Computational study of methane activation by mercury(II) complexes

— —� �

Computational Study of Methane( )Activation by Mercury II Complexes

THOMAS R. CUNDARI, AKIHIKO YOSHIKAWADepartment of Chemistry, University of Memphis, Memphis, Tennessee 38152

Received 17 September 1997; accepted 16 January 1998

ABSTRACT: A computational investigation of methane activation by HgII

Ž .complexes is reported. Calculated geometries and energetics of Hg II -containingreactants and products are consistent with available experimental data for awide range of diverse ligand types. Calculated reaction enthalpies and activationbarriers for HgII complexes cover a wide range of values for different ligands.This diversity suggests that the kinetics and thermodynamics of methane

Ž .activation by Hg II and related medium-valent complexes can be tailoredthrough rational modification of the ligand environment. Calculated activation

Ž .barriers and reaction enthalpies for methane activation by Hg II complexesindicates that harder, more electronegative, ligands are kinetically andthermodynamically preferred. Potential donor groups on the activating ligandcan stabilize the transition state versus the ground state reactants and henceresult in substantially lower methane activation barriers. � 1998 John Wiley &Sons, Inc. J Comput Chem 19: 902�911, 1998

Keywords: catalysis; effective core potentials; mercury chemistry; methaneactivation; quantum chemistry

Correspondence to: T. R. Cundari; e-mail: [email protected]

Contract�grant sponsor: National Science Foundation; con-tact�grant number: CHE-9614346

Contact�grant sponsor: Petroleum Research FundThis article includes Supplementary Material available from

the authors or via the Internet at ftp.wiley.com�public�journals� jcc� suppmat� 19�902 or http:�� journals.wiley.com�jcc

( )Journal of Computational Chemistry, Vol. 19, No. 8, 902 �911 1998� 1998 John Wiley & Sons, Inc. CCC 0192-8651 / 98 / 080902-10

METHANE ACTIVATION

Introduction

onversion of methane to methanol is eco-C nomically important, because the latter is amore valuable and more easily transportable liq-uid. The inertness of methane makes it difficult toobtain methanol in high yield.1 It is often difficultto stop oxidation of methane at the first step, asoxidation products are typically more reactive thanmethane. The first, and typically the most difficult,step in catalytic methane conversion is selectiveactivation of a C—H bond. An increasing numberof complexes that effect this reaction have beenstudied over the past decade.2 Complexes thatactivate C—H bonds through nonradical path-ways can be loosely divided into three groups. The

Ž 0 0 n.first group is high-valent d and d f com-2 � 4 � �plexes that activate by 2 � 2 addition of C—H

bonds across a metal�ligand single or multiplebond. The second group is low-valent, electron-rich, late transition metal complexes that activateC—H bonds by oxidative addition.2, 5 The third,and perhaps least understood, group possesseslate but electrophilic metals, for instance, Pt II orHgII.6 � 10 Alkane activation by these so-calledmedium-valent complexes has attracted much in-terest. Shilov demonstrated, almost 30 years ago,that Pt II salts activate C—H bonds and yield oxi-dized products.11 However, little mechanistic in-formation was available because of the complexnature of the reaction. Recently, through the workof several groups, most notably those of Sen,Labinger, and Bercaw, progress has been made inunderstanding Pt catalysts.6 � 8 Periana et al. haverecently reported a new family of high-yield, elec-

� Ž . �trophilic catalysts e.g., Hg OSO H , for methane3 2Žconversion to methyl bisulfate which can be hy-

. 10drolyzed to methanol .The main advantages of electrophilic methane

activators are that they are stable in the presenceŽ .of O and H O unlike most organometallics .2 2

From a chemical point of view, a big impedimentto their development is lack of an intimate under-standing of the methane activation mechanism. AsSen notes, ‘‘detailed mechanistic studies are re-quired to fully understand the reactivity profile ofthe electrophilic metal species and how it can beinfluenced by the proper choice of the metal andthe ligands.’’6 Numerous theoretical analyses of

methane activation by high- and low-valent com-plexes have been reported.12, 13 Previous workshowed a great degree of similarity, particularlyearly in the reaction coordinates when comparing� �2 � 2 and oxidative addition by high- and low-valent methane activators, respectively.12c, e Com-putational studies of methane activation bymedium-valent complexes are rare. Vinogradovaand Shestakov14 have reported an extended Huckel¨analysis of m ethane activation by cis-

II Ž .Pt Cl H O .2 2 2This article outlines a quantum chemical study

of methane activation by HgII salts, reaction 1, thefirst step in a putative catalytic cycle for methaneconversion. We focus on HgII

L —Hg—L � H C—Hs a 3

� Ž .L —Hg—CH � H—L 1s 3 a

Ž L � L � H, F, Cl, Br, I, OH, SH, CN, NC, SCN,a s

.NCS, NH , CH , C H , CF , CCl2 3 2 5 3 3

complexes in this initial research because the lackof an oxidation addition pathway simplifies the

Ž . Ž .analysis. Activating L and spectator L lig-a s

ands, which are soft, intermediate, and hard an-ionic bases, were studied to probe their effect on

Ž . Ž .reactants L HgL , 1 , products L HgCH , 2 , ands a s 3Ž� �� .transition states L Hg L �� CH , 3 , and hences a 4

the kinetics and thermodynamics of methane C—H� � IIactivation by 2� � 2� addition across a Hg —

ligand bond. For this study, we have assumed thatL and L are equivalent. The recently reporteda s

HgII methane conversion catalyst is complicated.10

Our goal at this stage is not to model the catalystexactly, as experimental data are limited. How-ever, as a first step toward understanding thesecatalysts we will analyze simple models to under-stand how L and L affect methane activation.a sBecause there have been very few theoretical anal-yses of medium-valent methane activators, it alsois of interest to assess reliable models for the studyof these and related systems.

Computational Methods

Calculations employ the GAMESS program.15

Ž .Effective core potentials ECPs and valence basisŽ .16sets VBSs are used for heavy atoms and a

�31G basis for H. The 5s, 5p, 5d, 6s, and 6p shells

JOURNAL OF COMPUTATIONAL CHEMISTRY 903

CUNDARI AND YOSHIKAWA

are treated explicitly for mercury; for main-groupelements the ns and np shells are treated explic-itly. The effective core potentials of Stevens et al.16

Ž . Ž .SBK are derived from Dirac�Hartree�Fock DHFcalculations for elements larger than neon andthus implicitly include Darwin and mass�velocityrelativistic effects. Spin-orbit coupling is averagedout in ECP generation.16 In our many studies withthese ECPs, no decrease in their accuracy has beenobserved upon going down a transition metal triad

Žto the heaviest metals for which relativistic effects. 17are greatest .

The mercury VBS is quadruple and triple-zetafor sp- and d-shells, respectively. VBSs for maingroup elements are valence double-zeta-plus po-larization. Geometries are optimized at the re-

Ž .stricted Hartree�Fock RHF level for closed-shellsinglets. Vibrational frequencies are calculated atstationary points to identify them as minima ortransition states. The level of theory, termed

Ž .SBK d , has been used extensively in studies ofd-block metal chemistry.12, 17

For species described well at the RHF level,electron correlation is a perturbation to the RHFenergy and can be calculated with Møller�Plesset

Ž . 18second-order perturbation theory MP2 . En-thalpic data are determined using MP2 energies atRHF-optimized geometries with zero-point energy

Ž .and temperature corrections to 298.15 K . Testcalculations on L � L � OH, H show little differ-a s

ence in geometries and energetics determinedusing either RHF- or MP2-optimized geometriesdespite the much greater expense of the latter

� �calculations. An RHF geometry� MP2 energyscheme yields good agreement with experimentalenthalpic data for high- and low-valent methaneactivators.12, 13c, h � j, 17 Calculated activation barrierstend to be high by � 4�6 kcal mol�1. Agreementwith experiment is better upon improvement of

Žthe model e.g., more realistic ligands, inclusion ofenthalpic corrections, and larger basis sets, particu-

. 12 12, 13c, i, jlarly on hydrogen . Calculations also sug-� �gest that an RHF geometry� MP2 energy scheme

tends to predict reaction enthalpies for bond acti-vation that are too exothermic. These issues aredifficult to resolve given the limited thermochemi-cal database for these metals. However, wherethere are experimental data with which to com-pare,12, 17 this approach accurately predicts trends

�in enthalpic data for related systems. The RHF�geometry� MP2 energy scheme is an attractive

choice for this research as the main goal is tounderstand trends among related complexes. Oneof the goals of the present research is to assess theutility of this approach for the study of HgII bond-ing, structure, and reactivity.

Results and Discussion

REACTANT GEOMETRIES, L HgL , ANDs aMETHANE

Metric data for RHF-optimized reactants aregiven in Table I. Geometric and energetic data forthese minima, and all other stationary points, areavailable as Supplementary Material.

For L � L � H, F, Cl, Br, I, CN, NC, NCS,a scalculated L Hg L ground states are of D sym-s a �h

Ž . Ž .metry. For Hg C H , the minima is C 1-C H .2 5 2 2 h 2 5For L � L � CH , CCl , CF , the lowesta s 3 3 3

energy conformers are D symmetry minima.3hSolid- and gas-phase data have been interpreted in

Ž . 19terms of D symmetry for Hg CF , whereas3d 3 2Ž . 20, 21experimental data for Hg CH are conflicting.3 2

Ž . Ž . Ž .For Hg OH , Hg SH , and Hg SCN , the lowest2 2 2Ženergy minima possess C symmetry see New-2.man projections for 1-OH, 1-SH, 1-SCN , although

C and C isomers are close in energy at the MP22 v 2 hlevel.

VOL. 19, NO. 8904

METHANE ACTIVATION

TABLE I.Calculated Metric Data for Reactants L HgL and Products L HgCH .s a s 3

Reactants Products

Hg—L , L L —Hg—L Hg—L Hg—C L —Hg—Ca s s a s s� �˚ ˚ ˚( ) ( ) ( ) ( ) ( )L , L A A Aa s

H 1.69 180 1.69 2.15 180F 1.95 180 2.00 2.11 180Cl 2.33 180 2.37 2.13 180Br 2.45 180 2.49 2.14 180I 2.64 180 2.68 2.14 180CN 2.07 180 2.11 2.12 180NC 2.00 180 2.06 2.11 180NCS 2.00 180 2.07 2.11 180SCN 2.41 179 2.46 2.13 179NH 2.05 180 2.07 2.13 1772OH 1.99 176 2.02 2.12 177SH 2.39 179 2.41 2.14 179CH 2.15 180 2.15 2.15 1803CF 2.17 180 2.19 2.13 1803CCl 2.17 180 2.20 2.13 1803C H 2.17 180 2.16 2.15 1802 5

The halide complex, HgF , has not been charac-2terized in the gas phase. The calculated HgF bond

˚lengths in HgF are 1.95 A. Using covalent radii2and electronegativities yields an estimated HgF

˚ 22, 23bond length of 1.93 A, in agreement with cal-culation. In gas phase electron diffraction experi-

24 Ž .ments, Gregg et al. measured Hg—Cl � 2.34 1˚ ˚Ž . Ž . Ž .A HgCl and Hg—Br � 2.44 1 A HgBr bond2 2lengths, indistinguishable from the calculated val-

˚ ˚ues of Hg—Cl � 2.33 A and Hg—Br � 2.45 A. In˚Ž .HgI , Hg—I bond lengths are 2.61 1 A, only2˚Ž .slightly shorter than those calculated 2.64 A .

˚The Hg—H bond lengths in HgH are 1.69 A,2close to the sum of the covalent radii of hydrogen

˚ ˚ 24Ž . Ž .0.30 A and mercury 1.44 A . Mercuric hydrox-Ž .ide, Hg OH , has not been characterized in the2

gas phase. Calculated HgO bond lengths in˚Ž .Hg OH , 1.99 A, are only slightly shorter than the2

˚Ž .HgO bond lengths 2.03 A in HgO, which formsŽ �zigzag chains O—Hg—O�179 ; Hg—O—Hg�

� . 25109 with long interchain distances.Ž .For Hg CH , electron diffraction yields Hg—3 2

˚ 20Ž .C � 2.083 5 A, whereas Raman spectroscopy in-˚ 21Ž .dicates Hg—C � 2.094 5 A, shorter than the cal-

˚Ž . Ž .culated Hg—C bond lengths 2.15 A in Hg CH .3 2Solid-state X-ray diffraction of Hg—methyl com-

˚plexes yields Hg—C bond lengths of 2.06�2.09 A

˚ 26Ž .ave.� 2.07 A; 29 examples . Experimentally,˚ 21Ž . Ž .HgC bond lengths in Hg CF are 2.109 16 A,3 2

˚Ž .� 3% shorter than those calculated 2.17 A . In˚ 27Ž . Ž .Hg CN , Hg—C � 2.015 3 A, based on neu-2

tron diffraction, which compares well with the˚calculated value of 2.07 A.

˚ 28Ž . Ž .In Hg SCN , Hg—S � 2.381 6 A, a little2˚Ž .shorter than calculated 2.41 A ; S—Hg—S � 180�

Ž . Ž . Žexptl., 179� calcd. and Hg—S—C � 97.6 5 � ex-.ptl., 98� calcd. correspond very well with calcu-

Ž .lated bond angles. In Hg SC H , the HgS bonds2 5 2˚ 29are 2.45 A, a little longer than calculated Hg—S

˚Ž .bond lengths in Hg SH , 2.39 A, perhaps due to2the greater bulk of ethyl.

Stable, low-coordinate complexes with Hg—�N bonds are rare. The complex Hg Namide

� Ž . 4�Si CH has been studied in solution, al-3 3 2

though, to our knowledge, no structure has been30 Ž .reported. For the bis acetamide complex,

Ž Ž . Ž . . 31 Ž .Hg N H C O CH , a value of Hg—N � 2.06 63 2

A has been determined from a X-ray structureŽ .analysis. A shorter Hg—N bond length, 1.97 3 , is

� Ž .Ž .� 32reported for Hg N CF TeF . These experi-3 5 2

mental bond lengths span the calculated Hg—N˚Ž . Ž . Ž .bond lengths for Hg NC and Hg NCS 2.00 A ,2 2

˚Ž . Ž .as well as for Hg NH 2.05 A .2 2



PRODUCT GEOMETRIES, L HgCHs 3

Pertinent metric data for mercury-containingproducts are shown in Table I; other data forL HgCH and H L are given in the Supplemen-s 3 a

tary Material. For products with L � H, F, Cl, Br,s

I, CN, NC, NCS, CH , CF , CCl , calculated min-3 3 3

ima for L HgCH have C symmetry. Fors 3 3vŽ .L HgCH complexes L � NH , SCN, OH thes 3 s 2

Ž .minima are of C symmetry. For L � SH 2-SHs sŽ .and L � C H 2-C H , the minima fors 2 5 2 5

L HgCH are C symmetry.s 3 1

For most ligands, the Hg—L bond in L HgCHs s 3is longer than that in L Hg L by as much as 0.07s a˚ Ž .A L � NCS . The Hg—C bonds in L HgCH ares s 3

˚Ž . Žshorter than those in Hg CH by 0.00 A L � H,3 2 s˚. Ž .C H to 0.04 A L � F, NC, NCS . The metric2 5 s

data suggest that reaction 1 tends to make the Hg—L bond weaker and the Hg—CH bond strongers 3in reactants versus products.

In experiments33 on ClHgCH , Hg—Cl �3

˚ ˚Ž . Ž .2.282 5 A and Hg—C � 2.060 20 A are � 3�4%˚shorter than calculated: Hg—Cl � 2.37 A, Hg—C

˚ 34 ˚Ž .� 2.13 A; in BrHgCH , Hg—Br � 2.406 5 A and3˚Ž .Hg—C � 2.074 15 A are shorter than calculated,

˚ ˚Hg—Br � 2.49 A, Hg—C � 2.14 A. X-ray dif-Ž .fraction analysis of NC HgCH yields Hg—3˚Ž . Ž . Ž .C cyanide � 2.05 1 A and Hg—C methyl �

˚ 34Ž .2.08 2 A, a little shorter than calculated, Hg—˚ ˚Ž . Ž .C cyanide � 2.11 A and Hg—C methyl � 2.12 A.

˚Calculated bond lengths of Hg—S � 2.41 A and˚ Ž .Hg—C � 2.14 A in HS HgCH are comparable to3

experimental models.35 � 39 For several solid-stateŽ .structures of the form RS HgCH , Hg—S � 2.373

˚ ˚ �Ž� 0.02 A and Hg—C � 2.09 � 0.01 A. In 2-ben-� 40 ˚. � Ž .zylpyridine HgCH , Hg—N � 2.10 2 A and3

˚Ž .Hg—C � 2.07 3 A are almost the same as calcu-Ž .lated bond lengths for H N HgCH : Hg—N �2 3

˚ ˚ ˚2.07 A and Hg—C � 2.13 A; Hg—N � 2.06 A and

TABLE II.[ ]�� aMetric Data for L HgL �� H CH Transition States.s a t 3

Hg—L Hg—L Hg—C Hg—H C —H L —Ha s X t X t a

˚ ˚ ˚ ˚ ˚ ˚( ) ( ) ( ) ( ) ( ) ( )L , L A A A A A Aa s

H 2.07 1.65 2.49 1.90 1.52 1.09F 2.31 1.98 2.40 2.05 1.32 1.26Cl 2.91 2.33 2.31 2.09 1.41 1.65Br 3.07 2.45 2.31 2.10 1.45 1.77I 3.33 2.63 2.34 2.08 1.47 1.97CN 2.65 2.08 2.35 2.13 1.39 1.47NC 2.59 2.02 2.33 2.05 1.34 1.42NCS 2.59 2.02 2.31 2.05 1.35 1.42

bSCN 3.35 2.40 2.29 2.08 1.37 1.87NH 2.19 2.06 2.83 2.30 1.62 1.182OH 2.27 2.02 2.51 2.14 1.40 1.25SH 2.86 2.38 2.39 2.10 1.45 1.72CH 2.53 2.14 2.53 1.92 1.51 1.513CF 2.82 2.15 2.39 1.96 1.33 1.693CCl 3.09 2.19 2.47 2.25 1.26 1.663C H 2.61 2.15 2.53 1.90 1.56 1.512 5

aCartesian coordinates for optimized transition states are given in the Supplementary material. Atom labels refer to those denotedin 3.b ( ) ( )The optimized geometry for L = L = SCN has a second, very small, imaginary mode 39i see text .a s

VOL. 19, NO. 8906

METHANE ACTIVATION

˚ ˚H —C � 2.11 A in 2-NC; and Hg—N � 2.07 Ag˚and Hg—C � 2.11 A in 2-NCS.

RHF-calculated metric data for L Hg L reac-s atants and L HgCH products show very goods 3agreement with available experimental informa-tion for this diverse series of hard, soft, and inter-mediate anionic base ligands. Furthermore, MP2-optimized L Hg L and L HgCH show little dif-s a s 3ference from analogous stationary points deter-mined with RHF wave functions.

TRANSITION STATES

� � Ž .Calculated 2� � 2� transition states TSs formethane activation by HgII—L bonds have aafour-center geometry that is distorted toward tri-angular due to the large angle about the H being

Ž .transferred in the TS H in 3 . The atoms thattŽ .make up the active site C , H , L , and Hg in 3x t a

are coplanar as found in related sigma-bondmetathesis TSs for methane activation by high-va-lent lanthanide and transition metal complexes.12, 13

TSs 3 are of C symmetry, except for L � L � CN,s a sOH, SH, which have no symmetry. For 3-SCN, theC geometry has a second, very small imaginarys

Ž .mode 39i and is thus not a true TS. All attemptsto locate a true TS for L � L � SCN failed, al-a sthough it seems reasonable that the transition state

for 3-SCN is close to this geometry. Selected met-� � Žric data for 2� � 2� transition states including

.3-SCN are given in Table II.As expected, the Hg—L bonds participating ina

C—H activation in the TSs are longer than theanalogous Hg—L bonds in L Hg L reactants anda s athe spectator Hg—L bond in the TS. Each Hg—Ls sŽ .L is the spectator ligand bond in the transitionsstate is almost the same length as in the corre-sponding L Hg L reactant. For 3-NH , the com-s a 2

˚ ˚mon bonds, Hg—C � 2.83 A, Hg—H � 2.30 A,t˚and C—H � 1.62 A are much longer than fort

other substituents. In other words, the Hg in 3-NH2seems to prefer NH binding over binding to the2methyl or hydride fragments.

� �Apart from 3-NH , two of the 2� � 2� transi-2tion states are somewhat geometrically different.

Ž .For L � L � CN 3-CN , the bond length of Hgs a˚—C is 2.65 A, whereas the terminal N is only 2.78a

˚ ŽA from Hg less than the sum of their van der˚.Waals radii, � 3.2 A . The geometry of 3-CN sug-

gests an interaction between this nitrogen atomand the mercury atom, and is

Ž . Žreminiscent of that in H C Hg pyridine-2-3.thiolato , 4, and related compounds



TABLE III.( )Calculated Methane Activation Enthalpies � Hrxn

‡ a, b( )and Activation Barriers � H .act

‡L , L �H �H E GPAa s rxn act

H 7.0 73.0 2.10 401F 0.6 35.7 9.81 365Cl 21.0 54.0 7.24 327Br 28.5 55.8 6.12 315I 35.1 61.7 5.14 306CN 12.3 65.5 5.52 346NC 10.6 52.9 NA 331NCS 9.5 49.2 NA 329SCN 20.6 62.2 NA NANH 0.5 46.4 3.98 3972OH 0.5 43.3 7.12 384SH 21.9 60.4 3.44 347Me 0.0 74.9 2.36 409CF �3.2 73.6 4.18 3773CCl 2.8 66.1 3.53 3273Et �1.4 75.0 1.77 421

a�H ‡ = calculated enthalpy of activation for reaction 1;ac t

�H = calculated enthalpy for reaction 1; E = Drago’sr x n(electrostatic parameter; GPA = gas phase acidity HL �a, s

+ � )H + L . NA = not available. All calculated enthalpies area , sreported in kilocalories per mole.b ( )The E parameters are obtained from ref. 43 Table 10-1 .Unless otherwise noted, gas phase acidities are from ref. 44;the values for CF� and NCS� are from a personal commu-3

(nication from John Bartmess Dept. of Chemistry, University) �of Tennessee�Knoxville , and the value for NC is esti-

mated from the experimental enthalpy for HCN � HNC iso-merization as reported in B. Gazdy, D. G. Musaev, and K.

( )Morokuma, Chem. Phys. Lett., 237, 27 1995 . The GPAs forCCl� and C H� are from P. Burk, and I. A. Koppel, Theor.3 2 5

( )Chim. Acta, 86, 417 1993 .

and experimental Hg �� N distances range from˚ ˚ 36, 38Ž . Ž .2.80 2 A to 2.980 5 A. A similar situation is

seen for 3-CCl ; in this case, there is a close con-3tact between two of the chlorines on the activating

˚Ž .ligand and the mercury Hg �� Cl � 2.98 A .

REACTION ENTHALPIES

There are enough data for HgII halides to assessthe accuracy of the computational methods forcalculation of thermochemical properties. We com-pared calculated � H with experimental valuesr x nestimated from the appropriate bond energiesŽ .41, 42BE :

Ž . Ž . Ž .� H estimated � BE Hg—L � BE C—Hr x n a

Ž . Ž . Ž .� BE Hg—C � BE H—L 2a

Estimated reaction enthalpies for F, Cl, Br, and Iare 3 kcal mol�1, 26 kcal mol�1, 31 kcal mol�1,and 39 kcal mol�1, respectively, whereas calcu-lated � H are 1 kcal mol�1, 21 kcal mol�1, 29r x nkcal mol�1, and 35 kcal mol�1. For absolute � Hr x nit is seen that calculated values are, on average,only 3 kcal mol�1 lower than experimental esti-mates. Additionally, relative � H as a functionr x nof halide are very accurately reproduced. Similar

� �agreement has been seen for 2� � 2� activationof methane C—H bonds by d0 transition metalcomplexes13 using similar computational methods,which is very encouraging for the study of theseand related methane-activating complexes.

Calculated reaction enthalpies are given in TableIII. With the exception of L � L � CF , C H ,s a 3 2 5reaction 1 is endothermic. The methane exchange

Ž .reaction involving Hg CH is, of course, ther-3 2moneutral. The most endothermic reaction en-

Ž . Žthalpy � H is seen for L � L � I 35 kcalr x n a s�1 .mol . The reaction becomes more endothermic

as the halide becomes heavier, F � Cl � Br � I.Ž . Ž �1 .The reactions involving Hg CN 12 kcal mol2

Ž . Ž �1 .and Hg SCN 21 kcal mol are more endother-2mic than the analogous reactions involving

Ž . Ž �1 . Ž . ŽHg NC 11 kcal mol and Hg NCS 10 kcal2 2�1 .mol , respectively.

Because it is a goal of this research to under-stand how methane activation by HgII complexesis effected by chemical interactions, we investi-gated correlations between � H and physico-r x nchemical parameters.43, 44 Because many of theseparameters are highly correlated with each other,we focus on gas phase acidities because theseprovide the largest database for the anions studiedŽ . Ž .Fig. 1 . The gas phase acidity GPA is the en-thalpy of reaction 3. The linear correlation betweenGPA and � H indicates that higher gas phaser x nacidities correspond to lower:

� � � Ž .HL H � L 3a , s a , s

reaction enthalpies. This can be reasonably as-cribed to two phenomena. First, a greater GPA for

Ž .HL translates into more driving force in eq. 1 ,abecause one HL is formed for each methane acti-avated. Second, the strength of interaction betweenHL and Hg L should show an inverse relation-a aship because HgII is a soft acid and the proton is ahard acid. Although the relatively low linear corre-lation coefficient makes it inadvisable to overinter-pret the results, it seems plausible that some com-bination of these phenomena is responsible for theobserved behavior.

VOL. 19, NO. 8908

METHANE ACTIVATION

FIGURE 1. Experimental gas-phase acidity of HLa, sversus calculated reaction enthalpy for reaction 1. Thebest-fit line is given along with the linear correlation

( )coefficient R .

ACTIVATION ENTHALPIES

Ž ‡ .Calculated enthalpies of activation � H byactŽ ‡L Hg L are, on average, very high � H � 59 �s a act

�1 .12 kcal mol as compared with neutral, high-va-� �lent, metal complexes that activate by a 2� � 2�

mechanism,3 suggesting that reaction 1 will bedifficult for many of the ligands. However, for

Ž ‡ �1. Ž ‡L � L � F � H � 36 kcal mol , OH � Ha s act act�1 . Ž ‡� 43 kcal mol , and NH � H � 46 kcal2 act

�1 .mol , activation barriers are relatively low.At the other extreme, HgII—L bonds, wherea

the activating ligand is a hydride or carbon base,have very high � H ‡ . The � H ‡ range from 66act actŽ . �1 Ž1-CCl and 1-CN to 75 kcal mol 1-CH and3 3

. �1 Ž1-Et with an average of 71 � 5 kcal mol Table. ‡ Ž . Ž .III . The � H values for Hg CN and Hg CClact 2 3 2

Ž �1 . II66 kcal mol are low compared with other Hgcomplexes that are ligated through a carbon atom.Thus, the extra interactions in 3-CN and 3-CCl3stabilize the transition state versus the groundstate reactants, resulting in a lower activationbarrier.

As in the case of � H , we investigated corre-r x nlations between � H ‡ and physicochemical pa-act

Ž .rameters. Drago’s electrostatic parameter E and� H ‡ show good linear correlation with a nega-act

Ž . Ž .tive slope R � 0.83; 13 datapoints Fig. 2 . Pa-rameter E is a measure of the relative importanceof electrostatic effects in ligand bonding; as Eincreases, a ligand tends to make bonds that aremore ionic. From a kinetic point of view, reaction 1is preferable at high E. Hence, the linear correla-tion points to the following conclusion—low � H ‡

actvalues result when L and L are hard, electro-a s

FIGURE 2. Drago’s electrostatic parameter for L�a , s

versus calculated activation barrier for reaction 1.

static ligands. Based on previous experimental and� �computational research on 2� � 2� mechanisms

for methane activation, two explanations seemŽ .plausible: 1 harder ligands with larger E values

result in a more electrophilic mercury center; andŽ .2 harder ligands with larger E values increaseHg��L�� polarization. Computational studies ofamethane activation by d0 for related series of com-plexes show that making the metal more elec-trophilic will generally facilitate C—H bond scis-sion,12 primarily through alteration of the reactioncoordinate early in the activation event near amethane adduct. As no methane adducts ofL Hg L complexes are observed in this study, ands athe transition states seem relatively ‘‘late’’ on thereaction coordinate, we prefer the latter interpreta-tion.

Summary and Conclusions

In this study, the results of a computationalinvestigation of methane activation by HgII com-plexes are reported. Several interesting results werenoted, the most important of which are as follows:

1. Calculated geometries of L Hg L reactantss aand L HgCH products are consistent withs 3available experimental data for HgII com-plexes for a wide range of diverse ligandtypes.

2. Reaction enthalpies for methane activationŽby halides for which there are sufficient data

.to assess the accuracy of the computationsare only a few kilocalories per mole lowerthan experimental estimates. Relative � Hr x n



values, as a function of halide, are also veryaccurately reproduced.

3. Calculated methane reaction enthalpies andactivation barriers for HgII complexes cover awide range of values for different activatingand spectator ligands. This suggests a degreeof sensitivity in methane activation by HgII

complexes that is sometimes not seen inhigh-valent methane activators. This diver-sity suggests that the kinetics and thermody-namics of medium-valent complexes can beexploited through rational modification of theligand environment.

4. To more deeply understand methane activa-tion by HgII complexes, correlations between� H or � H ‡ , and physicochemical param-r x n acteters for L were investigated. Correlationa, sof these parameters with � H ‡ and � Hact r x npoint to harder, more electronegative ligandsbeing more favorable both kinetically andthermodynamically.

5. Potential donor groups on the activating lig-and can interact with the electrophilic mer-cury in the transition state. Because this in-teraction is not present in the ground state ofthe HgII reactant it results in lower methaneactivation barriers. Our calculations suggestthat it may reduce methane activation barri-ers about 8�9 kcal mol�1.

The neutral, HgII complexes studied here havehigh barriers for methane activation as comparedwith high-valent d- and f-block analogs. However,this research has provided insight into important

� �chemical factors in 2� � 2� methane C—H acti-vation by HgII complexes. This research suggestsseveral further avenues to yield more insight intomethane activation not only by these complexesbut also by systems with lower C—H activationbarriers. These studies are now in progress.

Acknowledgment

Several of the more extensive calculations werecarried out at the Cornell Theory Center on an IBMSP-2.

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Computational study of methane activation by mercury(II) complexes