A modified LEPS surface for the ground state of the water molecule

Volume 52. number 3

A MODIFIED

CHtMICAL

LEPS SURFACE

I’IIYSICS LETTERS

FOR THE GROUND

1 December 1977

STATE OF THE WATER MOLECULE

Arthur GAUSS Jr. LMistic Modeling Division. Ballistic Hesearch Laboratory, Aberdeen Yroviug Grcmnd, Maryland 21005, USA

Recervcd 3 August 1977 Revised manuscnpt rcce~vecl 18 August 1977

A nlod~ficd LITS potential surface uang a Sate pameter which is a functron of the intcrnuclcar coordmatcs has been developed for the ground St&c of the wdtcr molecule. By adjusting the Sato parameter many of the known properties of the water poturltial

ax fattud with lhts surtocc.

An LEPS surface which approximates the equzlibrlum ground state for water (X I Al) has been developed. A single Sate parameter which is a function of the internuclear coordinates is used to alter the LIPS so that the wntcr molecule II: and near the equilibrium configuration can be modclcd. An earlier study [ 11 suggested the use of large values of the Sato parameter to produce wells or barriers along the reaction path. The general form of the LEPS potenrlal [2] IS V= Q; + Q; t Qj - [(CT;)3 -I-(a;)2

-I-(a;)2

X C(3 f A) exp[-2Pi(rl_rin)l eXp [-pi(ri-riO)]

)

and 0: = ai/(l

h

‘3

‘I

I3

0

Rg. 1. The internuclear

H

‘2

distances (rlr2r3)

and the an& U are

clefrned a\ shown.

A = A {f(O)) {(sin 2Th)‘” 3

where Th = arctan (rl /r2) and the pararncters A,m, arid B arc adjustable. This form of the Sato parameter could be applied to other three-atom complexes where two of the atoms are identical. It-has the proper symmetry, that is, it is invariant to interchange of r1 and r2. A single Sato parameter has been employed here. Single Sato

Q; = Q&Cl + A) = [Di”f4(1 -r A)]

- (2 + 6A)

H_

+ A) = [Or/4 (I + a)] Table 1

X I(1 + 3A)exp[--2P,(r,

- rio)

- (6 + 2A) exp I-P, (‘i - rjo)] 1,

i=

1,2,3.

The Morse parameters (07, pi, rio) are displayed in table I. The Sato parameter is given by 252

0-H

H-H

fi = tii = 106.53 kcal/mole p1 = p2 = 2.29 A-’ ‘10 = r2n = 0.9706 A _-_-_--_-

D$ = 109.5 kcal/mole p3 = 1.942 A-’

130 = 0.74 17 A .-__ _

-

52, number 2

Volurnc

CIIISMICAL

PHYSICS LETTERS

parameters have been used successfully by other workers on three-atom systems whcrc two of the atoms are identical [2,3]. The Sato parameter ranges from near zero for r1 = ‘to, r2 + 00 (or r2 = r2n, fl * -) to sIightIy greater than two near the minimum energy configuration (rt = r?, x 0.87 A, 0 = 106”). The function f(0) contains additional adjustable ~rameters. In the case of the water molecule f(6) has been chosen to be f(0) = [sin (Th I)] 6 f f [sin (Ih?,)] 4, where Tbl = 4 0 and ‘II12 = 3 0. The exponents, the constiint multiplying the [sin(Th?)14 term, and the constants inultiplying 0 in ‘Ih 1 and Th2 are the adjustable parameters. Thcsc Dammeters were varied so that the potential mmimurn WLLS at 0 = 106’, close to the actual angle of 104-lOSo [4]. in addition f(0) wasadjusted so that the difference between the depth of the potcntiul

well in the linear

3.6

2

_-r

-7--__

‘_-l__

-I_

7--

2.8

U z

2.0

g

a Is: z? 1.2

0.4 u.4

1.2 ‘,

2.0 ,OH

7.8

DISTANCE

3.6

(;i)

The third bracketed term in A clirninates the large negative values of the potential ttlat Occur for small vaIues of rI and r2 when A is large. This term approaches sern as rl and rz approach zero causing the Sate parameter to approach zero and tbc potential (v) to form ;I high wall (see figs .2,3 and 4). It goes to zero for farge values of r1 and r2 ciue to the exponential. 13~adJust3.6

-I---

7_ --1------, 7

I

--r--

r

_

*a -

“I

2.8

-

G z 2 2.0z

2.0

z5

g

0” _ p

2.8 *a III

1

U z 2

3.6

configuration and the depth ww * 1.8 eV (compare figs 2

in the IOG” configuration and 3), close to the 1.S eV difference shown in the potcntkil plot by IIerzberg [S]. The second bracketed tcrrn in a, [sin 2Th]“*, prevents the potential well from extending to large values of rI and r2 aiong the entrance or exit valleys; it also helps eliminate the double minima near the center of the potential well la problem when large (> 1) values of the Snto parameter are employed). A large value of the exponent, m = 16, was needed for the water potential surface.

1 Decernher 1977

,_ 1.2-

1.2

I

0.4 CI.4

r, Fig. 2.

I

I

1.2 .OH

1

I

,

2.0 2.8 DISTANCE (ii)

Hz0 ground state surfxc

for 0 = 170’ (contours

I

3.6

0.4 I

0.4

I

I ‘1 ,OH

in eV).

1

I

1.2

I

I

2.0 DISTANCE

Fig. 4. Hz0 ground state surfxe

2.8

I

I 3.6

(d)

for o = GO” (contours in eV).

253

Volume

52, number

2

CHEMICAL

PHYSICS

B one can ensure that the potential minimum will be near rL = r2 = flo. For the water moIecule B = 4 was chosen. For this H,O surface the minimum is near ing

LETl-ERS

1

December 1977

promise of applying a modified LEPS surface to many systems. We have already applied it to the HO, system and run trajectories on the resulting surface [7].

f’1 =‘2 = 0.87 A at 6 = 106“, the actual surface has its minimum at f1 = r2 = 0.96 A (at 8 = 104-105”) [4] _

The parameter A multiplying the whole expression is chosen to ensure that the depth of the potential well (at 0 = 106”) is close to the experimental value. In the cast of the water molecule A = IO2 was chosen. This value makes the well depth = 5 eV below the zero of the potential, the separated OH(‘II) + H(*S) state. Thus the overah binding energy is = 9.5 eV, which is close to the experimental estimate of 10 eV [6]. In the 0 + 112 channel the surface does not separate properly. It should go tc O(l D) + Hz, however, it actually separates to 0(3P) + Hz. The concept of a variable Sato parameter gives

254

References [l] 121 [3 J [4]

A. Gauss Jr., J. Chcm. Phys. 65 (1976) 4365. J.T. Muckcmman, J. Chem. Phys. 56 (1972) 2997. M. Bacr. J. Chcm. Phys. 60 (1974) 1057. 13-J. Rosenberg. W.C. Gmlcr and I. Shavitt, J. Chem. Phys. 65 (1976) 4022. [S ] G. ilerzherg. Electronic spectra of polyatomic molecules (Van Nostrand, Princeton, 1966). [6] B.J. Rosenberg lind I. Shavitt, J. Chem. Phys. 63 (1975) 2162. [ 71 A. Gauss Jr., J. Chem. Phys. (June 1977). submitted for publication.