Second-order density functional calculations of the MgFH potential energy surface

THEO CHEM ELSEVIER

Journal of Molecular

Second-order

Structure (Theochem)

426 (1998) 165- 169

density functional calculations energy surface

of the MgFH potential

Virgilio Sanz, Alfred0 Aguado, Miguel Paniagua* Departamento de Quit&a Fisica, Facultad de Ciencias C-XIV, Univemidad Autdnoma de Madrid, 28049 Madrid, Spain Received

19 September

1996; accepted

13 January

1997

Abstract

Second-order density functional methods are used to introduce the electron correlation in Two-Configuration Direct Minimization (TCDM) ab initio electronic energy calculations of the ground state (‘A’) three-dimensional MgFH potential energy surface (PES). The MgFH PES obtained here presents a good qualitative agreement with respect to previously reported MgFH PES, except for an important quantitative reduction (about 20%) of the transition state height. 0 1998 Elsevier Science B.V. Keywords:

Second-order

density functional;

MgFH potential energy surface

1. Introduction The Mg + FH - MgF + H reaction belongs to the group of exchange reactions of alkaline-earth metal atoms with hydrogen halides, and in recent years they have been studied experimentally in great detail [ 1- 161. Theoretical studies of the Potential Energy Surface (PES), PES fits and dynamical calculations have appeared more recently [17-351 but focused mainly on the lightest member, i.e. the BeFH system. To give a good classical and quantum-dynamical picture of these reactions, it is necessary to obtain a reliable PES as a starting point. However, a wellknown lack of PES calculations, when using ab initio methods without considering a major part of the electron correlation, is that if the PES is to be used for dynamical studies, it should be scaled in such a way that the barrier must be reduced without affecting the other critical features of the PES. This is a very * Corresponding

author. E-mail: [email protected]

difficult task because the final PES usually has a different shape from the ab initio one [36]. Moreover, considerable computational effort is supposed to extend the accurate ‘Multiple Reference single and Double excitations Configuration Interaction (MRDCI) calculations to M + HX reactions when M is a heavier member of the alkaline-earth family or when X is a heavier member of the halogen family. In a previous study [37], we have analysed the correlation energy error in the BeFH PES. This system has also been studied by the usual techniques, allowing a full comparison for the lowest ‘A’ adiabatic state. In particular, we have compared the results obtained using the MRDCI method with the corresponding results obtained from the Colle-Salvetti (CS) [38-421 and Moscard&San-FabiHn (MSF) [43-451 procedures, within the correlation factor method, using as the starting point the coefficients obtained in a Two-Configuration Direct Minimization (TCDM) calculation [46]. We have found that the CS and MSF results were in a good overall agreement in

0166-1280/98/$19.000 1998 Elsevier Science B.V. All rights reserved PII SO166-l280(97)00317-5

166

V. Sam et al./Journal of Molecular Structure (Theochem) 426 (I 998) 165-169

the differential energies with the more accurate ab initio MRDCI results, including the heights of the saddle points and the transition state. The CS and MSF absolute (total) energies are lower than those obtained from the MRDCI method. However, the good agreement in the differential energies makes it possible to calculate PES with sufficient accuracy using the CS or MSF procedures. In this paper, our aim is to report a globally reliable MgFH PES to allow future dynamical calculations. In fact, our previous work on the MgFH system [30-331 present the problems mentioned above because the calculations were performed using a TCDM procedure that takes into account only a part of the correlation energy. In this study, we have also tried to enhance the basis set with respect to our previous MgFH PES [30-331. In Section 2, we present a brief exposition of the calculations. Finally, in Section 3 the qualitative and quantitative features of the PES estimated by drawing isoenergetic contours of the spline interpolation of the ab initio points are discussed.

2. The calculations The choice of an appropriate basis set was determined to achieve the following: (i) accurate description of the atomic and F- negative ion ground states, (ii) accurate values of the relative energies, ye, o,, D,, and vibrational quanta for the diatoms (HF, MgF and MgH) with reasonably good agreement with respect to the known experimental values, and (iii) a groundstate surface for MgFH of good accuracy and sufficient flexibility to describe the different regions of the PES. To fulfil these conditions, we adopt the standard 6-3 11 G** basis set [47] for the three atoms. The final size is 50 atomic orbitals expanded in 84 primitive Gaussians. In our previous MgFH calculations [30-331, the basis set size was 33 atomic orbitals. Therefore, we expect that our present calculations will also improve the TCDM results. With the above basis set, RHF calculations were performed using a direct minimization procedure [48,49]. Then, a two-configuration calculation was carried out using a direct minimization program (TCDM) [46]. Using as the starting point the TCDM molecular orbital coefficients, we integrate

the equation

(1) where es is the Colle-Salvetti correlation energy and H(&B’) may be considered as the density functional [38-421. Then, the electronic TCDM energy plus es is the total electronic energy for a given atom arrangement in the Colle-Salvetti approximation. An alternative is the method suggested by Moscardb and San-Fabian [43-451 (MSF), also based upon the correlation factor approach. In this alternative we integrate the equation

E~SFW’;)=(~-1) ~P,P,W

(2)

where EySF is the Moscardo-San-Fabian correlation energy and E&J&) is the density functional given by equations (17, 18, 19,20) in Ref. [44]. Then, the electronic TCDM energy plus EFSF is the total electronic energy for a given atom arrangement in the MoscardoSan-Fabian approximation. The three internal coordinates were chosen as: the RHF distance, the RM~F distance and the MgFH angle (0). The grid of geometries for which the calculations were made was selected with respect to the TCDM diatomic equilibrium distances (in atomic units) and the angles 0 = 180” (collinear), 135”, 90”, 75”, 60” and 45” Rur=1.70+0.5i(i=-1,0,1,2,3,4,5,6)

(3)

R MgF=3.00+0.5j0’=-1,0,1,2,3,4,5,6)

(4)

For 19= 0” we have two different collinear sections. One of these sections corresponds to the approach of the Mg atom from the H end of the HF giving the collinear reaction Mg + HF - MgH + F. For this reaction, the grid of geometries for which the calculations were done was Rnr=1.70+0.5k(k=-1,0,1,2,3,4,5,6)

(5)

R MgH=3.00+0.51

(6)

(1=-2,

-1,0,1,2,3,4,5)

The other section for 19 = 0” corresponds to the insertion of the Mg atom between the H and F atoms, giving a deep minimum corresponding to the

167

V. Sanz et al./Journal of Molecular Structure (Theochem) 426 (1998) 165-169

HMgF triatomic was

molecule.

For this section the grid

R MgF=3.00+0.5m

(m=-1,0,1,2,3,4,5,6)

(7)

R MgH=3.00+0.5n

(n=-2,

(8)

-1,0,1,2,3,4,5)

When the SCF and TCDM calculations are complete, we run the correlation energy calculations using, in the same job, the CS and MSF functionals. The input needed for these calculations is: the coordinates of each atom, the basis set, the molecular orbital coefficients of the TCDM calculation, and several parameters needed for the numerical integration of the corresponding density functional.

Table 2 Several MgFH PES points obtained methods

with different

computational

PES point”

TCDM b

MSFb

CSb

Reactants (Mg + HF) Products (MgF + H) Saddle point (0 = 180”) Saddle point (0 = 135”) Saddle point (0 = 90”) Transition state (0 = 75”) Saddle point (0 = 60”) HMgF minimum

0’ 27.3 48.3 46.4 41.2 38.6 41.0 -31.1

0’ 25.7 41.2 46.0 42.6 34.2 37.7 -28.0

OC 34.0 44.9 45.2 43.1 34.8 39.7 -25.0

a See Table 3 below for the values for Rh18b,RHF and RMg~ of the saddle points. b Energies in kcal/mol with respect to the zero energy. ’ The zero energy is set at each column to the new corresponding energy value of the reactants.

3. Results and discussion Asymptotic properties of the surface are illustrated in Table 1, where we compare the calculated equilibrium frequencies and distances with the experimental data [50] for the HF, MgH and MgF diatoms. In this comparison we include several levels of approximation using the same basis set: TCDM, MSF (energies obtained as TCDM plus ErSF) and CS (TCDM + E,c’). In Table 2 we present several PES points, including all the computational methods mentioned above and selecting the saddle point energies and other relevant points of the PES. We can see that the inclusion of the electronic correlation affects the height of the saddle points and the energy difference between the two asymptotes (4. If we compare all the columns in this table, corresponding to different methods of Table I Experimental

w,(HF)

4MgF) w,(MgH) R,(HF) R,(MgF) R,(MgH) D,(HF) DAMgF) D,(MgH)

and calculated

values for the diatoms

Expa

TCDM

MSF

CS

4138 712 1495 1.73 3.31 3.27 141 110 33

4187 732 1623 1.70 3.33 3.29 104 77 26

4216 726 1642 1.69 3.37 3.22 109 83 27

423 1 726 1591 1.69 3.30 3.18 134 100 40

*w, in cm-‘, R, in au, and D, in kcal mol-‘. Experimental from Ref. [SO].

values

calculation, we can see that the basic features of the TCDM PES are preserved and the electronic correlation has a quantitative importance. In fact, in Table 3 we give the locations of the stationary points obtained using the CS approach which do not differ significantly from the MSF ones. However, the quantitative effects are very important to set the location and energies of the true stationary points of the PES, which are key quantities for dynamical studies. If we look at these quantitative effects, we can see that the CS or MSF tinctionals present a good general behaviour and a significant reduction of the barrier height, which plays a key role in determining the reactivity. To obtain a plot of the PES, we report fixed f3 contour maps of the calculated values corresponding to the CS or MSF methods (very close contour maps are obtained for both methods). Isoenergetic contours of these two-dimensional cuts of the PES hyperspace were obtained by means of a cubic spline interpolation procedure. Fig. 1 presents maps of horizontal cuts at 0 = 180”, 135”, 90”, 60” and the two different collinear sections for 0 = 0”. Fig. 2 presents a map at 8 = 75” in the saddle point surroundings. We can now compare our CS and MSF results with previous works [ 17-19,23-26,30-331 in order to assess the behaviour of second-order density functional methods within the correlation factor approach (CS and MSF) in the MgFH system. Consistent with the previous work, our results suggest that the constrained saddle point positions are in the exit channel. When the angle of approach is decreased, a quite

168 Table 3 Stationary

V. Sanz et al./Journal ofMolecular

points on the MgFH PES” (CS values)

RM~F 00

3.29 3.27 3.30 3.21 3.52 3.51 3.14

RHF

RWgH

1.69 M

a.

2.85 2.65 2.65 2.41 2.34 6.13

6.12 5.50 4.16 3.14 3.14 2.99

cc

a Energies in kcal mol-’ and distances

4

V

Identity

0.0 34.0 44.9 45.2 43.1 34.8 39.7 -25.0

Mg + HF, reactants asymptote MgF + H, products asymptote MgFH saddle point for 0 = 180” MgFH saddle point for 0 = 135” MgFH saddle point for 0 = 90” MgFH transition state for 0 = 75” MgFH saddle point for ~4 = 60” HMgF minimum

in atomic units.

pronounced well appears, corresponding to the stable H-Mg-F linear molecule (about 30 kcal mol-’ below reactants), the CS and MSF results reproduce this well. Moreover, the transition state is located in the product channel at an angle of 75”. Finally, the CS and MSF results support the presence of a complex (shallow well) in the entrance channel. In conclusion, there is good overall agreement between the second-order density functional (CS and MSF) results and those corresponding to previous work [17-19,23-26,30-331. However, we have a quantitative disagreement in the important matter of the height of the transition state. Here we obtain a reduction of the transition state height of about 20% (or about 8 kcal mall’) with respect to previous TCDM calculations (see Ref. [31]). Part of this reduction is due to the enhancement in the basis set, but the introduction of the electron correlation is responsible for the main differences. This is the

60”

180’

3

Structure (Theochem) 426 (1998) 165-169

5

6

6

RMeF

RM~,F

0” (FMgH)

135”

4 32 2 3

4

5

6

RMC,F

2

3

4

5

RM~F

75”

0” (FHMg)

90”

3 4

2.0 L

3

4 %rF

5

3e:

2.6

2

2

2.4 p: 2.2

6 RM<,H

Fig. 1. Potential contours for several angles of approach (19= 180”, 135”, 90”, 60”, O”(F-Mg-H) and O”(F-H-Mg)) as a function of the corresponding interatomic distances, Contour labels at -20, -10, 0, 10, 20, 30,40,50,60, 70, 80,90 and 100 kcal mol-’ with respect to the selected zero energy (reactants). Negative contours have been plotted using dashed lines. All the distances are in atomic units.

3.2

3.4

3.6 3.0

4

R Mgb Fig. 2. Potential contours for 0 = 75” (the transition state angle), plotted in the saddle point surroundings as a function of the corresponding interatomic distances. Contour labels at 31, 32, 33, 34, 34.8 (dashed line), 35,36,37,38,39,40,45 and 50 kcal mol-’ with respect to the reactants. Units as in Fig. 1.

V. Sam et al./Journal of Molecular Structure (Theochem) 426 (1998) 165-169

usual result when the correlation energy is introduced in PES calculations [37], with very important dynamical implications which will be studied in the future.

Acknowledgements Financial support from the Comisibn para la Investigacibn Cientifica y Tknica (CZCYT, ref. PB94-O 160, Spain) is gratefully acknowledged.

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