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Ab initio study of the intermolecular potential surface of He–NH3
5 November 1999
Chemical Physics Letters 313 Ž1999. 313–320 www.elsevier.nlrlocatercplett
Ab initio study of the intermolecular potential surface of He–NH 3 Zhiru Li a , Arthur Chou b, Fu-Ming Tao a b
b,)
National Laboratory of Theoretical and Computational Chemistry, Jilin UniÕersity, Changchun 130023, China Department of Chemistry and Biochemistry, California State UniÕersity at Fullerton, Fullerton, CA 92634, USA Received 24 June 1999
Abstract The intermolecular potential surface for the van der Waals complex He–NH 3 is studied by ab initio calculation using fourth-order Møller–Plesset perturbation theory ŽMP4. with a bond function basis set. The calculation gives a global ˚ u s 898, f s 608 Žin a Jacobi coordinate system. with a well depth of De s 32.96 cmy1, along minimum at R s 3.26 A, with barriers of 23.09 and 20.86 cmy1 for in-plane rotations at u s 08 and 1808, respectively, and a barrier of 10.45 cmy1 for out-of-plane rotation at u s 898, f s 08. The potential energy surface of He–NH 3 is compared to those of Ar–NH 3 and He–H 2 O, respectively. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Interactions of the ammonia ŽNH 3 . molecule with other species play an important role in understanding molecular interactions of biological systems. Intermolecular complexes of ammonia with rare gases can be studied as the simplest model system for such interactions. The NH 3 molecule is a prototype for amine groups in polypeptides and proteins. Consequently, the interactions of NH 3 may provide valuable information on how proteins interact with themselves and with solvent molecules. Over the past decade, the Ar–NH 3 complex has been a subject of extensive studies by high-resolution experiments as well as by state-of-the-art ab initio electronic structure theory. Theory and experiment agree nearly completely with each other on the intermolecular energy surface representing the interactions of Ar– ) Corresponding author. Fax: q714-278-5316; e-mail: [email protected]
NH 3 w1–4x. A complete three-dimensional potential surface was determined for the Ar–NH 3 system by Schmuttenmaer et al. using spectroscopic data w2,3x, and the effective angular potentials were determined by several research groups w5,6x, all in good agreement with ab initio theory w4x. The intermolecular potential surface of He–NH 3 is expected to differ from that of Ar–NH 3 . It would be interesting to obtain the He–NH 3 intermolecular potential surface and to compare it with the Ar–NH 3 surface. On the other hand, the potential energy surface would change more drastically as NH 3 is replaced by a similar hydride such as water. The He–H 2 O intermolecular potential surface was recently studied by high level ab initio theory w7x. It would be interesting to compare the He–NH 3 surface with the He–H 2 O surface. The experimental interest in the He–NH 3 system has been primarily focused on its collision dynamics. Specifically, the cross-sections and rate constants were measured for the rotational excitation of NH 3 in collision with He w8–10x. Reliable modeling of the
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 0 8 3 - 0
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collision dynamics requires an accurate potential surface of the He–NH 3 interaction. Experimental information on the He–NH 3 surface has been limited to beam scattering and pressure broadening data, which are insensitive to the attractive part of the potential. Theoretical calculation of differential cross-section for rotational excitation of He–NH 3 using an SCF ab initio potential surface was reported w9,10x, showing significant disagreement with experiment. To our best knowledge, no high-level ab initio potential surface has been published for the He–NH 3 system. We believe that an accurate potential energy surface of He–NH 3 is useful for future theoretical and experimental studies of the He–NH 3 system. In this study, we present an accurate intermolecular potential surface of He–NH 3 , using complete fourth-order Møller–Plesset perturbation ŽMP4. theory with an efficient basis set incorporating bond functions. The bond function basis set, whose effectiveness was systematically demonstrated in a series of studies w11–15x, has been widely used in recent accurate calculations of intermolecular potentials w16–23x. Such basis sets require a relatively small number of polarization functions, along with a few low-symmetry basis functions centered in the middle of the van der Waals bond. The bond functions were shown to be more effective than polarization functions in recovering the intermolecular correlation energy or dispersion energy. The high linear independence of bond functions with nucleus-centered basis functions was reported to be responsible for the efficiency of bond functions w14x. The use of bond functions allows very accurate calculations with the overall basis set being practically manageable in size. The rare-gas atom may be regarded as a structureless probe of molecular force fields around the NH 3 molecule. In earlier studies, we calculated accurate intermolecular potential surfaces of several similar systems: He–H 2 O w7x, Ar–HF, Ar–H 2 O, and Ar– NH 3 w4x. All of the calculated surfaces were in good agreement with the reliable empirical surfaces recently determined from high-resolution spectroscopic experiments. We expect the He–NH 3 surface presented in this study to be as equally accurate and reliable as the other surfaces published previously. We also expect the He–NH 3 surface to closely resemble the Ar–NH 3 surface. However, the He
atom is smaller in atomic radius and is much ‘harder’ or less polarizable than Ar, and so it is likely to more cleanly probe the molecular force fields of NH 3 . As will be shown in the present study, the He–NH 3 potential surface is considerably different from that of Ar–NH 3 , but much of the difference is attributed to the size effect of the probing rare gas.
2. Computational details The intermolecular potential surface for He–NH 3 is expressed in a body-fixed Jacobi coordinate system with the origin at the center of mass of NH 3 . The internal coordinates of NH 3 are held fixed at the experimental equilibrium bond length r ŽNH. s ˚ and bond angle /HNHs 106.688 w24x. 1.0124 A The intermolecular coordinates of He–NH 3 are described as follows. R is the center of mass distance between He and NH 3 , u is the angle between the R vector and C3 symmetry axis of NH 3 with u s 08 along the C3 Õ axis pointing away from the nitrogen atom Ž u is also called the polar angle., and f is the angle for out-of-plane rotation about the symmetry axis from a reference plane Ž f s 08. passing through the three atoms ŽHe, N, and an H atom. and the C3 axis. Fig. 1 shows the intermolecular coordinates for He–NH 3 .
Fig. 1. Intermolecular coordinates for the He–NH 3 system.
Z. Li et al.r Chemical Physics Letters 313 (1999) 313–320 Table 1 Basis set and basis functions Location At nucleus: He
H N
Basis functions 10s contracted to 5s 3p functions with exponents a p s 2.56, 0.64, 0.16 2d functions with exponents a d s1.28, 0.32 10s contracted to 5s, Ref. w32x 3p with a p s1.6, 0.4, 0.1 22s11p contracted to 7s5p, Refs. w30,31x 3d a d s1.6, 0.4, 0.1
At midbond: R BF s 12 R 3s Ž a s s 0.9, 0.3, 0.1. 3p Ž a p s 0.9, 0.3, 0.1. 2d Ž a d s 0.6, 0.2.
As a rare-gas complex, the He–NH 3 system is bound primarily by dispersion forces. It is therefore essential to calculate the He–NH 3 intermolecular potential at the correlated level. In the present calculation, we use complete MP4 perturbation method w25x. Several studies w11,26–29x have shown that the MP4 method is capable of recovering over 95% of
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correlation contribution to the intermolecular energy, which is comparable to the single and double excitation coupled-cluster theory perturbatively with triple excitations ŽCCSDŽT... The intermolecular energy, D E, is given as a difference between the total energy of the complex, He–NH 3 , and the sum of the total energies of the isolated He and NH 3 monomers. The full counterpoise ŽCP. method w30x is applied for the basis set superposition error ŽBSSE.. In this method, the basis set for the complex is used for the calculations of the monomer energies with appropriate nuclear charges set to zero. As in our calculations of other systems w4,11–15x, the basis set for He–NH 3 in the present work consists of the nucleus-centered part and the bond function set 3s3p2d. The nucleus-centered part is a very large set of sp Gaussian basis functions on the N atom Žs functions on He and H. extended with a small number of polar-ization functions. Specifically, the sp set for the N atom is w7s5px, contracted from well-tempered 22s11p of Huzinaga and Klobukowski w31,32x, and the s set for He or H is w5sx, contracted
Table 2 SCF and MP4 intermolecular energies Žcmy1 . of He–NH 3 at f s 08 R ˚. ŽA 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.5 5.0 5.5 6.0
SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4
u s 08
308
608
908
1208
1508
1808
335.03 224.36 173.27 106.71 89.52 39.92 46.16 8.95 23.77 y4.28 12.20 y8.99 6.23 y9.81 1.14 y6.98 0.15 y4.06 0.00 y2.30 y0.02 y1.34
425.82 305.66 212.71 127.54 106.03 44.77 52.74 8.25 26.18 y6.39 12.97 y11.04 6.36 y11.41 1.01 y7.64 0.11 y4.30 y0.02 y2.41 y0.04 y1.38
655.28 461.62 307.75 176.50 143.32 53.57 66.19 4.28 30.31 y12.84 13.72 y16.68 6.08 y15.54 0.66 y9.15 y0.02 y4.81 y0.07 y2.61 y0.04 y1.47
524.28 319.86 238.06 101.74 106.62 15.03 47.06 y15.06 20.41 y22.19 8.62 y20.96 3.51 y17.34 0.19 y9.09 y0.09 y4.63 y0.07 y2.48 y0.04 y1.40
309.04 165.68 145.07 47.69 67.51 0.55 31.10 y15.54 14.09 y18.77 6.23 y17.23 2.63 y14.33 0.11 y7.86 y0.13 y4.17 y0.09 y2.28 y0.07 y1.32
352.21 234.09 174.75 92.82 85.86 28.11 41.59 0.37 19.71 y10.10 8.99 y12.73 3.84 y12.16 0.02 y7.73 y0.35 y4.30 y0.26 y2.41 y0.15 y1.38
408.79 289.92 204.66 122.14 101.31 42.99 49.29 7.57 23.37 y6.87 10.64 y11.47 4.48 y11.85 y0.07 y7.97 y0.48 y4.54 y0.35 y2.52 y0.20 y1.47
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Table 3 SCF and MP4 intermolecular energies Žcmy1 . of He–NH 3 at f s 308 R ˚. ŽA 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.5 5.0 5.5 6.0
SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4
u s 08
308
608
908
1208
1508
1808
335.03 244.34 173.27 106.71 89.52 39.92 46.18 8.95 23.77 y4.23 12.02 y8.99 6.23 y9.81 1.14 y6.98 0.18 y4.06 0.00 y2.30 y0.02 y1.34
387.92 271.93 194.69 112.37 97.56 38.25 48.81 5.66 24.38 y7.26 12.19 y11.24 6.01 y11.35 0.97 y7.51 0.13 y4.24 y0.02 y2.39 y0.04 y1.38
451.59 282.59 213.24 98.43 100.01 21.22 46.62 y8.03 21.57 y16.77 9.88 y17.27 4.45 y15.03 0.50 y8.49 y0.02 y4.50 y0.04 y2.46 y0.02 y1.40
328.38 155.96 148.25 32.68 66.04 y12.14 28.97 y24.43 12.47 y24.45 5.20 y20.65 2.09 y16.35 0.09 y8.32 y0.07 y4.26 y0.04 y2.30 y0.04 y1.32
255.73 124.18 120.69 30.79 56.51 y5.66 26.18 y17.34 11.94 y18.90 5.27 y16.83 2.22 y13.83 0.07 y7.57 y0.15 y4.04 y0.11 y2.22 y0.07 y1.29
347.01 230.14 172.37 91.19 84.78 27.52 41.11 0.15 19.49 y10.10 8.89 y12.69 3.77 y12.14 0.02 y7.70 y0.35 y4.28 y0.26 y2.41 y0.15 y1.38
408.92 289.93 204.66 122.14 101.31 42.99 49.29 7.57 23.37 y6.87 10.64 y11.48 4.48 y11.85 y0.07 y7.97 y0.48 y4.54 y0.35 y2.52 y0.20 y1.47
Table 4 SCF and MP4 intermolecular energies Žcmy1 . of He–NH 3 at f s 608 R ˚. ŽA 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.5 5.0 5.5 6.0
SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4
u s 08
308
608
908
1208
1508
1808
335.03 244.36 173.27 106.71 89.52 39.92 46.16 8.95 23.77 y4.28 12.20 y8.99 6.23 y9.81 1.14 y6.98 0.15 y4.06 0.00 y2.30 y0.02 y1.34
351.51 239.64 177.36 97.86 89.39 32.00 45.01 3.18 22.63 y8.12 11.35 y11.41 5.66 y11.28 0.94 y7.37 0.11 y4.19 y0.02 y2.32 y0.02 y1.34
281.74 135.98 133.90 34.52 63.43 y5.11 29.96 y17.86 14.09 y19.68 6.56 y17.58 3.03 y14.46 0.35 y7.86 0.00 y4.19 y0.04 y2.28 y0.04 y1.32
172.27 29.04 76.33 y20.39 33.36 y32.55 14.35 y31.12 6.01 y25.74 2.43 y20.06 0.88 y15.25 y0.04 y7.57 y0.09 y3.88 y0.04 y2.15 y0.02 y1.25
208.19 87.77 98.91 16.13 46.70 y10.93 21.79 y18.79 10.00 y18.90 4.43 y16.39 1.84 y13.34 0.00 y7.26 y0.15 y3.88 y0.11 y2.13 y0.07 y1.25
341.92 226.21 170.05 89.59 83.75 26.93 40.64 0.02 19.27 y10.10 8.78 y12.66 3.75 y12.07 0.02 y7.64 y0.35 y4.26 y0.24 y2.39 y0.15 y1.36
408.79 289.92 204.66 122.14 101.31 42.99 49.29 7.57 23.37 y6.87 10.64 y11.48 4.48 y11.85 y0.07 y7.97 y0.48 y4.54 y0.35 y2.52 y0.20 y1.47
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from well-tempered 10s of Huzinaga w33x. The basis set is extended with three sets of first polarization functions for each atom with the Gaussian exponents listed in Table 1. The bond functions 3s3p2d are Gaussian primitives Žexponent values: a s s a p s 0.9, 0.3, 0.1 and a d s 0.6, 0.2. centered at R BF s Rr2, the midpoint between He and the center of mass of NH 3 . The same bond functions were used in all our previous calculations of other systems. These bond functions are appropriate for various intermolecular systems, mainly because intermoleular energies are promptly saturated by bond functions. Fig. 2. Angular dependence of the intermolecular energy at Rs 3.0 ˚ A.
3. Results and discussion Tables 2–4 present the intermolecular energies of He–NH 3 calculated at the SCF and MP4 levels for various values of the intermolecular coordinates Ž R, u , f .. The polar angle u varies from 08 to 1808 in increments of 308 for each out-of-plane rotation angle, f s 08, 308, or 608. For a given orientation, the
Table 5 MP4 potential parameters of He–NH 3 at different orientation angles
f
u
Rm ˚. ŽA
Vm Žcmy1 .
DVm Žcmy1 .
08
08 308 608 908 1208 1508 1808 08 308 608 908 1208 1508 1808 08 308 608 898 908 1208 1508 1808
3.95 3.92 3.84 3.60 3.63 3.84 3.91 3.95 3.90 3.72 3.48 3.57 3.83 3.91 3.95 3.87 3.60 3.26 3.27 3.48 3.84 3.91
y9.87 y11.63 y16.75 y22.51 y18.81 y12.83 y12.10 y9.87 y11.61 y17.45 y25.10 y18.91 y12.75 y12.10 y9.87 y11.61 y19.69 y32.96 y32.75 y19.30 y12.74 y12.10
23.09 21.33 16.21 10.45 14.15 20.13 20.86 23.09 21.35 15.51 7.86 14.05 20.21 20.86 23.09 21.35 13.27 0.00 0.21 13.66 20.22 20.86
308
608
˚ intermolecular separation R varies from 2.8 to 6.0 A in various increments. Table 5 gives the radial potential parameters for the different orientations. These potential parameters were obtained by interpolation from a four-term polynomial fit of the radial potential data given in Tables 2–4. Figs. 2–4 show the angular Ž u . dependence of the MP4 potential at three ˚ respectively. fixed distances R s 3.0, 3.4, and 3.8 A, Fig. 5 shows the angular Ž u . dependence of the minimum energy. Our discussions below are based primarily on the MP4 results. The SCF results are briefly discussed at the end of the section. Interpolation of the MP4 results in Tables 2–4 ˚ gives a global potential minimum near Ž R s 3.26 A, u s 898, f s 608. with a well depth of De s 32.96 cmy1 . No experimental information is presently available for comparison of the minimum geometry and well depth. We would expect the minimum ˚ and distance R m to be overestimated by 0.02–0.05 A the well depth De to be underestimated by 5–8%, based on the known results of the method on other similar systems such as He 2 w11x, He–CO w14x, Ar–H 2 O and Ar–NH 3 w4x As a result, the actual well depth for the He–NH 3 interaction potential is likely to be near De s 35 cmy1 . The main source of error in our calculations may be the truncation error of the perturbation theory at the fourth-order level for electron correlation. Studies on He 2 w11,28,29,34x show that the well depth is slightly underestimated and is completely recovered by full CI theory. The calculated minimum geometry for He–NH 3 ˚ u s 898, is at the Jacobi coordinates R s 3.26 A,
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Fig. 3. Angular dependence of the intermolecular energy at Rs 3.4 ˚ A.
f s 608, corresponding to a T-shaped configuration with the He atom located nearly perpedicular to the C3 axis of NH 3 and in the bisectional plane of the two HN bonds. Such a minimum configuration is ˚ u s 908, compared to that for Ar–NH 3 Ž R s 3.63 A, f s 608., in which the corresponding angle is /ArHNs 1028 w4x. The minimum position of He in He–NH 3 differs by 28 from that of Ar in Ar–NH 3 . On the other hand, the minimum geometry for He– ˚ u s 1058, H 2 O was determined to be Ž R s 3.15 A, f s 08. w7x, corresponding to a T-shaped configuration with the He atom located nearly perpedicular to the OH bond in the H 2 O molecular plane. The hydrogen bond angle in He–H 2 O, /HeHOs 1128, is greater than that in He–NH 3 , /HeHNs 1008.
Fig. 4. Angular dependence of the intermolecular energy at Rs 3.8 ˚ A.
Fig. 5. Angular dependence of the minimum intermolecular energy.
As expected for all He complexes, the He–NH 3 system is very weakly bounded and its potential energy surface is flat in the attractive region with little anisotropy. The in-plane rotation Žat a fixed value of f s 608. of He around the ammonia molecule is hindered by a barrier of 23.09 cmy1 at a ˚ and u s 08, correspondsaddle point of R s 3.95 A ing to the symmetric He–NH 3 configuration, and by ˚ and u s 1808, a barrier of 20.86 cmy1 at R s 3.91 A corresponding to the symmetric He–NH 3 configuration. The out-of-plane rotation Žat a constant u s 898. ˚ is hindered by a barrier of 10.45 cmy1 at R s 3.6 A and f s 08. All the barrier heights are comparable to the barrier heights found for other He complexes. For example, the barrier height for He–HCN is 9.0 cmy1 in going from the linear He PPP HCN global minimum to the linear He PPP NCH saddle point w35x. For He–H 2 O, the barriers are 13.4 and 12.6 cmy1 for in-plane rotation at u s 08 and 1808, respectively, and 20.0 cmy1 for out-of-plane rotation at u s 1058, f s 908. The He–NH 3 potential surface does not exhibit any local minimum other than the global minimum. With these barriers, along with the small atomic mass of He, we expect the probability distribution of the He atom to be significantly dispersed from the minimum position in the complex, even for the ground vibrational state. Therefore, the equilibrium geometry of the complex may not be directly observed by spectropscopy without an understanding of the full potential energy surface.
Z. Li et al.r Chemical Physics Letters 313 (1999) 313–320
There is a substantial radial-angular coupling of the He–NH 3 potential, especially in the repulsive region and in the radial minimum region. At short ˚ as shown in Fig. 2, the distances such as R s 3.0 A, potential is most repulsive at the orientation of Ž u s 308, f s 08., and is least repulsive at Ž u s 908, f s 608.. The angular dependence of the short-range repulsion appears to be due to the presence of NH bonds, which protrude in the direction near u s 708, f s 08. Near the global minimum distance such as ˚ as shown in Fig. 3, the potential energies R s 3.4 A, are mainly attractive. The most repulsive regions are near u s 08 and 1808, corresponding to the direction of the NH 3 lone pair and the common direction of the NH bonds, respectively. The maximal attraction remains near u s 908, f s 608. At a larger distance ˚ beyond the global minimum, as such as R s 3.8 A shown in Fig. 4, the potential energies are all attractive. More importantly, the long-range potential becomes almost completely isotropic with respect to the out-of-plane rotation from f s 08 to 608. However, it remains considerably anisotropic with respect to the in-plane rotation from u s 08 to 1808. It is quite surprising to note that the effect of the electron lone pair of N is similar to that of the three NH bonds in the interaction of NH 3 with the He atom, particularly in the long range beyond the potential minimum. It would be interesting to further compare the interaction potential of He–NH 3 with that of Ar– NH 3 . As discussed, the potential minima of the two systems correspond to nearly the same orientation, but at the different distances that reflect the van der Waals radii of the two rare gases. The general landscapes of the two potentials are very similar: large radial-angular coupling in the short range, isotropy in the out-of-plane rotation in the long range, and similar interactions at the common direction of the three NH bonds, u s 08, and at the lone pair end, u s 1808. Our explanation for the resemblance between the minimum geometries of the two systems is rather simple. We believe that the van der Waals force fields around ammonia vary little in the interaction with different stable atoms or molecules. This is supported by the similar angular-radial coupling in the He–NH 3 and Ar–NH 3 potentials, as discussed earlier. It is particularly true for the repulsive wall around ammonia. A major difference of He from Ar
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is that the He atom has a smaller van der Waals radius than Ar, implying that the He atom should have a closer contact with the repulsive wall of ammonia than the Ar atom. Also, the He atom has fewer electrons and is less polarizable than Ar, which results in smaller dispersion energy. As a result, the well depth of the He–NH 3 potential is significantly smaller than that of Ar–NH 3 , and so are the rotational barriers. The comparison between the He–NH 3 and He– H 2 O potentials is parallel to the comparison between the Ar–NH 3 and Ar–H 2 O potentials. First of all, the global minimum for He–H 2 O is in the molecular plane of H 2 O, f s 08, while for He–NH 3 it is between two NH bonds, f s 608. This difference might originate from the two lone pairs on the O atom of H 2 O, which causes repulsion out of the molecular plane of H 2 O. The SCF interaction energies are all repulsive except for the small attrative tails at large distances ˚ .. This confirms that the He–NH 3 comŽ R 0 4.5 A plex is bounded primarily by dispersion forces, as expected for a rare-gas complex.
4. Summary and remarks The intermolecular potential surface for the He– NH 3 van der Waals complex is studied by high-level ab initio calculations using an efficient basis set containing bond functions. The potential surface is characterized by a shallow global minimum with the He atom perpendicular to the C3 axis of the NH 3 molecule and by small barriers for the in-plane and out-of-plane rotations of He around NH 3 . The He– NH 3 potential in the repulsive and minimum regions has a considerable angular-radial coupling, similar to the Ar–NH 3 potential. Further comparisons of He– NH 3 with Ar–NH 3 reveals that the major differences between the two potentials are mainly attributed to the smaller atomic radius of He than Ar, and that ammonia has essentially the same force fields for its van der Waals interactions with different atoms such as He and Ar. It must be added that the minimum geometry of He–NH 3 should be understood with care because He has a small atomic mass and the He–NH 3 system is very weakly bound with a potential of little anisotro-
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py. The zero-point vibration effect in the system may be extremely large, even in its vibrational ground state. The ground-state energy of He–NH 3 should be estimated to be near y8 cmy1 , as is for He–HCN w35x. Consequently, all angular configurations are accessible to the system, and the minimum geometry, as given in the present work, will be very different from a vibrationally averaged geometry.
Acknowledgements F.-M.T. acknowledges the supports from the Petroleum Research Fund of American Chemical Society ŽPRF No. 30399-GB6., The Research Corporation ŽCottrell College Science Award., and California State University, Fullerton. Z.R.L. acknowledges the support from the National Natural Science Foundation of China.
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w9x G.C.M. van der Sanden, P.E.S. Wormer, A. van der Avoird, J. Schleipen, J.J. ter Meulen, J. Chem. Phys. 103 Ž1995. 10001. w10x G.C.M. van der Sanden, P.E.S. Wormer, A. van der Avoird, J. Chem. Phys. 105 Ž1996. 3079. w11x F.-M. Tao, Y.-K. Pan, J. Chem. Phys. 97 Ž1992. 4989. w12x F.-M. Tao, J. Chem. Phys. 98 Ž1993. 2481. w13x F.-M. Tao, J. Chem. Phys. 98 Ž1993. 3049. w14x F.-M. Tao, J. Chem. Phys. 100 Ž1994. 3645. w15x F.-M. Tao, W. Klemperer, J. Chem. Phys. 99 Ž1993. 5976. w16x H. Partridge, C.W. Bauschlicher, Mol. Phys., in press. w17x H. Partridge, C.W. Bauschlicher, J. Chem. Phys. 109 Ž1998. 4707. w18x P.J. Marshall, M.M. Szczesniak, J. Sadlej, G. Chalasinski, M.A. Horst, C.J. Jameson, J. Chem. Phys. 104 Ž1996. 6569. w19x H. Koch, B. Fernandez, O. Christiansen, J. Chem. Phys. 108 Ž1998. 2784. w20x B. Kukawska-Tarnawska, G. Chalasinski, M.M. Szczesniak, J. Chem. Phys. 105 Ž1996. 8213. w21x R. Bukowski, J. Sadlej, B. Jeriorski, P. Jankowski, K.K. Szalewicz, S.A. Kucharski, H.L. Williams, B.M. Rice, J. Chem. Phys. 110 Ž1999. 3785. w22x K.W. Chan, T.D. Power, J. Jai-Nhuknan, S.M. Cybulski, J. Chem. Phys. 110 Ž1999. 860. w23x K. Higgins, W. Klemperer, J. Chem. Phys. 110 Ž1999. 1383. w24x W.S. Benedict, N. Gailar, E.K. Plyler, Can. J. Phys. 35 Ž1957. 1235. w25x C. Møller, M.S. Plesset, Phys. Rev. 46 Ž1934. 618. w26x F.-M. Tao, Y.-K. Pan, J. Phys. Chem. 95 Ž1991. 3582. w27x F.-M. Tao, Y.-K. Pan, J. Phys. Chem. 95 Ž1991. 9811. w28x D.E. Woon, Chem. Phys. Lett. 204 Ž1993. 29. w29x D.E. Woon, J. Chem. Phys. 100 Ž1994. 2838. w30x S.F. Boys, F. Bernardi, Mol. Phys. 19 Ž1970. 553. w31x S. Huzinaga, M. Klobukowski, J. Mol. Struct. 167 Ž1988. 1. w32x T.W. Dingle, S. Huzinaga, M. Klobukowski, J. Comput. Chem. 10 Ž1989. 753. w33x S. Huzinaga, J. Chem. Phys. 42 Ž1965. 1293. w34x T. van Mourik, J.H. van Lenthe, J. Chem. Phys. 102 Ž1995. 7479. w35x S. Drucker, F.-M. Tao, W. Klemperer, J. Phys. Chem. 99 Ž1995. 2646.
Chemical Physics Letters 313 Ž1999. 313–320 www.elsevier.nlrlocatercplett
Ab initio study of the intermolecular potential surface of He–NH 3 Zhiru Li a , Arthur Chou b, Fu-Ming Tao a b
b,)
National Laboratory of Theoretical and Computational Chemistry, Jilin UniÕersity, Changchun 130023, China Department of Chemistry and Biochemistry, California State UniÕersity at Fullerton, Fullerton, CA 92634, USA Received 24 June 1999
Abstract The intermolecular potential surface for the van der Waals complex He–NH 3 is studied by ab initio calculation using fourth-order Møller–Plesset perturbation theory ŽMP4. with a bond function basis set. The calculation gives a global ˚ u s 898, f s 608 Žin a Jacobi coordinate system. with a well depth of De s 32.96 cmy1, along minimum at R s 3.26 A, with barriers of 23.09 and 20.86 cmy1 for in-plane rotations at u s 08 and 1808, respectively, and a barrier of 10.45 cmy1 for out-of-plane rotation at u s 898, f s 08. The potential energy surface of He–NH 3 is compared to those of Ar–NH 3 and He–H 2 O, respectively. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Interactions of the ammonia ŽNH 3 . molecule with other species play an important role in understanding molecular interactions of biological systems. Intermolecular complexes of ammonia with rare gases can be studied as the simplest model system for such interactions. The NH 3 molecule is a prototype for amine groups in polypeptides and proteins. Consequently, the interactions of NH 3 may provide valuable information on how proteins interact with themselves and with solvent molecules. Over the past decade, the Ar–NH 3 complex has been a subject of extensive studies by high-resolution experiments as well as by state-of-the-art ab initio electronic structure theory. Theory and experiment agree nearly completely with each other on the intermolecular energy surface representing the interactions of Ar– ) Corresponding author. Fax: q714-278-5316; e-mail: [email protected]
NH 3 w1–4x. A complete three-dimensional potential surface was determined for the Ar–NH 3 system by Schmuttenmaer et al. using spectroscopic data w2,3x, and the effective angular potentials were determined by several research groups w5,6x, all in good agreement with ab initio theory w4x. The intermolecular potential surface of He–NH 3 is expected to differ from that of Ar–NH 3 . It would be interesting to obtain the He–NH 3 intermolecular potential surface and to compare it with the Ar–NH 3 surface. On the other hand, the potential energy surface would change more drastically as NH 3 is replaced by a similar hydride such as water. The He–H 2 O intermolecular potential surface was recently studied by high level ab initio theory w7x. It would be interesting to compare the He–NH 3 surface with the He–H 2 O surface. The experimental interest in the He–NH 3 system has been primarily focused on its collision dynamics. Specifically, the cross-sections and rate constants were measured for the rotational excitation of NH 3 in collision with He w8–10x. Reliable modeling of the
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 0 8 3 - 0
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Z. Li et al.r Chemical Physics Letters 313 (1999) 313–320
collision dynamics requires an accurate potential surface of the He–NH 3 interaction. Experimental information on the He–NH 3 surface has been limited to beam scattering and pressure broadening data, which are insensitive to the attractive part of the potential. Theoretical calculation of differential cross-section for rotational excitation of He–NH 3 using an SCF ab initio potential surface was reported w9,10x, showing significant disagreement with experiment. To our best knowledge, no high-level ab initio potential surface has been published for the He–NH 3 system. We believe that an accurate potential energy surface of He–NH 3 is useful for future theoretical and experimental studies of the He–NH 3 system. In this study, we present an accurate intermolecular potential surface of He–NH 3 , using complete fourth-order Møller–Plesset perturbation ŽMP4. theory with an efficient basis set incorporating bond functions. The bond function basis set, whose effectiveness was systematically demonstrated in a series of studies w11–15x, has been widely used in recent accurate calculations of intermolecular potentials w16–23x. Such basis sets require a relatively small number of polarization functions, along with a few low-symmetry basis functions centered in the middle of the van der Waals bond. The bond functions were shown to be more effective than polarization functions in recovering the intermolecular correlation energy or dispersion energy. The high linear independence of bond functions with nucleus-centered basis functions was reported to be responsible for the efficiency of bond functions w14x. The use of bond functions allows very accurate calculations with the overall basis set being practically manageable in size. The rare-gas atom may be regarded as a structureless probe of molecular force fields around the NH 3 molecule. In earlier studies, we calculated accurate intermolecular potential surfaces of several similar systems: He–H 2 O w7x, Ar–HF, Ar–H 2 O, and Ar– NH 3 w4x. All of the calculated surfaces were in good agreement with the reliable empirical surfaces recently determined from high-resolution spectroscopic experiments. We expect the He–NH 3 surface presented in this study to be as equally accurate and reliable as the other surfaces published previously. We also expect the He–NH 3 surface to closely resemble the Ar–NH 3 surface. However, the He
atom is smaller in atomic radius and is much ‘harder’ or less polarizable than Ar, and so it is likely to more cleanly probe the molecular force fields of NH 3 . As will be shown in the present study, the He–NH 3 potential surface is considerably different from that of Ar–NH 3 , but much of the difference is attributed to the size effect of the probing rare gas.
2. Computational details The intermolecular potential surface for He–NH 3 is expressed in a body-fixed Jacobi coordinate system with the origin at the center of mass of NH 3 . The internal coordinates of NH 3 are held fixed at the experimental equilibrium bond length r ŽNH. s ˚ and bond angle /HNHs 106.688 w24x. 1.0124 A The intermolecular coordinates of He–NH 3 are described as follows. R is the center of mass distance between He and NH 3 , u is the angle between the R vector and C3 symmetry axis of NH 3 with u s 08 along the C3 Õ axis pointing away from the nitrogen atom Ž u is also called the polar angle., and f is the angle for out-of-plane rotation about the symmetry axis from a reference plane Ž f s 08. passing through the three atoms ŽHe, N, and an H atom. and the C3 axis. Fig. 1 shows the intermolecular coordinates for He–NH 3 .
Fig. 1. Intermolecular coordinates for the He–NH 3 system.
Z. Li et al.r Chemical Physics Letters 313 (1999) 313–320 Table 1 Basis set and basis functions Location At nucleus: He
H N
Basis functions 10s contracted to 5s 3p functions with exponents a p s 2.56, 0.64, 0.16 2d functions with exponents a d s1.28, 0.32 10s contracted to 5s, Ref. w32x 3p with a p s1.6, 0.4, 0.1 22s11p contracted to 7s5p, Refs. w30,31x 3d a d s1.6, 0.4, 0.1
At midbond: R BF s 12 R 3s Ž a s s 0.9, 0.3, 0.1. 3p Ž a p s 0.9, 0.3, 0.1. 2d Ž a d s 0.6, 0.2.
As a rare-gas complex, the He–NH 3 system is bound primarily by dispersion forces. It is therefore essential to calculate the He–NH 3 intermolecular potential at the correlated level. In the present calculation, we use complete MP4 perturbation method w25x. Several studies w11,26–29x have shown that the MP4 method is capable of recovering over 95% of
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correlation contribution to the intermolecular energy, which is comparable to the single and double excitation coupled-cluster theory perturbatively with triple excitations ŽCCSDŽT... The intermolecular energy, D E, is given as a difference between the total energy of the complex, He–NH 3 , and the sum of the total energies of the isolated He and NH 3 monomers. The full counterpoise ŽCP. method w30x is applied for the basis set superposition error ŽBSSE.. In this method, the basis set for the complex is used for the calculations of the monomer energies with appropriate nuclear charges set to zero. As in our calculations of other systems w4,11–15x, the basis set for He–NH 3 in the present work consists of the nucleus-centered part and the bond function set 3s3p2d. The nucleus-centered part is a very large set of sp Gaussian basis functions on the N atom Žs functions on He and H. extended with a small number of polar-ization functions. Specifically, the sp set for the N atom is w7s5px, contracted from well-tempered 22s11p of Huzinaga and Klobukowski w31,32x, and the s set for He or H is w5sx, contracted
Table 2 SCF and MP4 intermolecular energies Žcmy1 . of He–NH 3 at f s 08 R ˚. ŽA 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.5 5.0 5.5 6.0
SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4
u s 08
308
608
908
1208
1508
1808
335.03 224.36 173.27 106.71 89.52 39.92 46.16 8.95 23.77 y4.28 12.20 y8.99 6.23 y9.81 1.14 y6.98 0.15 y4.06 0.00 y2.30 y0.02 y1.34
425.82 305.66 212.71 127.54 106.03 44.77 52.74 8.25 26.18 y6.39 12.97 y11.04 6.36 y11.41 1.01 y7.64 0.11 y4.30 y0.02 y2.41 y0.04 y1.38
655.28 461.62 307.75 176.50 143.32 53.57 66.19 4.28 30.31 y12.84 13.72 y16.68 6.08 y15.54 0.66 y9.15 y0.02 y4.81 y0.07 y2.61 y0.04 y1.47
524.28 319.86 238.06 101.74 106.62 15.03 47.06 y15.06 20.41 y22.19 8.62 y20.96 3.51 y17.34 0.19 y9.09 y0.09 y4.63 y0.07 y2.48 y0.04 y1.40
309.04 165.68 145.07 47.69 67.51 0.55 31.10 y15.54 14.09 y18.77 6.23 y17.23 2.63 y14.33 0.11 y7.86 y0.13 y4.17 y0.09 y2.28 y0.07 y1.32
352.21 234.09 174.75 92.82 85.86 28.11 41.59 0.37 19.71 y10.10 8.99 y12.73 3.84 y12.16 0.02 y7.73 y0.35 y4.30 y0.26 y2.41 y0.15 y1.38
408.79 289.92 204.66 122.14 101.31 42.99 49.29 7.57 23.37 y6.87 10.64 y11.47 4.48 y11.85 y0.07 y7.97 y0.48 y4.54 y0.35 y2.52 y0.20 y1.47
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Table 3 SCF and MP4 intermolecular energies Žcmy1 . of He–NH 3 at f s 308 R ˚. ŽA 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.5 5.0 5.5 6.0
SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4
u s 08
308
608
908
1208
1508
1808
335.03 244.34 173.27 106.71 89.52 39.92 46.18 8.95 23.77 y4.23 12.02 y8.99 6.23 y9.81 1.14 y6.98 0.18 y4.06 0.00 y2.30 y0.02 y1.34
387.92 271.93 194.69 112.37 97.56 38.25 48.81 5.66 24.38 y7.26 12.19 y11.24 6.01 y11.35 0.97 y7.51 0.13 y4.24 y0.02 y2.39 y0.04 y1.38
451.59 282.59 213.24 98.43 100.01 21.22 46.62 y8.03 21.57 y16.77 9.88 y17.27 4.45 y15.03 0.50 y8.49 y0.02 y4.50 y0.04 y2.46 y0.02 y1.40
328.38 155.96 148.25 32.68 66.04 y12.14 28.97 y24.43 12.47 y24.45 5.20 y20.65 2.09 y16.35 0.09 y8.32 y0.07 y4.26 y0.04 y2.30 y0.04 y1.32
255.73 124.18 120.69 30.79 56.51 y5.66 26.18 y17.34 11.94 y18.90 5.27 y16.83 2.22 y13.83 0.07 y7.57 y0.15 y4.04 y0.11 y2.22 y0.07 y1.29
347.01 230.14 172.37 91.19 84.78 27.52 41.11 0.15 19.49 y10.10 8.89 y12.69 3.77 y12.14 0.02 y7.70 y0.35 y4.28 y0.26 y2.41 y0.15 y1.38
408.92 289.93 204.66 122.14 101.31 42.99 49.29 7.57 23.37 y6.87 10.64 y11.48 4.48 y11.85 y0.07 y7.97 y0.48 y4.54 y0.35 y2.52 y0.20 y1.47
Table 4 SCF and MP4 intermolecular energies Žcmy1 . of He–NH 3 at f s 608 R ˚. ŽA 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.5 5.0 5.5 6.0
SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4 SCF MP4
u s 08
308
608
908
1208
1508
1808
335.03 244.36 173.27 106.71 89.52 39.92 46.16 8.95 23.77 y4.28 12.20 y8.99 6.23 y9.81 1.14 y6.98 0.15 y4.06 0.00 y2.30 y0.02 y1.34
351.51 239.64 177.36 97.86 89.39 32.00 45.01 3.18 22.63 y8.12 11.35 y11.41 5.66 y11.28 0.94 y7.37 0.11 y4.19 y0.02 y2.32 y0.02 y1.34
281.74 135.98 133.90 34.52 63.43 y5.11 29.96 y17.86 14.09 y19.68 6.56 y17.58 3.03 y14.46 0.35 y7.86 0.00 y4.19 y0.04 y2.28 y0.04 y1.32
172.27 29.04 76.33 y20.39 33.36 y32.55 14.35 y31.12 6.01 y25.74 2.43 y20.06 0.88 y15.25 y0.04 y7.57 y0.09 y3.88 y0.04 y2.15 y0.02 y1.25
208.19 87.77 98.91 16.13 46.70 y10.93 21.79 y18.79 10.00 y18.90 4.43 y16.39 1.84 y13.34 0.00 y7.26 y0.15 y3.88 y0.11 y2.13 y0.07 y1.25
341.92 226.21 170.05 89.59 83.75 26.93 40.64 0.02 19.27 y10.10 8.78 y12.66 3.75 y12.07 0.02 y7.64 y0.35 y4.26 y0.24 y2.39 y0.15 y1.36
408.79 289.92 204.66 122.14 101.31 42.99 49.29 7.57 23.37 y6.87 10.64 y11.48 4.48 y11.85 y0.07 y7.97 y0.48 y4.54 y0.35 y2.52 y0.20 y1.47
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from well-tempered 10s of Huzinaga w33x. The basis set is extended with three sets of first polarization functions for each atom with the Gaussian exponents listed in Table 1. The bond functions 3s3p2d are Gaussian primitives Žexponent values: a s s a p s 0.9, 0.3, 0.1 and a d s 0.6, 0.2. centered at R BF s Rr2, the midpoint between He and the center of mass of NH 3 . The same bond functions were used in all our previous calculations of other systems. These bond functions are appropriate for various intermolecular systems, mainly because intermoleular energies are promptly saturated by bond functions. Fig. 2. Angular dependence of the intermolecular energy at Rs 3.0 ˚ A.
3. Results and discussion Tables 2–4 present the intermolecular energies of He–NH 3 calculated at the SCF and MP4 levels for various values of the intermolecular coordinates Ž R, u , f .. The polar angle u varies from 08 to 1808 in increments of 308 for each out-of-plane rotation angle, f s 08, 308, or 608. For a given orientation, the
Table 5 MP4 potential parameters of He–NH 3 at different orientation angles
f
u
Rm ˚. ŽA
Vm Žcmy1 .
DVm Žcmy1 .
08
08 308 608 908 1208 1508 1808 08 308 608 908 1208 1508 1808 08 308 608 898 908 1208 1508 1808
3.95 3.92 3.84 3.60 3.63 3.84 3.91 3.95 3.90 3.72 3.48 3.57 3.83 3.91 3.95 3.87 3.60 3.26 3.27 3.48 3.84 3.91
y9.87 y11.63 y16.75 y22.51 y18.81 y12.83 y12.10 y9.87 y11.61 y17.45 y25.10 y18.91 y12.75 y12.10 y9.87 y11.61 y19.69 y32.96 y32.75 y19.30 y12.74 y12.10
23.09 21.33 16.21 10.45 14.15 20.13 20.86 23.09 21.35 15.51 7.86 14.05 20.21 20.86 23.09 21.35 13.27 0.00 0.21 13.66 20.22 20.86
308
608
˚ intermolecular separation R varies from 2.8 to 6.0 A in various increments. Table 5 gives the radial potential parameters for the different orientations. These potential parameters were obtained by interpolation from a four-term polynomial fit of the radial potential data given in Tables 2–4. Figs. 2–4 show the angular Ž u . dependence of the MP4 potential at three ˚ respectively. fixed distances R s 3.0, 3.4, and 3.8 A, Fig. 5 shows the angular Ž u . dependence of the minimum energy. Our discussions below are based primarily on the MP4 results. The SCF results are briefly discussed at the end of the section. Interpolation of the MP4 results in Tables 2–4 ˚ gives a global potential minimum near Ž R s 3.26 A, u s 898, f s 608. with a well depth of De s 32.96 cmy1 . No experimental information is presently available for comparison of the minimum geometry and well depth. We would expect the minimum ˚ and distance R m to be overestimated by 0.02–0.05 A the well depth De to be underestimated by 5–8%, based on the known results of the method on other similar systems such as He 2 w11x, He–CO w14x, Ar–H 2 O and Ar–NH 3 w4x As a result, the actual well depth for the He–NH 3 interaction potential is likely to be near De s 35 cmy1 . The main source of error in our calculations may be the truncation error of the perturbation theory at the fourth-order level for electron correlation. Studies on He 2 w11,28,29,34x show that the well depth is slightly underestimated and is completely recovered by full CI theory. The calculated minimum geometry for He–NH 3 ˚ u s 898, is at the Jacobi coordinates R s 3.26 A,
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Fig. 3. Angular dependence of the intermolecular energy at Rs 3.4 ˚ A.
f s 608, corresponding to a T-shaped configuration with the He atom located nearly perpedicular to the C3 axis of NH 3 and in the bisectional plane of the two HN bonds. Such a minimum configuration is ˚ u s 908, compared to that for Ar–NH 3 Ž R s 3.63 A, f s 608., in which the corresponding angle is /ArHNs 1028 w4x. The minimum position of He in He–NH 3 differs by 28 from that of Ar in Ar–NH 3 . On the other hand, the minimum geometry for He– ˚ u s 1058, H 2 O was determined to be Ž R s 3.15 A, f s 08. w7x, corresponding to a T-shaped configuration with the He atom located nearly perpedicular to the OH bond in the H 2 O molecular plane. The hydrogen bond angle in He–H 2 O, /HeHOs 1128, is greater than that in He–NH 3 , /HeHNs 1008.
Fig. 4. Angular dependence of the intermolecular energy at Rs 3.8 ˚ A.
Fig. 5. Angular dependence of the minimum intermolecular energy.
As expected for all He complexes, the He–NH 3 system is very weakly bounded and its potential energy surface is flat in the attractive region with little anisotropy. The in-plane rotation Žat a fixed value of f s 608. of He around the ammonia molecule is hindered by a barrier of 23.09 cmy1 at a ˚ and u s 08, correspondsaddle point of R s 3.95 A ing to the symmetric He–NH 3 configuration, and by ˚ and u s 1808, a barrier of 20.86 cmy1 at R s 3.91 A corresponding to the symmetric He–NH 3 configuration. The out-of-plane rotation Žat a constant u s 898. ˚ is hindered by a barrier of 10.45 cmy1 at R s 3.6 A and f s 08. All the barrier heights are comparable to the barrier heights found for other He complexes. For example, the barrier height for He–HCN is 9.0 cmy1 in going from the linear He PPP HCN global minimum to the linear He PPP NCH saddle point w35x. For He–H 2 O, the barriers are 13.4 and 12.6 cmy1 for in-plane rotation at u s 08 and 1808, respectively, and 20.0 cmy1 for out-of-plane rotation at u s 1058, f s 908. The He–NH 3 potential surface does not exhibit any local minimum other than the global minimum. With these barriers, along with the small atomic mass of He, we expect the probability distribution of the He atom to be significantly dispersed from the minimum position in the complex, even for the ground vibrational state. Therefore, the equilibrium geometry of the complex may not be directly observed by spectropscopy without an understanding of the full potential energy surface.
Z. Li et al.r Chemical Physics Letters 313 (1999) 313–320
There is a substantial radial-angular coupling of the He–NH 3 potential, especially in the repulsive region and in the radial minimum region. At short ˚ as shown in Fig. 2, the distances such as R s 3.0 A, potential is most repulsive at the orientation of Ž u s 308, f s 08., and is least repulsive at Ž u s 908, f s 608.. The angular dependence of the short-range repulsion appears to be due to the presence of NH bonds, which protrude in the direction near u s 708, f s 08. Near the global minimum distance such as ˚ as shown in Fig. 3, the potential energies R s 3.4 A, are mainly attractive. The most repulsive regions are near u s 08 and 1808, corresponding to the direction of the NH 3 lone pair and the common direction of the NH bonds, respectively. The maximal attraction remains near u s 908, f s 608. At a larger distance ˚ beyond the global minimum, as such as R s 3.8 A shown in Fig. 4, the potential energies are all attractive. More importantly, the long-range potential becomes almost completely isotropic with respect to the out-of-plane rotation from f s 08 to 608. However, it remains considerably anisotropic with respect to the in-plane rotation from u s 08 to 1808. It is quite surprising to note that the effect of the electron lone pair of N is similar to that of the three NH bonds in the interaction of NH 3 with the He atom, particularly in the long range beyond the potential minimum. It would be interesting to further compare the interaction potential of He–NH 3 with that of Ar– NH 3 . As discussed, the potential minima of the two systems correspond to nearly the same orientation, but at the different distances that reflect the van der Waals radii of the two rare gases. The general landscapes of the two potentials are very similar: large radial-angular coupling in the short range, isotropy in the out-of-plane rotation in the long range, and similar interactions at the common direction of the three NH bonds, u s 08, and at the lone pair end, u s 1808. Our explanation for the resemblance between the minimum geometries of the two systems is rather simple. We believe that the van der Waals force fields around ammonia vary little in the interaction with different stable atoms or molecules. This is supported by the similar angular-radial coupling in the He–NH 3 and Ar–NH 3 potentials, as discussed earlier. It is particularly true for the repulsive wall around ammonia. A major difference of He from Ar
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is that the He atom has a smaller van der Waals radius than Ar, implying that the He atom should have a closer contact with the repulsive wall of ammonia than the Ar atom. Also, the He atom has fewer electrons and is less polarizable than Ar, which results in smaller dispersion energy. As a result, the well depth of the He–NH 3 potential is significantly smaller than that of Ar–NH 3 , and so are the rotational barriers. The comparison between the He–NH 3 and He– H 2 O potentials is parallel to the comparison between the Ar–NH 3 and Ar–H 2 O potentials. First of all, the global minimum for He–H 2 O is in the molecular plane of H 2 O, f s 08, while for He–NH 3 it is between two NH bonds, f s 608. This difference might originate from the two lone pairs on the O atom of H 2 O, which causes repulsion out of the molecular plane of H 2 O. The SCF interaction energies are all repulsive except for the small attrative tails at large distances ˚ .. This confirms that the He–NH 3 comŽ R 0 4.5 A plex is bounded primarily by dispersion forces, as expected for a rare-gas complex.
4. Summary and remarks The intermolecular potential surface for the He– NH 3 van der Waals complex is studied by high-level ab initio calculations using an efficient basis set containing bond functions. The potential surface is characterized by a shallow global minimum with the He atom perpendicular to the C3 axis of the NH 3 molecule and by small barriers for the in-plane and out-of-plane rotations of He around NH 3 . The He– NH 3 potential in the repulsive and minimum regions has a considerable angular-radial coupling, similar to the Ar–NH 3 potential. Further comparisons of He– NH 3 with Ar–NH 3 reveals that the major differences between the two potentials are mainly attributed to the smaller atomic radius of He than Ar, and that ammonia has essentially the same force fields for its van der Waals interactions with different atoms such as He and Ar. It must be added that the minimum geometry of He–NH 3 should be understood with care because He has a small atomic mass and the He–NH 3 system is very weakly bound with a potential of little anisotro-
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py. The zero-point vibration effect in the system may be extremely large, even in its vibrational ground state. The ground-state energy of He–NH 3 should be estimated to be near y8 cmy1 , as is for He–HCN w35x. Consequently, all angular configurations are accessible to the system, and the minimum geometry, as given in the present work, will be very different from a vibrationally averaged geometry.
Acknowledgements F.-M.T. acknowledges the supports from the Petroleum Research Fund of American Chemical Society ŽPRF No. 30399-GB6., The Research Corporation ŽCottrell College Science Award., and California State University, Fullerton. Z.R.L. acknowledges the support from the National Natural Science Foundation of China.
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