Ab initio Calculations of the Interaction Potentials of Ar-HCN and Ar-HCO

Chapter 11

Downloaded by NORTH CAROLINA STATE UNIV on January 10, 2013 | http://pubs.acs.org Publication Date: June 10, 1997 | doi: 10.1021/bk-1997-0678.ch011

Ab initio Calculations of the Interaction Potentials of Ar-HCN and Ar-HCO 1

Jianxin Qi, Max Dyksterhouse, and Joel M . Bowman

Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, GA 30322

First results of ab initio calculations of potential surfaces of Ar-HCN and Ar-HCO are reported. Single reference, configuration interaction (CISD) calculations, using double zeta and triple zeta basis sets, and counterpoise correction are done using the code MOLPRO. Limited test calculations are also done using the CEPA method, and also limited CISD calculations are done with triple zeta basis sets for all atoms. The electronic energies are fit using a novel sum-of-pairs potential. In this fit the pair potential depends on the Ar-atom internuclear position vector. This representation is shown to be excellent for fitting the interaction potential surface for fixed molecular geometries of HCN and HCO. Potential surfaces are given for HCN in the vicinity of its equilibrium geometry, HNC, and an approximate HCN/HNC saddle point geometry. The potentials for Ar -HCO are reported for three geometries, equilibrium HCO, the H-CO saddle point geometry, and one for a nearly dissociated H+CO. A comparison of the fits to the ab initio energies with previous conventional Lennard-Jones, and new ab initio two-body, sum-of-pairs potentials is given for Ar-HCN. The rare gas-molecule interaction is the simplest one that can induce molecular energy transfer, association, dissociation, isomerization, etc. Thus, rare gas-molecule systems have been used in many theoretical and experimental studies of these important chemical processes. In recent years, there have been several quasiclassical 'Corresponding author

150

© 1997 American Chemical Society In Highly Excited Molecules; Mullin, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.

11. QI ET AL.

Interaction Potentials ofAr-HCN and Ar-HCO

151

trajectory calculations on the energy transfer process of highly excited SFg [1] and CS2 [2] in collision with He, Ar, Xe, and the energy transfer and dissociation from highly excited OCS in collision with Ar. More recently, there have been quantum state specific scattering studies on collision induced isomerization of A r - H C N system [3], (with H C N treated as a semi-rigid bender), collision induced dissociation and energy transfer of highly vibrationally excited HCO in collisions with A r [4], similar


studies for A r - H C N (with the H C N vibrations treated exactly) [5], and quantum/classical comparisons of energy transfer in CS2 [6]. In all cases, because ab initio interaction potentials were not available for these systems, these dynamical studies used simple Lennard-Jones sum-of-pairs potentials. There have been a number of ab initio calculations of rare gas-polyatomic van der Waals systems. Specifically for Ar-HCN, Clary et al. [7] reported an ab initio interaction potential surface with a fixed equilibrium H C N geometry, based on the C E P A method. This potential cannot be used to calculate the collision processes mentioned above that involve geometry changes of H C N . It also cannot describe vibrational predissociation of van der Waals complexes, nor the interesting dependence of van der Waals spectra on internal excitation. More recently, Tao et al. [8] reported ab initio SCF, MP2, and MP4 calculations of the A r - H C N van der Waals complex. These authors investigated the effect on the potential surface of bending H C N by 15 and 30 degrees from the linear geometry. No ab initio calculations have been reported for the Ar-HCO potential. In this chapter, ab initio calculations of the A r - H C N and Ar-HCO interaction potentials are reported for three H C N and three HCO geometries. The calculations were done using M O L P R O [9]; details of the calculations will be given below. The ultimate goal of these calculations are realistic six degree-of-freedom potentials for these systems that will be used in dynamics calculations. Thus, an efficient and accurate method to fit the ab initio electronic energies is crucial. We present a novel fitting approach to the ab initio calculations, and also compare the resulting potential surfaces to two sum-of-pairs potentials, one based on the standard Lennard-Jones form, and the other based on new ab initio two-body potentials. Although the emphasis in this work is not on the van der Waals complexes, we do make some comparisons with previous calculations on the Ar-HCN system, which did focus on the van der Waals system [7, 8].

In Highly Excited Molecules; Mullin, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.

152

HIGHLY EXCITED MOLECULES

Calculations The coordinate system, details of the ab initio method, basis sets, and tests are described in this section. Coordinate System. Before going into the details of the calculation, we describe the


coordinates used to represent our results. The coordinates are body fixed spherical coordinates with the origin at the center of mass of CN(O), with the ζ axis along CN(O), and Η in xz plane. As shown in Fig.l the CN(O) distance is denoted by rCN(0)> the position of Η is (RH, γ, 0), and the position of Ar is (R, θ, φ). In order to represent the relative position of Ar to a given atom we also introduce a local, atomcentered coordinate system. The position of Ar relative to this coordinate system is denoted (RArX, θ χ , φ χ ) , where X denotes the atom H, C, Ν (or O). Ab initio Calculations. The ab initio calculations were performed using the M O L P R O program package [9]. The calculations were done at the CISD level with the Davidson correction. The interaction energies were calculated using the supermolecule model, in which the whole system is treated as a molecule. The reference energies were calculated for a separation between A r and the molecule of 20 angstroms, i.e., R = 20 angstroms. Basis Sets. The choice of basis sets was based on the consideration of polarization of atoms. The polarization of Ar and Η atoms are harder to describe using small basis sets, so the relatively large A V T Z basis sets [10] were used for these atoms. For other atoms A V D Z basis sets were used. The basis set superposition error (BSSE) was corrected using the standard counterpoise method [11]. Test of the CISD Method. We performed several tests of the CISD method and the basis sets. The CISD interaction energies, with the Davidson correction, were checked against C E P A calculations for A r - H C N and Ar-HCO, using the same basis sets. Fig. 2 compares interaction energies for three sets of calculations (without the counterpoise corrections) for the collinear A r - H C N configuration, and for the geometries indicated for Ar-HCO, with HCO at its equilibrium and transition state geometries. As seen the agreement using these two methods is excellent.



11. QI ET AL.

Interaction Potentials of Ar-HCN and Ar-HCO

Fig. 1: Coordinate system for Ar-HCN(O)


153

154


6=0° 2000 1600 Ο CI(SD) with Davidson cluster correction X CEPA1

1200 800


400 0 -400 9

R(bohr)

15

13

11

θ=72°, φ=0° 1000

r

τ

:

ι

.

.

.

;

•— ι

1

800 600

«

CI(SD) with Davidson cluster correction

0

CEPA1

X

400 200 0

8

a s

-200 9

R(bohr)

11

13

15

13

15

θ=126°, φ=0°

1000 800 600

Ο CI(SD) with Davidson cluster correction X

CEPA1

400 200 0 F-200 9

R(bohr)

11

Fig. 2: Comparison of CISD and CEPA1 interaction energies. Upper panel: Ar with linear H C N ; middle panel: Ar with minimum HCO geometry; lower panel: Ar with transition state HCO geometry.


11. QI ET AL.


155

It should be noted that CISD is a single reference method, which for H C N should be perfectly adequate. For HCO there are two conical intersections with the ground state X 2 A \ Fortunately the intersection regions are at the linear H C O and H O C geometries that are far removed in energy from the H C O minimum and the dissociation reaction path, which are the regions of the HCO potential of interest to us. We did perform CISD calculations on isolated HCO to determine the equilibrium HCO geometry and dissociation energy, D . The results are shown in Table 1, along Downloaded by NORTH CAROLINA STATE UNIV on January 10, 2013 | http://pubs.acs.org Publication Date: June 10, 1997 | doi: 10.1021/bk-1997-0678.ch011

e

with previous results from Keller et al. who use a CASSCF+MRCI method with quite large basis set [12], and also from earlier CISD calculations of Harding [13]. As seen, there is good agreement with these previous calculations, especially with the recent ones of Keller et al. Next we examine the adequacy of the basis sets chosen for A r - H C N and ArHCO. Table 1. Stable HCO geometry and dissociation energy a

BBH

b

this work

WKS

rco(bohr)

2.229

2.233

2.259

r (bohr)

2.094

2.110

2.124

< HCO(deg)

125.4

124.5

124.2

De(eV)

0.852

0.834

0.785

CH

a

R e f . 12

b

R e f . 13

Test of the Basis Sets. As noted above, we used A V T Z basis sets for A r and H and A V D Z basis sets for C , Ν and O. The latter might be considered relatively small, and perhaps also lead to some basis set imbalance. Therefore, we performed some comparisons of interaction energies using the A V T Z / A V D Z basis with energies using A V T Z basis sets for all atoms. These calculations were done with the counterpoise correction. The results of these comparisons are shown in Fig. 3 for Ar-HCN and ArHCO, for the angles indicated. As seen, there is very good agreement, except at the highest energies shown, where the energies for the smaller basis are a few percent higher than for the bigger basis. (Note, that the A V T Z calculations take about three times the computer time as ones with the smaller basis.) Thus, based on these tests and the one shown in Fig. 2, we conclude that for both A r - H C N and Ar-HCO, the CISD method, with the Davidson and counterpoise corrections, and the smaller basis should provide realistic interaction potential surfaces.


156


500 400

~

6=0° ο χ

300

Ο

A V T Z for Ar, H; A V D Z for C . Ν

200

x

AVTZ

100 Downloaded by NORTH CAROLINA STATE UNIV on January 10, 2013 | http://pubs.acs.org Publication Date: June 10, 1997 | doi: 10.1021/bk-1997-0678.ch011

0 -100 -200 13

9 11 R(bohr)

15

0=72°, cp=0°

500 400 300

Ο

A V T Z for Ar, H; AVDZ for C , 0

X

AVTZ

200 100 0

»

«

8

-100 9 11 R(bohr)

13

15

0=126°, φ=0°

500 400 300

Ο

A V T Z for Ar, H; A V D Z for C , 0

200

x

AVTZ

100 0 -100

«8

!

9 11 R(bohr)

13

15

Fig. 3: Comparison of CISD interactions energies for basis sets indicated. Upper panel: A r with linear H C N geometry; middle panel: A r with minimum H C O geometry; lower panel: Ar with transition state HCO geometry.


11. QI ET AL.


157

Results and Surface Fitting The difficulties in constructing a potential surface from ab initio energies are well known, and our ultimate goal of having six degree-of-freedom potentials for both A r - H C N and Ar-HCO is still a distant one. Among the various strategies we are considering is one based on a novel sum-of-pairs representation. Recall that in the


usual sum-of-pairs approach the potential is written as

X where X represents atoms H,C,N or H,C,0, and V^ x(R^ x)is the (isotropic) twor

r

body interaction between isolated atom X and Ar, e.g., a Lennard-Jones potential. The appeal of the sum-of-pairs potential is that the potential is full dimensional, and can be used in studies in which the molecular geometry changes. However, the potential is not expected to be very realistic, and for van der Waals systems it has long been abandoned even as a zero-order model. It has not been examined yet in any detail for rare-gas polyatomic molecule interactions where the molecular geometry changes. We will do that in a limited way below. Table 2. Molecular geometries used in the calculations HCN HCN

HNC

transition

2.196

2.196

2.196

R (bohr)

3.282

2.918

2.258

7(deg)

0.0

180.0

76.9

r (bohr) CN

H

HCO HCO

Saddle point

2.288

2.153

2.288

R (bohr)

3.043

4.213

5.669

7(deg)

34.77

47.26

34.77

rco(bohr) H

H+CO

Clearly an isotropic two-body potential cannot in general represent the interaction of the atom in the molecule with a rare-gas atom, since the true interaction depends on the direction as well as the magnitude of the interatomic position vector. Thus, a reasonable generalization of the isotropic two-body potential is a two-body


158


interaction that depends on the interatomic distance position vector. We use this approach to fit the A r - H C N and Ar-HCO interaction potentials for molecular geometries given in Table 2. For Ar-HCN the three H C N geometries are linear H C N , linear HNC, and a bent structure that is close to HCN/HNC saddle point [14]. Details of the Fitting. The functional form of the new two-body representation of


the interaction potential is

V (tf,^ç>,tf„,r, ) = int

(2)

ν

Σ ΑΑΚΑ**Θχ>

7

X=C,H,0(N)

where V x(RArX. θχ, ψχ) = V° (R ) Ar

ArX

ArX

2

+ V (R x)cos{e ) ArX

Ar

2

+ V x(R )cos

x

Ar

4

2

+ VArx(RArx)stne cos

Ab initio Calculations of the Interaction Potentials of Ar-HCN and Ar-HCO

Recommend Documents