L, Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian, Pittsburgh PA, 1995. [12a] D.E, Woon, T.H. Dunning Jr., J. Chem. Phys. 98 (1993) 1358. [12b] R.A. Kendall, T.H. Dunning Jr., R.J. Harrison, J. Chem. Phys. 96 (1992) 6796. [12c] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007. [13] C. MOiler, M.S. Plesset, Phys. Rev. 46 (1934) 618. [14a] G.D. Purvis, R.J. Bartlett, J. Chem. Phys. 76 (1982) 1910. [14b] M. Urban, J. Noga, S.J. Cole, R.J. Bartlett, J. Chem. Phys. 83 (1985) 4041.
E.P.F. Lee et aL / Chemical Physics 224 (1997) 191-199
[14c] K. Raghavachari, G.W. Trucks, J.A. Pople, M. HeadGordon, Chem. Phys. Lett. 157 (1989) 479. [15] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [16] P. Hobza, R. Burcl, V. Spirko, O. Dopfer, K. Miiller-Dethlefs, E.W. Schlag, J. Chem. Phys. 101 (1994) 990. [17] J.A. Platts, S.T. Howard, K. Wozniak, Chem. Commun. 63 (1996). [18] G.I. Gellene, J. Phys. Chem. 100 (1996) 15393. [19] P. Mack, J.M. Dyke, T.G. Wright, Chem. Phys. 218 (1997) 243. [20] A. Nowek, J. Leszczynski, J. Chem. Phys. 105 (1996) 6389. [21] Y. Ohshima, Y. Sumiyoshi, Y. Endo, J. Chem. Phys. 106 (1997) 2977. [22a] S.E. Novick, S.J. Harris, K.C. Janda, W. Klemperer, Can. J, Phys. 53 (1975) 2007. [22b] M.F. Jarrold, L. Misev, M.T. Bowers, J. Chem. Phys. 81 (1984) 4369.
199
[23] I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, Chichester, UK, 1976. [24] O. Dopfer, G. Reiser, K. Miiller-Dethlefs, E.W. Schlag, S.D. Colson, J. Chem. Phys. 101 (1994) 974. [25] T.G, Wright, E. Cordes, O. Dopfer, K. Miiller-Dethlefs, J. Chem. Soc. Faraday Trans. 89 (1993) 1609. [26] M. Takahashi, J. Chem. Phys. 96 (1992) 2594. [27a] K. Tsuji, K. Shibuya, K. Obi, J. Chem. Phys. 100 (1994) 5441. [27b] K. Tsuji, K. Shibuya, K. Obi, Laser Chem. 15 (1995) 157. [28a] M. Bogey, H. Bolvin, C. Demuynck, J.L, Destombes, Phys. Rev. Lett. 58 (1987) 988. [28b] M. Bogey, H. Bolvin, C. Demuynck, J.L. Destombes, B.P. Van Eijck, J. Chem. Phys. 88 (1988) 4120.
Chemical Physics 224 (1997) 191-199
The geometric structure and stability of the NO + . complex Edmond
P.F.
CH 4
cationic
Lee *, Paul Mack, Timothy G. Wright *
Department of Chemistry, Universit3,of Southampton, Highfield, Southampton, S017 1BJ, UK
Received 30 July 1997
Abstract Ab initio calculations have been performed, mainly at the MP2 level of theory, using a variety of basis sets, to elucidate the structure of the NO +- CH 4 cationic complex. The complex has an equilibrium geometry of C s symmetry, in which the NO + moiety eclipses a C - H bond of the methane molecule. The geometry is compared to those of related complexes. Harmonic vibrational frequencies are also calculated, together with the interaction energy and some thermodynamic quantities for the complex formation, employing a number of the theoretical methods. In particular, the interaction energy was calculated at the CCSD(T) level of theory. The implications of these results on the resonance-enhanced multiphoton ionization (REMPI) spectroscopy of the NO - CH 4 complex are briefly discussed. © 1997 Elsevier Science B.V.
1. Introduction The NO +. CH 4 molecular complex is interesting as it consists of a closed core cation interacting with a molecular species. Recently, some effort has been put into the calculation of the geometry and vibrational frequencies of the Ar • NO + cationic complex [1-5], in which the closed shell NO + cation is interacting with a closed-shell atom. In the case of the molecular partner, CH4, there clearly arises the difficulty of deciding where the NO + moiety is positioned relative to the methane molecule. On first sight, it might be expected that the NO + fragment would be positioned to create the complex with the highest symmetry, viz, along a C 3 axis, either with the O or N atom pointing towards a H atom, or along
* Corresponding authors. Fax: +44-1703-593781; e-mail: [email protected], [email protected],uk
a C 3 axis which passes through the centre of a CH 3 face, with the latter seeming the more likely, since the hydrogens will be 6 + and the carbon will be 6-. (The latter geometry is that adopted by the CH 4 • HC1 complex [6].) In both cases, it is not obvious whether the structure with the N or O atom pointing towards CH 4 (see Fig. 1) would be the preferred one, because in the cation both the O and N atoms are positively charged [1] and hence both could be considered as electrophilic and therefore the binding atom. In addition to these possibilities, and by comparison with the predicted geometry of the A r - N O + complex [1,4], the CH 4 group could be positioned in a pseudo-T-shaped configuration. Consequently, the strategy that needs to be adopted is to determine which of the configurations are minima, and then which is the global minimum (should more than one minimum exist). The geometry o f the complex has added interest
0301-0104/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PI1 S030 I-01 04(97)00293-0
192
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
H
0
N
H,,,,,Itl C
H
i
H
[]
H
N
0
O
N
H ,,,H C
!
H.
H
I
Cl,,,,'"' H
H
[]
N
O
H
I
.Clll,,,,-'H
H Fig. 1. Stationary points of the NO+'CH4 cationic complex, under the restraint of C3v Symmetry, as calculated at the MP2(full)/6-31G * level of theory. These are all transition states, as indicated by the presence of imaginary frequencies, see text for details.
since recently, Akiike et al. [7] measured the (1 + 1) resonance-enhanced multiphoton ionization (REMPI) spectrum of NO • CH 4 via the A state (the A state of NO is formed when the 7r* electron on NO is excited to the 3s Rydberg orbital). The structure that was recorded therein was interpreted in terms of internal rotation of the C H 4 group, and a geometry of C3v symmetry was deduced by comparison with the work of Ohshima and Endo on CH 4 • HC1 (which was found to have C3v symmetry from the rotational spectrum) [6]. The interesting point about the A state of NO • C H 4 is that the radius of the Rydberg electron orbit of the A state of NO is expected to be similar to the diameter of CH 4, and so there is a competition as to whether the C H 4 group is inside the Rydberg orbit (giving essentially a Rydberg state, with a relatively strongly bonded N O + . C H 4 core), or outside (in which case the C H 4 moiety is bound only by dispersive forces). In order to decide this, it is necessary to have a good idea of the dissociation energy of the cation and its vibrational frequencies, in order to compare them to those of the A state. (If the A state is Rydberg in character, then the dissociation energy and vibrational frequencies should resemble those of the cation.) Comparison may also be made with the REMPI spectrum of the (~ state of N O . C H 4 (corresponding to a 3pTr ~ 7r* excitation on NO), which has been studied by Miller [8]. At this point it is worth noting that Bush et al. [9] in their work on the A state of Kr. NO, deduced that the krypton atom was outside the Rydberg electron orbit (on average), and that a similar conclusion held for the ~, state of A r . NO [10]. If this is the case for N O . C H 4 , then it is expected that the properties of the cation would be different from those of the A. and (~ state. In this work, the aim was to determine the geometry, vibrational frequencies and interaction energy of the ground electronic state of the NO +. C H 4 cationic complex.
2. C o m p u t a t i o n a l
details
All calculations were performed with Gaussian94 [11] using standard split-valence 6-31G and 6-311G basis sets, which were augmented with various standard diffuse and polarization functions. In addition,
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
the augmented correlation-consistent polarized triple zeta valence (aug-cc-pVTZ) basis set of Dunning and coworkers [12a,12b,12c] was also employed. Geometry optimization and hamaonic vibrational frequency calculations were carried out using M011erPlesset perturbation theory to second order (MP2) [13], with additional single point calculations performed at the CCSD(T) level [ 14a, 14b, 14c] in order to obtain more reliable interaction energies. (All calculations employ the frozen core approximation, unless explicitly noted otherwise.) Full geometry optimization calculations were carried out using analytic gradient methods, within the specified symmetry constraints. Whether the geometries obtained were minima or not was determined by the number of imaginary vibrational frequencies obtained in the analytic second derivative (frequency) calculations. One important point to be noted here is that the shallowness of the surface can lead to small imaginary frequencies if the optimization has not been forced to a tight convergence. In the work here, tight convergence thresholds were set, instead of the default values in the optimization procedure, if the lowest unprojected frequencies were found to be larger than 10i c m - J : for a perfect convergence, all vibrational frequencies should have real values, with six zero frequencies for a non-linear molecule, corresponding to rotation and translation. In some cases, if a tight optimization was not used, then the lowest unprojected frequencies were found to have values larger than 10i cm -~, and were found to affect the magnitude of the projected vibrational frequencies of the lowest intermolecular vibrational modes significantly. Interaction energies for the cation-molecule complex formation were initially calculated from the difference in the total electronic energies of the complex and the monomers with their respective basis sets. Counterpoise corrected interaction energies were obtained employing the full counterpoise correction (CP) of Boys and Bernardi [15], in order to correct for basis set superposition error (BSSE). Only one minimum was found in this study, but there were a number of transition states. All energies for the transition states found were counterpoise corrected for BSSE at the MP2(full)/6-311 + + G(2df,2p) level of theory. In addition, for the minimum geometry, as well as the 6-311 + + G(2df,2p)
193
basis set, the aug-cc-pVTZ basis set was also used at the MP2 level. In order to examine higher-order correlation effects on the interaction energy, single point CCSD(T)/aug-cc-pVTZ energy calculations were also performed at the MP2/aug-cc-pVTZ geometry. Finally, thermodynamic data were calculated under the rigid-rotor, simple harmonic oscillator (RRHO) approximation. (It should be noted that the MP2/aug-cc-pVTZ frequency calculation on the complex was not completed, owing to insufficient computing resources being available; the M P 2 / 6 3 1 1 + + G(2df,2p) frequencies were used in the evaluation of the thermodynamic data with the MP2/aug-cc-pVTZ interaction energies.)
3. Results Initial survey optimizations were performed at the MP2(full)/6-31G * level under C 3v symmetry. There are four possible isomers, as illustrated in Fig. 1. None of these structures were found to be minima, with the structures shown in Fig. l a and b both having two imaginary frequencies, and those in Fig. lc and d having four imaginary frequencies. Consequently, it appears that there is no minimum of C3v symmetry. Thus a minimum energy geometry was sought by reference to the previous calculations on A r - N O + (vide supra). These suggested a structure in which the methane is bonded off of the NO + axis, although the relative orientations of the two moieties is not immediately clear. By optimizing the likely structures of C S symmetry, two stationary points were found, which differed only in the orientation of the NO + moiety relative to CH4: These are shown in Fig. 2. The structure shown in Fig, 2a is a minimum on the potential energy surface, whereas that shown in Fig. 2b is a saddle point, i Next all of the six geometries (the four in Fig. 1, and the two in Fig. 2) were reoptimized at the MP2(full)/6-311 +
J There was one imaginary frequency (63.8i cm -~, of a" symmetry) even at the MP2/6-311 + + G(2dL2p) level; however, it should be noted that at the MP2/aug-cc-pVTZ level, this structure was found to be only 0.25 kcal m o l - I higher in energy than the minimum.
194
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
Side View
Front View
©
N
H3
H~
N
H2
~.
Fig. 2. Stationary points of the NO+.CH4 complex under C~ symmetry, and using various levels of theory. (a) Optimized geometry of the minimum energy structure, see text for details. (b) Saddle point (one imaginary frequency), see text for further details.
+ G(2df,2p) level of theory, and corrected for BSSE by a full CP correction, the results are shown in Table 1. As may be seen, with the rather large basis set used, the BSSE is quite small, and does not change the relative energy ordering, at least at this level of theory. Having noted this, any experiment will almost certainly detect an average geometry which samples both the minimum and the C s saddle point (see Fig. 2a and b), since the low-frequency vibrations imply that the molecule will be undergoing large amplitude motions, even with only the zero-point vibrational energy present. A series of calculations were then performed on the structure shown in Fig. 2a, the only minimum. The results of these calculations are summarized in Table 2. As may be seen, a reasonably thorough study o f the effects of diffuse and polarization functions, as well as the underlying valence basis set, has been made to ascertain whether the calculated geometry was reasonably stable with respect to variations in the overall basis set. It is clear that the calculated structure is very similar in all cases, and all levels of calculation carried out confirm that this structure is a minimum on the potential energy surface, as evinced by the all real computed vibrational frequencies presented in Table 3. Nevertheless, the intermolecular
bond distance, as measured between the C and N atoms (rcr~), is very sensitive to the basis set employed. Some trends appear in the computed values. First, the addition of a set of diffuse functions on all atoms ( + + ) seems to destabilize the intermolecular bond slightly, as inferred from the increase in the intermolecular bond length, when using the 6-31G * and 6-31 + + G * basis sets; however, this effect is smaller on going from 6-311G * * to 6-311 + + G * * than it is from 6-31G * to 6-31 + + G *, suggesting that the larger increase in rcN for the latter is possibly due to an inadequacy of the underlying 6-31G basis set. [The apparently more stable complex predicted here (shorter rcN) with the basis sets without diffuse functions may be considered as having a similar origin as that of the basis set superposition error.] Secondly, there is a minimal effect on going from M P 2 / 6 - 3 1 G * to M P 2 ( f u l l ) / 6 - 3 1 G * , suggesting, as might have been expected, that the combined c o r e - c o r e and c o r e - v a l e n c e correlation have minimal effects on the computed quantities considered here. Thirdly, it is clear that the polarization functions, in all cases, are having a strong influence on the description of the intermolecular bonding region, appearing to stabilize the bond. In summary, all of these trends appear to suggest that there is a subtle balance in the way that the basis set describes the complex. Clearly, both the valence and intermolecular regions of the system need to be described adequately with an underlying basis of at least triple-zeta quality; in addition, polarization functions are extremely important in stabilizing the complex. It should be noted that the total numbers of basis functions (nbasis) for the complex with the two
Table 1 Interaction energies for the six stationary points found at the MP2(full)/6-311 + + G(2df,2p) level of theory Structure Energy/E h
Interaction energy (no CP)/ kcal mol- i
Interaction energy(+CP)/ kcal mol - t
Fig. la Fig. lb Fig. lc Fig. ld Fig. 2a Fig. 2b
2.89 3.44 1.20 1.55 5.56 5.34
2.41 2.70 0.90 1.03 4.93 4.71
-
169.833676 169.834554 169.830973 169.831540 169.837935 169.837574
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
195
Table 2 Optimized geometric parameters for the C~ minimum energy structure of the NO +. C H 4 cationic complex Level of theory
MP2/ 6-31G"
MP2(full)/ 6-31G*
MP2/ 6-31 + + G *
MP2/ 6-311G* ~
MP2/ 6-311+ + G * ~
MP2/ 6-311+ + G(2df,2p)
MP2/ aug-cc-pVTZ
rCN/A
2.799
2.792
2.851
2.824
2.846
2.735
2.718
rNO///k
rcH ~/~,
1.105 1.092
1.104 1.092
1.105 1.093
1.087 1.093
1.087 1.093
1.083 1.088
1.084 1.089
rCH2/A
1.091
1.090
1.091
1.090
1.090
1.085
1.086
1.095 88.5 101.8 108.3 111.2 ±62.9
1.094 88.1 102.0 108.3 111.2 +62.9
1.094 87.5 99.3 108.2 111.2 +62.8
1.094 87.6 99.3 108.3 111.1 ±62.6
1,094 87.0 96.9 108.3 111.0 +62.6
1.090 87.3 99.9 108.5 111.1 ±62.6
1.092 86.0 99.7 108.4 111.1 -t-62.5
rcH 3, rcR4/A Z. NCH/° /ONC/° / HCH/° /_HICH3.4/° AOHJCH3.4/°a
a Where A represents a dihedral angle.
largest b a s i s sets e m p l o y e d , n a m e l y the 6-311 + + G ( 2 d f , 2 p ) and a u g - c c - p V T Z bases, are 142 a n d 230, r e s p e c t i v e l y , e v e n t h o u g h t h e s e t w o b a s e s m a y be c o n s i d e r e d to be o f s i m i l a r overall quality. A l t h o u g h
S i n c e the N O +. C H 4 c o m p l e x c o n s i s t s o f a dia t o m i c b o n d e d to a p o l y a t o m i c , there are five interm o l e c u l a r m o d e s : T h e r e are t h r e e o f a' s y m m e t r y a n d t w o o f a" s y m m e t r y . It is c l e a r f r o m the vj
rcN s e e m s to c o n t i n u e d e c r e a s i n g w i t h the i n c r e a s e o f b a s i s size, it s e e m s likely that f u r t h e r d e c r e a s e s
m o d e (the l o w e s t v i b r a t i o n o f a' s y m m e t r y ) , see T a b l e 3, that this i n t e r m o l e c u l a r vibrational fre-
w o u l d b e small, as the i n c r e a s e in n b a s i s f r o m the
q u e n c y is d e m o n s t r a t i n g a s t r o n g d e p e n d e n c e on the
6-311 + + G ( 2 d f , 2 p ) to a u g - c c - p V T Z b a s e s is v e r y c o n s i d e r a b l e already.
level o f theory: To a l e s s e r extent, this is true o f the o t h e r i n t e r m o l e c u l a r v i b r a t i o n s as well. In o r d e r to
Table 3 Harmonic vibrational frequencies for the C s minimum energy structure of the NO +. C H 4 cationic complex a'b Vibrational mode
MP2/ 6-31G*
MP2(full)/ 6-31G*
MP2/ 6-31 + + G *
MP2/ 6-311G* *
MP2/ 6-311 + + G * *
MP2/ 6-3ll + + G(2df,2p)
1 (a') I 2 (a') 1 3 (a') 1 4 (a') t 2 5 (a') t 2 6 (a') e 7 (a') NO 8 (a') a I 9 (a') t 2 10 (a') t 2 11 (a") 1 12 (a") 1 13 (a") t 2 14 (a") e 15 (a") t 2
113.9 152.2 166.2 1349.2 1421.8 1603.6 2101.4 3071.9 3218.5 3244.8 80.9 199.6 1433.6 1617.0 3192.5
114.3 154.8 168.8 1349.0 1422.5 1604.2 2106.2 3073.0 3219.9 3245.5 81.2 201.1 1434.0 1617.9 3194.6
102.5 (99.5) 144.4 (120.8) 167.7(137.4) 1345.9 (1016.4) 1414.1 (1068.1) 1583.5 (1120.3) 2102.6 (2102.1) 3064.8 (2169.4) 3203.1 (2371.9) 3233.4 (2391.2) 54.0 (42.9) 158.4 (114.6) 1422.9 (1073.0) 1581.3 (1118.7) 3187.1 (2361.7)
113.1 157.0 172.8 1313.9 1374.8 1563.9 2156.6 3042.8 3185.8 3213.7 67.9 197.7 1384.0 1573.3 3169.9
103.5 148.5 182.3 1313.6 1371.6 1563.1 2151.9 3039.4 3178.7 3211.4 52.7 161.1 1379.5 1560.3 3167.5
130.3 (126.0) 171.6 (136.8) 192.8 (166.3) 1308.5 (988.9) 1362.2 (1029.3) 1565.8 (1107.8) 2149.3 (2144.1) 3042.2 (2158.3) 3184.4 (2356.3) 3213.0 (2376.4) 77.3 (61.9) 215.4 (155.2) 1372.8 (1035.2) 1577.3 (1115.9) 3163.5 (2342.8)
a The symmetry symbols in the first column identify to which vibration of the isolated C H 4 moiety the vibrations belong; the 1 indicates an intermolecular vibration; the NO implies the vibration is the NO + stretch. b Frequencies given in parentheses are those corresponding to the fully-deuterated species, NO +. CD4.
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
196
Table 4 C a l c u l a t e d i n t e r a c t i o n e n e r g i e s , e n t h a l p i e s , e n t r o p i e s , G i b b s free e n e r g i e s a n d e q u i l i b r i u m c o n s t a n t s f o r the r e a c t i o n : N O + +
CH 4
NO + .
CH 4 Quantity AEJkcal
MP2/6-311 mol
i
A Ee + CP/kcal
mol
i
A H 0 =- D 0 / k c a l
mol - i
A/q298 ( C P ) / k c a l m o l - i AS298/cal mol- t K i AG298 ( C P ) / k c a l K v29s
+ + G(2df,2p)
-5.50
-6.19
- 4.94
- 5.63
- 3.81
-- 5,46 b
- 4.50"
- 4.33 ~ - 4.72 ~ - 17.8 ~'
+ 1.11
+ 0.43"
+ 0.58"
0.15
0.49"
a W h e r e the v i b r a t i o n a l c o n t r i b u t i o n h a s b e e n c a l c u l a t e d u s i n g the M P 2 / 6 - 3 1 1 C a l c u l a t e d at the M P 2 / a u g - c c - p V T Z
CCSD(T)/aug-cc-pVTZ
- 4.89 ~ - 17.8"
- 4.20 -- 17.8
moli
MP2/aug-cc-pVTZ
0.38 ~
+ + G(2df,2p) vibrational frequencies.
geometry.
gain a better insight into the nature of the vibrational modes, the normal coordinates were examined, and also the vibrational frequencies of the fully deuterated species were calculated in a couple of selected cases: MP2/6-31 + + G* and MP2/6-311 + + G(2df,2p), values included in parentheses in Table 3. Neither of these lines of attack yielded an unambiguous assignment of the modes; in particular, the intermolecular stretch was not obviously identifiable. It seems clear that the latter will have a' symmetry; however, the two most likely candidates, from the normal modes (v 2 and v3), seem to be a mixture of stretching and bending. From the normal mode analysis, the ~'2 vibrational motion appears to have a stronger contribution from the intermolecular stretch, and so is tentatively assigned to be such. It is not obvious how the intermolecular stretch would be~ have upon deuteration, but comparison with the deuteration shifts obtained by Hobza et al. [16] in their work on the phenol-water cation appears to suggest that the intermolecular stretch should decrease slightly upon deuteration, although the effect may be larger here, on percentage mass considerations. This is at least consistent with the observed behaviour here (Table 3). By following the usual convention for naming the intermolecular vibrations, the following tentative assignments can be made: t,~ (in-plane bend); v 2 (stretch); v 3 (in-plane wag); ~'ll (torsion); and ~'t2 (out-of-plane wag); where in-plane implies the C~ symmetry is retained, and out-of-plane implies that it is lost. The intramolecular vibrational frequencies change very little upon complexation (uncomplexed values not given here), as expected, owing to the weak interaction. Of significance, how-
ever, is that the degenerate vibrations of methane do change noticeably, with the t 2 vibrations splitting into two vibrations of a' symmetry and one of a" symmetry, with the e vibration splitting into a vibration of a' symmetry and one of a" symmetry (Table 3). Table 4 shows the calculated interaction energies at the three highest levels of theory (excluding the values of Table 1), together with calculated thermochemical quantities. It may be seen that the computed BSSE is quite small (ca. 0.6 kcal tool l), which reflects the size of the basis sets used, and demonstrates that they are close to being complete. The computed A E c at the CCSD(T)/aug-ccp T V Z / / M P 2 / a u g - c c - p V T Z level, including the CP correction for BSSE is - 5 . 4 6 kcal tool 1. The fact that this value obtained from the higher-order correlated CCSD(T) calculations is only slightly less negative than the MP2 counterpart, suggests that the high-order correlation effects on the computed relative energies are small, and that the CCSD(T) optimized geometry would probably be very close to the MP2 geometry reported here.
4. Discussion
Considering first the geometry of the complex, it is clear that the C H 4 moiety is not bonding through any of its CH o- bonds, as has been observed in recent work on ylides [17]. If the C H 4 moiety is considered as a sphere, then the Jacobi angle may be calculated to be 69.8 °, with the Jacobi bond length of 2.863 A, at the MP2/aug-cc-pVTZ level of theory.
E.P.F. Lee et al. / Chemical Physics 224 (1997) 191-199
It is remarkable how similar this geometry is to that of both A r . NO + (Ref. [4]) and A r . CO~-, (studied recently by Gellene [18]); there are also large similarities with the structures of N O + - X ( X = H 2 0 , CO 2 and N 2) [19]. Of interest, is that the geometry of the A r . HCO ÷ complex (isoelectronic with A t . NO ÷) is linear, as determined from ab initio [20] and microwave [21] studies. It is clear that the explanation of the geometries of these complexes is not straightforward. One picture that has been put forward is that of the H O M O - L U M O interaction [22a,22b], where the orientations of the H O M O on the electron donor ( C H 4 here) and the L U M O on the electron acceptor (NO ÷ here) determine the geometry. The L U M O here would be the ~ * orbital on NO, with the H O M O being an sp 3 hybrid orbital on methane [23], this would indicate that, subject to steric interactions, the NO + molecule would attempt to overlap one of its lobes with the sp 3 orbital, which has density on and between the H atoms of a pair of CH bonds. Indeed the minimum energy geometry (Fig. 2a) does appear to suggest that this picture works here, and is also consistent for A r . NO÷: this is despite the fact that the NO ÷ moiety carries + 0.98 e at the MP2 level, employing Mulliken population analysis, implying that almost no transfer of electronic charge occurs. It would appear that this geometry must also have a maximized combination of charge-induced dipole and dispersion interactions. (It should be noted that Mulliken charge densities are very basis set dependent, but the overall positive charge computed on NO ÷ is over + 0 . 9 2 e in all cases.) Of course, this explanation does not appear to hold for the linearity of the A r . HCO ÷ complex. The intermolecular vibrational frequencies are of a magnitude comparable to those in the hydrogenbonded phenol-water complex [16], indicating that the interaction is reasonably strong. The interaction energy for NO ÷. CH 4 is ca. 5.5 kcal mo1-1, which is equivalent to 2100 cm -~ (0.26 eV); this may be compared to the binding energies of the phenol-water complex (4600 cm 1) [24], the phenol-methanol complex (5400 c m - i ) [25] and A r . NO + (950 c m - 1) [l,26,27a,27b], showing that the interaction is considerable. The value of -/¢298 (Table 4) indicates that a -p significant concentration of the cation-molecule complex should be present when there are reasonable
197
quantities of NO + and C H 4 : At low temperatures, the formation of the complex should be even more favourable. The detection of NO +. CH 4 by mass spectrometric means would be difficult, owing to the similarity of the mass with that of NO + , and the deuterated analogue may be a better choice. Finally it is noted that, at the M P 2 / a u g - c c - p V T Z level of theory, the dipole moment of the complex (with respect to the centre-of-mass) is 4.05 Debye, indicating that it could be observed by microwave spectroscopy; the calculated rotational constants are 46.5, 5.4 and 5.0 GHz. This would be a very challenging experiment, as there appear only to have been two gas-phase microwave studies of cationic molecular complexes to date: A r . H + (Refs. 3 [28a,28b]) and A t . HCO + (Ref. [21]).
4.1. Discussion of multiphoton ionization spectra As noted in the introduction, there have been two studies of the N O . C H 4 using multiphoton ionization spectroscopy. In each case the electronic transition involved excites the NO 7r * electron to a NO Rydberg orbital, the 3 s orbital for the ,g, state (studied by Akiike et al. [7]), and the 3pTr orbital for the (~ state (as studied by Miller [8]). Vibrational frequencies were observed in both studies: For the A state there appeared to be a progression with two spacings of 27 and 43 cm -t whilst for the (~ state one progression was assigned, with a spacing of 96 c m - 1 initially, falling to 71 cm i to higher wavenumber. Assuming these progressions to be the intermolecular stretch (this assumption is based on the fact that the excitation of the ~-* electron to a Rydberg orbital on NO must change the electron distribution dramatically; additionally, if the CH 4 moiety were inside the orbit of the Rydberg electron, the intermolecular distance would be expected to change dramatically, as a charge-induced dipole effect would be present) then it may be seen that both of these are much lower than the value of ca. 172 cm-1 [the value of t, 2 at the M P 2 / 6 - 3 1 1 + + G(2df,2p) level of theory]. Obviously, it is likely that anharmonic effects are going to be important for a weakly-bonded complex; however, it is unlikely that they will lead to such a lowering of the frequency to the values seen in the MPI spectra, based on the observed lowering as seen in the studies on A r . NO + (Refs.
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[1,5]). Also, the dissociation energies of the A and (~ states are ca. 216 and ca. 890 cm -~ (the latter value arises from the work of Miller (Ref. [8]), combined with the D'~ value of 121 cm 1 obtained in the work of Akiike et al. [7]). It is clear that the intermolecular vibrational frequencies are vastly different from those of the cation; additionally, so is the D O value, which may be calculated from the energy differences in Table 1, combined with the intermolecular vibrational frequencies (Table 3), yielding a value of ca. 3.8 kcal mol -~ (1330 cm 1), and this indicates that the bonding of the A and (2 states are much weaker than that of the cation. Consequently, the conclusion must be that as for A r . NO and K r . NO, the CH 4 molecule is mainly outside of the Rydberg orbital in both the A and the (~ states. Finally, with regard to the geometry, Akiike et al. [7] have concluded that the geometry of the ~, state is of C3v symmetry; the geometry of the cation, calculated here, is of Cs symmetry. Thus, assuming the geometry of Akiike et al. is correct, this is further evidence that the interaction of the NO and CH 4 in the A state is not the same as that of the cation, with dispersion effects dominating in the long-range interaction of the ,g, state, but c h a r g e - d i p o l e effects being dominant in the cation.
5. Conclusions The NO +. CH 4 complex has been studied using MP2 calculations, and relatively large basis sets. The geometry has been found to be a C s structure, in which the NO + is situated eclipsing one CH bond, and bisecting two others. The harmonic vibrational frequencies have been calculated both for the fully protonated and the fully deuterated forms; the normal modes, and isotopic shifts lead to the conclusion that the intermolecular vibrational modes are heavily mixed. The interaction energy was calculated, and it was shown that the NO +. CH 4 complex is relatively strongly bonded. Calculated thermochemical quantities indicate that the complex ought to be relatively easy to form; the calculated dipole moment and rotational constants indicate that the microwave spectrum should be quite strong. Consideration of vibrational frequencies and dissociation energies for the A and (~ excited electronic states of N O . CH 4
show that these are mainly dispersion bound complexes, with the CH 4 moiety outside of the Rydberg orbit.
Acknowledgements The authors are grateful to the EPSRC for the provision of computer time, both at ULCC and at the Rutherford Appleton Laboratories. Prof. J.M. Dyke is thanked for useful discussions. PM is grateful to the EPSRC and the M O D (Porton Down) for a C A S E studentship. E P F L is grateful to the M O D (Porton Down) for funding. T G W is grateful to the EPSRC for an Advanced Fellowship.
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