Ab initio molecular orbital calculations on beryllium and magnesium atom reactions with water

Volume

75. numbcr

1

CHEMICAL

PHYSICS

LETTERS

AB INITIO MOLECULAR ORBITAL CALCULATIONS ON BERYLLIUM AND MAGNESIUM ATOM REACTIONS L A. CURTISS

Recerved

1980

WITH WATER *

and D J. FRURIP

25 Apnl

1980.

m rinal

form

30 June

Ab uutlo molecular orbltal calculations and Mg OHz, .md for speaes resultmg HBcOBeH. and HhlgOhlgH

1980

are reported from mscrtlon

1. Introduction

Expenrnental studies of the reactions of dwalent metal atoms with water m Inert gas matrices have recently been reported by Hauge et al. [l] . In particular, magnesium and uon atoms are found to form adducts with the water molecule m mert gas matrrces and after photolysls of the matm the metal atom is inserted into an O-H bond of the water molecule. The experimental results indicate that the bondmg of the metal atom-water complex mvolves an mteraction through the water oxygen. A downward shift in the mfrared frequency of the bendmg mode of water IS observed. Because of the recent mterest III these reactions we have carried out ab initio molecular orbital calculations to determme the nature of the mterachons between water and certam dlvalent metal atoms. There have been some previous theoretical studies of a smgle atom interactmg with a molecule. Losonczy et al. [2] found that neon and water at the HartreeFock level have a very weak attraction (0.17 kcal mol-‘) due to th e mteraction of a permanent dipole moment particle

1 October

(the water molecule)

with a polarizable

for beryllwm of the metal

and magnesmm atom complcws atom(s) Into tbc water molcculc.

with water. Be HBeOH, HhQKltf.

. OH2

studied the mterachons of Li, Na, and F atoms with NH,, H20, HF, PH,, H,S, and HCI. They find the Li ._. OH2 adduct to have a dissociation energy of 12.2 kcal mol-’ using a double-zeta basis set. Addition of d functions to Li m a larger basis set reduces the dissociation energy by 1.8 kcal mol-* _ Inclusion of correlation ener,y has only small effects on the geometry and dissociation energy. Other theoretlcai studies have been reported on the reactions of beryllium with methane [4], acetylene [S] , and ethylene [S]. In tlus paper we report on a theoretical mvestigation mto the interaction of two divalent metal atoms, berylhum and magnesium, with the water molecule. In this study we have considered the metal atom (M&water adduct, M . . . OH,, and the molecules formed by insertion of one or more metal atoms into the OH bond(s) of water, HMOH and HMOMH. In section 2 the theoretical methods mcludmg basis sets and geometries are described.. In sectlon 3 the optunlzed geometries and interaction energes for the various species are reported. Fmally, in section 4 the nature of the bonding 1s discussed and comparison with experiment IS made. All calculations reported here are for Be and Mg in their IS ground state.

(neon). They estimated that the dlsperslon

energy would

result in an added attraction

lmately

kcal

0.135

mol-I_

Trenary

et al.

of approx[3]

have

* Work performed under the auspices of the hfate&l Sciences Program of the Dwis~on of Basw Energy Sciences of the Department of Energy.

2_ Theoretical

methods

Standard LCAO SCF methods were used in this study of beryllium and magnesium atom reactions with 69

Volume

75, number

1

CHEhlICAL

PHYSICS

water Two basrs sets were used in the calculahons Tbe first, referred to as basis I, is a “spht valence shell” gaussian-type orbital basis set. For H, Be, and 0 the 6-31G basis ’ is used and for Mg the basis of Cole et al. [S] (a 12~10~ pnrmhve gausslan set contracted to 4~2~) is used. The second, referred to as basis II, is the same as basis I except that d functions are added to Be, 0, and Mg. For Be and 0 single sets of d func-

tions havmg exponents of 0.4 [7] and 0 8 [9], respectively, are added For Mg the d functron of Cole et al [S] is added. Molecular scale factors were used in the Be valence shells [7] rn all calculatrons on HBeOH and HBeOBeH. In calculations on Be . . . OH, unscaled (or atomic) scale factors were used for Be [7] smce rt rs a weakly bound complex and Be IS not m a molecular envrronment. Thrs assumptron was tested by optrmizing the Be scale factors for one case and found to make httle drfference For Mg .._ OH,, HMgOH, and HMgOMgH the rMg atomic exponents of Cole et al. [S] were used rn all calculations The structures of the metal atom-water adduct and metal atom-water inserhon molecules are dlustrated in fig. 1. In the case of M _.. OH2 the metal atom IS located a drstance r(M-0) from the oxygen. 0 is the angle between the C2 axis of Hz0 and the axrs passing through the M-O bond. x describes rotatron of Hz0 about its C, axrs. In the case of HMOH the metal atom 1s located m the H-O bond with fl being the angle * The H and 0 basis sets are from rb from ref

LEl-l-ERS

3. Results Optrmrzed structural parameters are grven rn table 1 for the beryllmm-water species and in table 2 for the magnesmm-water specres Calculated total energtes and bindmg energies are grven in table 3. Be . . OH,. The optimized geometry of Be . . OH2 at the basrs II level rndrcates that rt IS a weakly bound Table 1 Optumzed structures of Be OHz. HBeOH. HBeOBeH. Hz0 (bond lengths m A and bond angles III deg) Species

Parameter

Be

r(O-H) LHOH r(Be-0) f3

OH2 b,

X

I

AH37 --__M_--___O----__-_

HBeOBeH

M

H--

H--

70

1. Structures

M of hl

&HI

&MY-” OHz, HMOH, and HMOMH

qd)

a) Baas I 0 114 1 0

957(0 957) 7 (114 9) 709(1 687) 0 (0 0)

-

and

Basis II 0 105 3 72

948 6 662 9

0.0

1 323 1.368 0931 180 0

1 330 1.381 0 932 145.0

P

1.324 1 396 1800

1 331 1 394 180 0

r(H-0) LHOH

0 950 1115

0 948 105 5

P

Hz0 e,

fig

r(H-Be) r(Be-0) r(O-H’)

HBeOH c,

/-

1980

between H-M-O and O-H. In tire geometry ophmrzations the metal atom is grven the freedom to move out of the O-H bond. The HMOMH structure is simrlar to that of HMOH except that the second metal atom is located in the other O-H bond. The various geometrical parameters of the structures were optrmrzed wrth respect to the total energy to +O.Ol A m bond drstances and +I” in bond angles. AlI of the basis I calculations were carried out usmg the GAUSSIAN 70 computer program [lo] and all of the basrs II calculatrons were done using the HONDO computer program [ 1 I].

[6] ; the Be basis set IS

(71

1 October

r(H-Be) r(Be-0)

a) Defined in fig 1. b, Atonuc scale factors used for Be. Numbers m parentheses obtamed usmg optunlzed valence scale factors for Be of 0 96 (mner) and 0 89 (outer). c) hlolecuiar scale factors used for Be [ 7 1. d)The two M-O bond distances were optumzed separately, but came out equal The same holds true for the H-hi bond distances e, Basis I results from ref. [6]. Baas II results from ref [ 161

Volume 7.5. number

CHEMiCAL

1

PHYSKS

Table 2 Optrmrzed structures of Mg . OH2. HhfgOH, and HMgOhfgH (bond lengths m A and bond angles m deg) Parameter

Spcnes hfg

I

a)

Basis I

Basrs II

0 953 1123 2 385 00

107 4 2 440 00

#q&-O) r(O-H’) P

1.743 1 743 0 936 180 0

1 740 1758 0.941 180 0

r(H-h¶g) r(Mg-0) P

1 754 1776 1800

r(O--HI LHOH r(Mg-0) e

OH2

0951

X

r(N-Mg)

HXlgOH

HhfgOBlgH b,

a) Defiicd

m fig 1

b, See footnote

-

d) of table 1

of Be and H20 The Be atom lies 72.9O out of the Hz0 plane and at a drstance of 3.66 a from the oxygen atom. Thus structure was tested and found to be a defmrte muumum m the potentral energy surface. To move the Be atom into the Hz0 plane keeping the Be-O distance constant requnes only about 0.1 kcal mol-’ ‘Dus reflects the fact that movement of Be about the oxygen stde of the water molecule ((8 I < 90”) is very easy. However, configuratrons

complex

Table 3 Total enerses,

i980

with Be located on the hydrogen side of the water molecule (IS I > 90”) are considerably fess stable. The water molecule geometry is nearly unchanged in the complex. The Be __.OH, complex has a very small brndmg energy of -4.62 k&I moi-‘. Basks I (no d functions) gives a stronger Be ___OH, complex having a bmding energy of -4.82 kcal nolLE and a Be-O bond length of I.709 a. Apparently, the d functions are important in tfte mteraction between Be and H20. Optinuzmg the Be scale factors at the basis I level in the Be . . OH, complex resulted m a 30% increase m the interactron energy and only small changes in the geometry. b?g. OH_. The optimrzed structure of Mg . . . OH, at the basis II level has C, symmetry with Mg in the Hz0 plane (0 = O”) 2.440 a from the oxygen and with a bmding energy of -2 33 kcal molNt_ Agam it takes very httte energy to move the Mg out of the water plane. The interactron of Mg with Hz0 is stronger than that of Be with Hz0 (bindmg energy = -0.62 kcd moi”) at the basis iI level. This is aiso reflected by larger changes is the Hz0 geometry in the Mg . . . OH, complex than in the Be _._ OH, complex. The basrs I (no d functrons) results for the Mg _. ON, complex are very sunilar to the basis Ii results. HBeOH, HBeOBeH. The HBeOH motecuie has been studred previously by D111et al. [12]. In their cdcdabans the mimmal STO-3G basrs was used and the mole-

E, and brndmg energies “), SE

Species

Be

1 October

LETTERS

OHzb)

HBeOH c, ffBeOBeH c) hfg _ OH2 HMgOH ~~~Oh~~H

Basis I

Basis Ii

E (au)

AE
-90.56362 (-90 56625) -90 68574 -105.3892f -275 55820 -275 59323 -475 18775

-4 82 (-6 47) -8t 4 -164 8 -2 42 -24.4 404

AE (kcal moi-r )

E (auk

-0.62

-90.58236 -90 -10.5 -275 -275

70388 41867 58534 61048

-78.1 -167 3 -2 33 -18.1

a) Corresponds to AE for the reacuons M * OH2 -+ M _ OHa, hf + OHz -c HhfOH. 2M + OH2 -L HMOMH. The total energies (au) of the reactants usmg basrs I are &Be) = - 14 57058, E(hfg) = -199 56898 and E(H20) = -75.98536; usmg basrs II E(Ee) I14.57062, &(hfg) = -199 57088, and E(H20) = -76 01075. The atoms were calculated in the ground states (‘S) and references for the Hz0 geometnes are gtven m footnote e) of table 1 Energtes of Be. Mg. and Hz0 at the Hartree-Fock lrmrt are -14 573

fI7],-199615 [l’if,and -76067au [18l,respecuvely. b)Total enewes obtamed usm~ atomrc scale factors for Be (numbers UI parentheses c, Total energies obtamed

usmg molecular

obtatned

usmg optunlzed

scale factors for Be).

scale factors for Be.

71

Volume 75, number I

CHEMICAL

PHYSICS LETTERS

cufe was found to be linear. At the basis If level WC find HBeOH to be nonalinear (P = 145”). However, as will be discussed in the next section the j3 binding motion has a very shallow potential energy curve. The O-H bond distance decreases from 0.948 .h in the water molecufe to 0.932 /I in Hf3eOl-I. Tf1e H-Be and Be-O distances are 1.330 and 1.381 A, respectively. For the double beryllitl~n atom insertion product (fi~~O~ef~) J ~oniplete~y tinear structure is obtained at the basis II level (table 1). The H-Be and Be-0 distances are only sffgfltfy longer than those in HBeON. In the cases of both HBeOH and HBeOBcN the molecules were made non-finear by angles other than fl (e.g. LHBeO). Ail such geometry changes fed to increases in energy. The ba& f (no d functions) results are nearly the same as E.I&e obtained at the basis 11ievel indicating that d functions are not very important in d~ter~ninin~ tfle structures of these metal atom insertion products. HMgOH, HMgOAfgH The optimized HMgOff strutture is linear and very similar at both the basis I and If levels. As in the HBeOff case the 0-fi distance decreases from its value in the f+,O mofeculc (0.948 to 0.941 ik basis II). The f-I--Mg and Mg.--0 distances are I.740 and I .7S8 ii, respectively, at UIC basis II level. Only basis 1 level calculations were carried out on HMgOMgH, The result was a Iinear structure with f-f--Mg and Mg--0 bond lengths only slightly longer than those in f~fMgOf-I.

4. Ikussion

I huge Et af. f I 1 observe 211infrared hami at IS78 Wl

’ when il~~~~~~si~l~~l ;rtwrts xc in 311inert

~~).~(~~l~l~ns~~lwith

gas m;lt ris. Tl~c rwrmai ff20 f>clkctillg frcquc’ncy is 1552.3 cm . a difference of I5 cm- 1, Tftq ~lltti~~llt~this new fmd to ;I ~)ll~-t0~0?i~~ti;,~. uesium-water adduct, Mg .,, Ofi?. At higher magncsium concentrations other b,ands appear which are attributed to magnesium-water adducts involving more than one magnesium atom. WC have calculated the bel~c~it~~force col7stal~ts f’or f $0 in the Be ... OI-f2 and Mg .,. OFi complexes. The resufts are given in table 4. At the basis II level the f520 bending Ibcc constant dccrcases in both adwater

1 October 1980

?hblc 4 Force constants a) for the HOH bend in the M ... OH2 adducts ____~___

.__ _____~__.--l-__“ll--_.

Spccics

_____

_x

FHON b, _- ..__- .__- .., ._.

_ _.

Ii20 Be ,). 0112 c) _-.

.A!;,.. 011,

._.._.._- .___

basis I

b3sis I!

0.837 0.841 10.843) 0,857

0.938 0.9f I 0.887

-. .._-- . - .___. - ...__-I_

a) C;ltcuIated at the theoretical equilibrium structures. Ele.,. OH2 and Mg ... OH2 from tables 1 and 2, rcspcctivcly. Hz0 from table 1. b) in units of mdync/A; scaled by the inverse square of the OH distsnce (0.957 A). ClAtomic scatc factors used for Be (member in parentheses

obtained using optimized valence scale factors for Be).

ducts. For Mg . .. OH, the decrease corresponds approximately to a decrease in the ff20 bending frequency of 44 cmlf . This is somewhat larger than that found experimentally, but in the same direction. The sensitivity of the change in the Hz0 bending force Constant to the basis set is flIustrated by tfte fact that at the basis I level the bending force constant increases in both the adducts (table 4). Hence, a calculation with a Iarger basis set possibly including correlation energy is needed to definitely confirm the agreement between tfleory and experiment on the direction of the change in the fi20 bending frequency in the M ... OH2 complexes. kfauge et al. [I] noted that as the size of the intcractiotr energy of the M . .. OH, complex increases the r~lagnitude of the shift in the Hz0 bending frecfuency increases *. We also find this to be true. The Mg .II OH2 complex has a larger decrease in the Hz0 bending frctlucncy (e44 cm-‘) than Be .., OH2 (“23 cm ’ ) and it has 3 iarger interaction energy (-2.33 kcal mol._ ’ f than Be .. . off, (- 0.62 kcal mol“ i )* TIE major interaction in the M .. . OH> complexes involves the 33, molecular orbital of H,O and the symmetry allowed valence orbitals of the metal atom. The other valence orbit& of f+,O interact with the metal atom orbitals, but to a smaller degree. A Muiliken population analysis of the Be . . . OH, and Mg ... OH2 complexes shows that there is a small amount of transfer of electrons from H20 to the metal atom, most of it tl~rough the 3al orbital of H,O. ’ This observation is based in part on the theoretical cnkulalions of Trcnary et al. 13J of the binding energy of the Li .,. OH2 and Na .., OH2 compleses.

Volltmc 75, number

1

CHEMICAL

PHYSlCS LETTERS

4.2. HMOH arid HMOMH Wllen the magnesium-water adducts in the inert gas matrix are photolyzed by radiation the bands around 1578 cm-’ disappear and bands appear at 742 and 937 cm-‘, Hauge et al. [I] assign these bands to bending modes of HMgOH and HMgOMgH species, rcspectivcly. The only structural data that they deduce from tlleir data is that HMgOH is linear while HMgOMgH is bent with an MgOMg angle @ in fig. 1)of 164’. The results of our geometry optimizations indicate that HMgOH and HMgOMgH are both linear. However, the potential energy curve for changes in /3 is very shallow meaning it would take very little energy to make these molecules non-linear. For example, to bend HMgOMgH by 10’ requires only 0.4 kcal moIV1 (basis I). Another example is HBeOH which has a fl value of 145’ (basis II), but the difference between this bent structure and a linear structure is only 0.6 kcaf mol-‘. Hence, the discrepancy between theory and experiment on the HMgOMgH linearity question could easily be the result of the effect of the inert gas matrix, or alternatively, deficiencies in the calculation. Analysis of the molecular orbitals of the J-IMOH species indicates that the metal atom in the O-H bond loses charge to both 0 and H via u bonds while gaining some charge via n bonds through its empty p orbitals of the right symmetry. The net transfer is about one electron away from the metal atom to the 0 and H making these molecules quite ionic. The bonding picture in the HMOMH species is very similar. The change in energy for insertion of a single Mg atom into Hz0 is calculated to be ~-18.1 kcal mol-’ (hasis II). This is in agreement wit11the estimate of IHaugcet al. [I] of --I9 kcal mol-’ for this reaction. The Bc insertion results in a much larger energy change of --78.1 kcal mol-’ (b asis If ). Tl~e insertion of a second metal atom is nearly additive in the energy change (table 3). The insertion products, HMOH and HMOMH, are considerably more strongly bound than the complexes, M ... OH,. Our calculations show that the complexes, despite being weakly bound, do represent definite minima in the potential energy surfaces. Presumably, this is why the Mg ... OH, complex can be observed experimentally. We have also carried out limited calculations which indicate that there is a

I October

1980

barrier to insertion of tlie metal atom into tile water molecule. This barrier is apparently overcome by the, energy provided by the photolysis of the inert gas mstrix. More detaiJed calculations arc required to determine tile actual barrier and patli of insertion. At tlJC basis II IWCJtile Mg . . . OH, interaction crierby is grcatcr tlian tliat of Be OJ1_l. In contrast, tl~e energy changes for the Be insertion reactions ;irc greater than for the Mg insertion reactions. The latter trend is consistent with the experimental Be0 botld energy being greater than the experimentaf MgO bond energy [I 31. Although the opposite trend for the much weaker M ... OH, interaction could be due to the basis sets used (see footnote a of table 3 for comparison with Hartree--Fock limits), we believe that the trend is more likely due to the fact that the Mg atom is more polarizable than Be whicJ1 leads to its larger binding energy. Tile larger binding energy tllat we find for Mg . .. OH2 is consistent with the finding of Margrave et al. [I 41 tllat the HOII bending frequency change is larger for Ca .., 0112 than for Mg . . . 01J2 indicating ;I larger interaction energy for the CJ complex. A recent theoretical study of Al .. . OH, and HAIOH by KurtL and Jordan [15] has come to our attention. They report results for the bonding, geometries, and energies of these species which are similar to those rcported here for the BCand Mg species.

5. Conclusions From these calculations on magnesium and beryllium atom reactions wit11water we can make the following conclusions: (I) Divalent metal atoms such as maguesiun~ and beryllium form compleses with water which arc very weakly bound. The interaction energy (<3 kcal moJ ’ ) is less tl~irn a r~ornJ31 JJY~TO~~ “-11 hl?lJd (5--7 kCiIl IlJd ’ ) ml also less than Trcnary et 31. [3] found for intcractions of monovalent atoms such as lithium and sodium with water (S-12 kcal moJ-I). (2) The divalent metal a:om is bonded to the, water molecule in tllese complexes througll the oxygen atom. The force constant of the H,O bend decreases in the complex in the best calculations (basis set including d functions). This is in agreement with what was found experimentally by Hauge et al. [I]. (3) The molecules formed by insertion of one or 73

Volume

75, number

i

CHEMICAL

more berylhum

PHYSICS

or magnesium atoms mto the O-H bond(s) of H,O, HMOH and HMOMH, are found to be hnear in most cases However, It takes very httle energy to make the molecules non&near (
References ] R H Hauge. S E Gransdcn, J W Kauffman and J L hlargravc. Procccdmgs of the 10th hlatcrmls Research Symposium on Charactcrlzatlon of High Temperature Vapors and Gases, NatIonal Bureau of Standards, Gathersburg, Ilfaryland (Sept. 18-22, 1978) p 557 ] hl Losonczy, J W Moskow~tz and I; H Stlllmger, J Chcm Pk.. 59 (1973) 3264

74

LETTERS

1 October

1980

H r Schaefer III and P A. Kollman, _I Chem [31 hI Trenary. Phys 68 (1978) 4047; J. Am Chem Sot 99 (1977) 3885 I G. Cslzmadla and 0 P I41 P.G bfezey, F BernardI, Straus. Chem Phys. Letters 59 (1978) 117. III. J Am. Chem Sot 98 151 WC Swope and H I- Schaefer (1976) 7962 J A Poplc, J Chem [61 W J Hehre, R Ditchfleld_and Phys 56 (1972) 2257. I71 J S Bmklcy and J A Pople, J Chem Phys 66 (1977) 879 Phys 58 I81 J L. Cole. A K Q SIU and E F Hayes, J Chcm (1973) 857 and J.A Pople, Thcoret Chum Acta 28 [91 P C Hanharan (1973) 213 R Dltchfield, MD Newton [lOI W J Hehrc. 1%’A Lathan, and J A. Pople, QCPE IO (1974) 236 [I 11 hl Dupws, J Rys and H F Kmg, QCPE 10 (1976) 338 [ 121 J D. Ddl, P R. von Schleyer, J S Bmkley and J A Pople. J Am Chem Sot 99 (1977) 6159. [ 13 J D R StuU and H Prophet, eds . JANAF Thermochem~cal Tables, 2nd Ed (1971) [ 141 J L. hkugrnvc, R H Hauge. S E Gransden and J W Kauffman, 177th National hfeetmg of the American Chcmnxl Soclcty, Honolulu, Hawau (April, 1980) [is] H A Kurtz and K D Jordan, J. Am. Chem Sot 102 (1980) 1177 [I61 P.C Harlharan and J A Pople, hfol Phys 27 (1974) 209 [171 E Clement], IBM J Res Develop 9 (1965) 1. suppl [ 181 W.C Ermler and C W Kern, J Chem Phys 61 (1974) 3860