12232
J. Phys. Chem. 1993,97, 12232-12238
Structure and Dissociation Energy of the Weakly Bound Complex CHs+(Hz) Seung-Joon Kim,’. Peter R. Scbreiner,’hbPaul von Ragu6 Scbleyer,lhband Henry F. Schaefer III*Ja Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, and Institut f i r Organische Chemie der Universitiit Erlangen-Niirnberg, Henkestrasse 42, D-91054 Erlangen, Germany Received: September 13, 1993’ The possible low-lying stationary points of CHs+(H2) have been investigated using high level ab initio quantum mechanical techniques. All structures were optimized up to the TZ2P CISD level of theory. The global minimum structure (1) was also optimized at theTZ2P CCSD(T) and TZ2P+d CCSD levels. Four C,structures, which have H2 bound to one of two protons of the three-center-two-electron bond of the CHI+ subunit, have essentially the same energy. Consequently, several internal degrees of freedom in CHs+(H2) are virtually completely unrestricted. We determined the dissociation energy DOof CHs+(Hz) to be 1.46 kcal/mol [TZZP+d CCSD(T)]. Harmonic vibrational frequencies have been evaluated for all structures at the TZZP S C F level of theory; for the energetically lowest-lying structure ( l ) , we also determined the vibrational frequencies up to the TZ2P CCSD level. The H-H stretching frequency shift (-83 cm-I) predicted theoretically is in excellent agreement with the recently determined experimental value (-83.6 cm-l). The average value of theoretical rotational constants for the energetically lowest lying stationary points (1-4) and one other minimum (7) compares moderately well with the experimental result.
behavior.19JO An important feature is that the first two CH4 Introduction ligands attack the two protons of the 3c-2e bond. This result is Protonated alkanes (C,Hz,+p)+ are highly reactive intermein qualitatively good agreement with the experimentalobservation diates in the acid-catalyzed transformations of hydrocarbons as of a large difference in AHo,,+, between n = 2 and n = 3.7J The well as in various electrophilic reactions? The simplest protonated experimentaland theoretical binding energiesbetween CH5+and alkane, the methonium ion (CHs’), exemplifies this class of H2 were found to be less than 2 kcal/mol by Hiraoka, Kudaka, nonclassical ions. These penta (or higher) coordinatedcarbonium and Yamabe.21 Boo et al.9 estimated a binding energy of 1-2 ions involve at least one threexenter-electron (3c-2e) b ~ n d . ~ . ~ kcal/mol through a correlation of the H-H stretching vibrational The history of CH5+ dates back to its first discovery during frequency shifts and binding energies of hydrogen cluster ions mass spectroscopicalstudies on the protonation of alkenes and H,+ (n = 5,7,9,11, 13, 15).22 In the present paper, the primary alkanes in 1952 by Tal’roze and Lyubimova.4 While the authors goal is to predict the binding energy between H2 and CH5+. In easily observed cations derived from alkenes, the only protonated addition, various possible structures, and their harmonic vibraalkane to be detected was CH5+. The ion was describedvia “high tional frequencies and relative energies, are obtained using large pressure” mass spectrometry and it is now a common gas-phase basis sets and sophisticatedmethods for the description of electron reagent for chemical ionization mass spectrometry.5 Although correlation. We will compare the dissociation energy of CH5+CH5+ was proposed as a reactive intermediate in super acid (H2) with similar complexes, like H3+(H2) and CzHs+(Hz). solution reactions$ the experimental geometrical parameters for CHs+ have not yet been reported. Theoretical Approach The many earlier theoretical studies1”14on CH5+all concluded that the global minimum of CH5+ has C, symmetry. The more We used DZ, DZP, TZ2P, and TZ2P+d contracted Gaussian recent investigation^,^^-^^ however, suggest that the two C, basis sets in this research. The DZ basis set was the standard structures and the C , structure have essentially the same energy H u z i n a g a - D ~ n n i n g ~double ~ , ~ ~ zeta C(9sSp/4s2p) and H(4s/ at 0 K, which implies that there is virtually no energy barrier to 2s) contracted basis. The DZP basis improves upon the DZ basis complete hydrogen scrambling. The harmonic vibrational freby adding a single set of polarization functions (d functions on quencies for CH5+ have been predicted theoretically to aid the carbon and p functions on hydrogen) with orbital exponents of experimental detection of this ~ a t i o n . ’ ~Thermodynamic J~ data (Yd(c) = 0.75 and ap(H) = 0.75. While the T Z basis consisted (AHon-l,,,and ASo,,+,) for the reaction CH5+(CH4),1 CHI of the Huzinaga-Dunning (lOs6p/5s3p) set for C and the (5s/ + CHs+(CH4), (n = 1-9) have been measured using a pulsed 3s) set for H, the TZ2P basis was augmented with two sets of electron-beam high-pressure mass spectr~meter.~,* polarization functions with exponents of ad(C) = 1.5,0.375 and A very recent study on the IR spectrum of CHs+(H2) by Boo ap(H) = 1.5,0.375. The TZ2P basis set was augmented with d and Lee9is an attempt to indirectly access the structural features functions on H (for hydrogens 2, 3, 7, and 8) with ad(H) = 1.0 of CH5+. Since hydrogen scrambling occurs easily in CH5+,the to give the TZ2P+d basis. idea is to stabilize the structure through attachment of small The self-consistent field (SCF), the single and doubleexcitation neutral molecules, e.g., H2 or CH4. One may assume that the configuration interaction (CISD), and coupled cluster including attachment mainly restricts the proton rearrangements but does all single and double excitations(CCSD) methods were employed. not significantly alter the structure of CH5+. Using the wellIn addition, in the most important cases the effects of triple characterized structures for H3+, CH4, and H2 as a reference for, excitationswere added perturbativelyto the CCSD wave function e.g., the shifts in vibrational frequencies, one should be able to [CCSD(T)]. All structures were initially fully optimized using deduce the CH5+ structure. On the basis of the present study, analytic gradient techniques at the SCF25 and CISD26 levels of we will discusss about the effect of molecular hydrogen attachment theory with the DZ, DZP, and TZ2P basis sets. The CISD to CH5+ in this context. energies were corrected for unlinked quadruple excitations by Theoreticalinvestigationson the structures and binding energies using Davidson’s and the correctedenergies are denoted of C H ~ + ( C H ~ ) , C ~for U nS=~ 1~ ~4 give S informationonclustering as CISD+Q. For the lowest-lying structures, we included *Abstract published in Advance ACS Absrracrs, November 1, 1993. additional electron correlation for their geometry optimizations,
+
0022-3654/93/2097- 12232%04.00/0 0 1993 American Chemical Society
Structure of the Weakly Bound Complex CH5+(H2)
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12233 H ?.?if H, ,
I
,
I
,
*I
,
,
H,
I
/
1 198 '%, ,
I
I 198
H, f
0741
3 C, rym ( 0 )
10 C,, sym (2)
Figure 2. Further CHs+(H2) low-lying structures of C, and Cksymmetry, optimized at the TZ2P CISD level: (a) structures 7 and 8, (b) structures 9 and 10. The number in parentheses indicates the number of imaginary frequencies.
individual monomers (CH5+ and H2) with and without ghost orbitals at the optimized CH5+(H2) geometry.
Results and Discussion 5 C, sym. ( 1 )
6 C, sym (2)
Figure 1. Six CHs+(H2) low-lying stationary points of C, symmetry, optimized at the TZ2P CISD level: (a) structures 1 and 2, (b) structures 3 and 4, (c) structures 5 and 6. The number in parentheses indicates the number of imaginary frequencies.
namely, CCSD and CCSD(T),28 and increased the basis setup to TZ2P+d. With the CISD, CCSD, and CCSD(T) methods, one core and one virtual molecular orbital were kept frozen. At the SCF level of theory, harmonic vibrational frequencies were obtained from analytic second derivative methodsz9whereas at correlated levelsof theory they weredetermined by finite central differences of analyticgradients. SCFlevel zero-point vibrational energies (ZPVE) and vibrational frequencies were scaled by a factor of 0.91 to account for anharmonicity and electron correlation.30 At the CISD and CCSD levels, the scaling factor was 0.95 to correct primarily for anharm~nicity.~' For the separated species CH5+ and H2, we used a "supermolecule'' approach, composed of the two molecules separated by about 500 A, to avoid the size-consistency problem associated with the truncated CI method. The basis set superposition error (BSSE) was obtained from the single-point energies for the
Structures. In analogy to the CH5+(CH&,7*sstructures, the first H2 attaches to one of the two protons involved in the 3c-2e bond of the CHs+(C,) structure. Six possible structures arising from this approach were optimized at various levels of theory and are shown in Figure 1. Four more energetically lower-lying stationary points are presented in Figure 2. Optimization of C1 structures arising from H2 approaching the C, transition structure of CH5+always converged to structure 1, regardless of the starting geometry. Among these optimized structures, we found three true minima, with the global minimum being 1, C,. For the latter, higher levels of theory were employed to further optimize the geometry. Table I contains selected geometrical parameters for structure 1at various levels of theory. Note that electron correlation effects are important and change the geometrical parameters significantly. In going from the TZ2P SCF to the TZZP CISD level, the bond distance between H(2) and the center of the H2 moiety, rzc,decreases from 2.086 to 1.890 A, while the Hz bond length, r23, of the CH5+ moiety increases from 0.878 to 0.928 A. The C-H(2) and C-H(3) bond distances decrease by about 0.020.03 A. However, the geometries change very little from TZZP to TZZP CCSD(T). The effect of d-functions on four (2, 3, 7, and 8) of the seven hydrogens is minimal at the SCF level, but
Kim et ai.
12234 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE I: Theoretical Geometrical Parameters for the Energetically Lowest-Lying Structure of CHs+(H2)(1) at Various Levels of Theow.
r1z r13 r14
rls r23
r 3 ria elZb
eZl4 8,1s
DZP
SCF TZ2P
TZ2P+d
DZP
CISD TZ2P
1.234 1.220 1.093 1.081 0.882 2.016 0.740 159.8 80.3 111.0 117.7
1.233 1.219 1.089 1.077 0.878 2.086 0.739 161.1 80.5 111.2 117.7
1.232 1.219 1.OS9 1.077 0.879 2.088 0.739 161.1 80.5 112.2 117.6
1.213 1.192 1.105 1.089 0.943 1.890 0.747 164.7 76.7 109.6 118.8
1.211 1.189 1.097 1.082 0.928 1.890 0.744 164.4 78.2 109.8 118.4
CCSD TZ2P
TZ2P+d
DZP
1.202 1.180 1.099 1.082 0.945 1.876 0.745 165.8 76.7 109.4 118.6
1.215 1.192 1.109 1.092 0.951 1.875 0.750 165.0 76.4 109.4 118.9
1.213 1.189 1.100 1.084 0.936 1.877 0.749 164.7 77.9 109.7 118.5
CCSD(T) DZP TZ2P 1.214 1.189 1.111 1.093 0.962 1.853 0.750 165.7 75.7 109.2 119.1
CHj+ -
1.213 1.187 1.103 1.086 0.941 1.854 0.749 165.3 77.4 109.5 118.7
C
TZ2P 1.200 1.200 1.104 1.086 0.936
-
78.5 109.6 119.2
a Bond lengths in angstroms, angles in degrees. * The subscript c refers to the center of the HZ moiety in CHs+(Hz). The reported geometrical parameters for CH5+ are at the CCSD(T) level of theory.
TABLE 11: Rotational Constants for Structures 1-4, and 7 at Various Levels of Theory Structure 1 (Global Minimum) A
B C
DZP SCF
TZ2P SCF
DZP CISD
4.046 0.737 0.732
4.072 0.732 0.727
4.054 0.808 0.806
TZ2P CISD 4.088 0.812 0.808
DZP CCSD 4.035 0.812 0.810
TZ2P CCSD 4.066 0.8 15 0.812
DZP CCSD(T) 4.034 0.821 0.8 19
TZ2P CCSD(T) 4.061 0.824 0.921
Structure 2 A
B C
DZP SCF 4.057 0.734 0.7 12
TZ2P SCF 4.092 0.81 1 0.787
DZP CISD 4.057 0.808 0.785
TZ2P CISD 4.092 0.811 0.787
DZP CISD 3.905 0.814 0.805
TZ2P CISD 3.980 0.822 0.814
DZP CISD 3.905 0.814 0.808
TZ2P CISD 3.980 0.823 0.814
DZP CISD 3.614 0.698 0.683
TZ2P CISD 3.649 0.706 0.689
Structure 3 A B C
DZP SCF 3.927 0.745 0.736
TZ2P SCF 3.973 0.740 0.731
Structure 4 A
B C
DZP SCF 3.927 0.745 0.736
TZ2P SCF 3.973 0.740 0.73 1 Structure 7
A
B C
DZP SCF 3.551 0.639 0.621
TZ2P SCF 3.545 0.63 1 0.614
it is significant at the CISD level, where the structure appears to become more compact (the bond lengths for the hydrogens 2 and 3 decrease as well as the distance to the center of mass of hydrogens 7 and 8 becomes shorter). Consequently, the dissociation energy (discussed below) for the loss of H2 from CH5+(H2) increases. A comparison of structure 1 with the CHs+C, structure17at the TZZP CCSD(T) level shows an elongation of the r12 and r 2 3 bond distances by 0.013 and 0.011 A, respectively, while r13 is shortened by 0.013 A due to the attachment of H2. The bond elongation of r12 and r23 is reasonable because their bonds are weakened by the electrostatic interaction between H(2) and the H2 moiety. This phenomenon also is observed in CHs+(CH4)19 and Hs+32 clusters. Structure 2 is the transition state for the out-of-plane rotation of the H2 moiety. A natural bond orbital analysis33 shows that structure 1 is more stable than structure 2 due to (a) the smaller electron donor effect from the bonding H(7)-H(8) u-molecular orbital to the antibonding u*-CH(2) orbital; and (b) the larger *-donating character of the H(7)-H(8) bonding u-orbital into the empty out-of-plane p-orbitals of H(2) and H(3). Conse-
quently, the distance between CHs+ and H2 ( r a ) of 1 (1.890 A) is shorter than that of 2 (1.915 A). The other geometrical parameters for structures 1 and 2 remain largely unaffected. Figure l b shows structure 3 (C,), a minimum, and structure 4 (Cs),a transition state for the H2 rotation. The geometrical parameters for structure 3 are very similar to those of structure 1except for thedifferent attachment sitesof H2. The C,symmetry transition structure 5 (Figure IC)is involved in the H2 migration that connects 1 and 3. The bond distances r k and r3Efor 5 are about 0.4 A longer than those of structures 1 and 3. The C, structure 6 has two imaginary vibrational frequencies, which correspond to the in-plane and out-of-plane rotations of Hz. ByattachingH2 toH(4), weobtained theCSstructure7(Figure 2a), which is also a minimum. The bond distance r k of 2.212 A is 0.322 A larger than raof 1 and the angle is almost linear. The C, structure 8 is the transition state for the H2 migration between 1 and 7. The bond distance r k for structure 8 increases by 0.144 A relative to that for structure 7 and the angle bLk decreases from linear to 151.1O . We also examined two low-lying stationary points of CZ, symmetry (9,10, Figure 2b) correspondingto H2 attachment to
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12235
Structure of the Weakly Bound Complex CHs+(Hz)
TABLE III: Harmonic Vibrational Frequencies (in cm-l, SCF Scaled by 0.91, CISD and CCSD Scaled by 0.95) of CHs+(Hz) (1) at the Various Levels of Theory’ ~
assignment H r H 8 str (a’) asym CH3 deg str (a”) syml CH3 deg str (a’) sym CHI breath. (a’) H r H 3 str (a’) CH2 (HrH3) asym str (a’) CHI (HrH3) sym str (a’) asym CHI bend (a”) CHI rock/bend (a’) CH3 bend/rock (a’) asym CH3 rock (a”) CH3 deg bend/rock (a’) Hr(H7,Hn) asym str (a”) torsional twist (a”) Hr(H7,Hd sym str (a’) H2Hd-h wag (a’) H2H7H8 twist (a”) torsional twist (a”) 0
DZP SCF 4142 309 1 3022 2941 2767 2100 1527 1446 1432 1280 1255 947 465 306 23 1 165 104 75
TZ2P SCF 41 19 3063 2993 2917 2742 2080 1532 1455 1440 1283 1257 966 487 294 233 156 104 76
DZP CISD 4225 3161 3072 2967 2678 2237 1553 1441 1429 1285 1270 820 523 394 29 1 235 115 109
TZ2P CISD 41 18 3115 3033 2934 2640 2202 1576 1455 1427 1280 1255 877 549 340 312 224 124 65
DZP CCSD 4163 3130 3041 2934 2644 2218 1533 1426 1415 1270 1261 794 523 400 295 240 116 109
TZ2P CCSD 4107 308 1 2998 2898 2600 2179 1556 1439 1410 1262 1242 856 545 340 316 230 124 58
CHs+ b
3079 2993 2891 2633 2295 1547 1427 1401 1236 1234 856
-
145
-
Atoms are numbered on the left-hand side. At the TZ2P+f CCSD level of theory.
TABLE I V Harmonic Vibrational Frequencies (in cm-l, Scaled by 0.91) for the Different C, Stationary Points of CHs+(Hz) at the TZ2P SCF Level of Theory CH
