Quantum chemical potential energy surfaces for HXeCl

Chemical Physics 244 Ž1999. 25–34 www.elsevier.nlrlocaterchemphys

Quantum chemical potential energy surfaces for HXeCl Max Johansson b

a,)

, Matti Hotokka a , Mika Pettersson b, Markku Rasanen ¨¨

b

a ˚ Akademi UniÕersity, FIN-20500 Abo, ˚ Finland Department of Physical Chemistry, Abo Laboratory for Physical Chemistry, UniÕersity of Helsinki, P.O.B. 55, FIN-00014 Helsinki, Finland

Received 22 October 1998; in final form 29 March 1999

Abstract Relativistic pseudopotential calculations are reported for HXeCl at the CISD level. Potential energy surfaces for the singlet ground state and two excited singlet states are shown for the linear case. The two lowest triplet states are also shown. The potential energy curve for the bending motion is shown for the singlet ground state. The optimized ground state structure is linear, with R XeCl s 267.4 pm and R XeH s 175.8 pm. The depth of the minimum is 0.9 eV. This structure agrees favorably with the earlier reported nonrelativistic ab initio results. The second excited singlet state of the linear system also shows a minimum at R XeCl s 249 pm and R XeH s 267 pm. The depth of this minimum is 2.0 eV. The second triplet state shows a van der Waals minimum at R XeCl s 320 pm and R XeH s 360 pm with a depth of 0.02 eV. The harmonic fundamental frequencies for the ground state, calculated at the CISD level are 263 cmy1 for n XeCl , 547 cmy1 for d Ždoubly degenerate. and 1788 cmy1 for n XeH . The corresponding scaled frequency for n XeH agrees well with the experimental one. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Quantum chemical; Potential energy surfaces; HXeCl

1. Introduction Pettersson et al. have discovered stable neutral hydrogen-containing rare-gas compounds of the type HRgX ŽRg s Kr,Xe; X s Cl,Br,I,CN,NC,SH. w1–4x and XeH 2 w5x by irradiating HX containing rare gas matrices with UV light. These authors also report nonrelativistic all-electron and core-potential ab initio calculations at the UMP2 w1–5x and CCSDŽT.

)

Corresponding author. E-mail: [email protected]

w3,4x levels of theory, corroborating the assumption that these species are stable chemically bound compounds. Last and George w6x also found the linear ionic compound ŽHXe.q Cly to be computationally stable within the semiempirical DIIS method Ždiatomics-in-ionic-systems.. The primary aim of this study was to examine the potential energy ŽPE. surfaces for the ground state and two excited states in HXeCl in order to facilitate the spectroscopic investigations of the molecule. In particular, bound excited states were searched in order to facilitate absorptionremission measurements for the molecule. Special interest was paid to possible dissociation paths for the compound. An-

0301-0104r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 9 . 0 0 1 4 4 - 5

M. Johansson et al.r Chemical Physics 244 (1999) 25–34

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other aim was to examine the capabilities of combining relativistically parameterized pseudopotentials ŽPPs. with CISD calculations. Runeberg et al. w7x have performed similar calculations on XeH 2 at MRCISD and CCSDŽT. levels of theory with both relativistically and nonrelativistically parameterized PPs for Xe. The results in this study are compared with both the ab initio and experimental results of Pettersson et al. w1x.

Table 2 Basis set for hydrogen Shell

Exponent

Coefficient

s s s s s s p p p

68.18 10.2465 2.34648 0.673320 0.224660 0.082217 0.337072 0.079830 0.024684

0.00255 0.01938 0.09280 1.00000 1.00000 1.00000 0.09205 0.47406 1.00000

2. Computational details In order to be able to take at least part of the relativistic effects into account, relativistically parameterized PPs were used together with the program package COLUMBUS w8x. Since the point group of HXeCl is C`v , the PE surfaces for the linear cases were calculated in C2v symmetry. The PE curve for the bending motion was calculated in Cs symmetry. The atomic basis sets used were Gaussian type atomic orbitals and the PPs used were those of Nicklass et al. w9x for xenon and Bergner et al. w10x for chlorine. These PPs are of the energy adjusted type with l-dependent projection operators. For xenon we used a PP with operators up

to l s 4, including a spin–orbit operator with l-values up to 3, even though the CISD calculation lacked spin–orbit splittings. Only the eight outermost valence electrons were treated explicitly, while the remaining 46 core electrons were approximated by this PP. The valence basis set for xenon consists of a 6s6p3d1f set, contracted to 4s4p3d1f. This set has been optimized for the PP and was provided with the PP w9x. For chlorine we used a quasi-relativistic PP, with l-values up to 3 w10x. Analogously with the PP for xenon, only the seven outermost valence electrons were treated explicitly. A 6s6p basis set for

Table 3 Optimized bond lengths in bent HXeCl Table 1 Basis set for chlorine Shell

Exponent

Coefficient

s s s s s s p p p p p p d d d f

78.1952870785305 9.62000047898046 2.37033221038981 0.607984865800331 0.262681901702151 0.09587839779253089 9.82002197845337 4.26200774390627 0.814213177861422 0.318804067472540 0.114555281461634 0.03719516154541021 2.475622939 0.791709148 0.290294639 0.753606638

0.008419 y0.149605 7.439550 1.000000 1.000000 1.000000 y0.015245 y0.051782 0.503595 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

Bond angle w8x

R Xe H wpmx

R XeCl wpmx

180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0

176 180 177 177 177 175 172 164 162 162 162 163 164 197 237 269 180 162 143

267 267 270 272 276 282 288 295 298 298 296 296 298 295 294 302 297 301 301

M. Johansson et al.r Chemical Physics 244 (1999) 25–34

chlorine was optimized. Polarization functions were added to match the basis set for xenon, finally giving 6s6p3d1f, shown in Table 1, which was then contracted to a 4s4p3d1f set w11x. The basis set for hydrogen was the 6s3p set of Huzinaga w12x, contracted to 4s2p, see Table 2. A standard SCF based single configuration was used in the CISD calculation as the reference configuration. The molecular orbitals, used as expansion vectors in the CI calculation, were generated with a normal RHFrUHF procedure for singletsrtriplets. The configuration state functionals ŽCSFs. were generated by using the graphical unitary group approach ŽGUGA. w13–17x. The Direct CI method w18–20x was used to solve the CI equations, solving for the ground state and two excited states in each symmetry. In the CI calculation, no core orbitals were explicitly frozen, but the use of PPs imply a set of implicitly frozen core orbitals.

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The basis sets and PPs were tested by performing ground state calculations on HCl, XeH and XeCl in C2v symmetry and comparing the computational results against the experimental ones w21x. The number of CSFs were 519 695 for HCl, 510 710 for XeCl and 422 446 for XeH. In order to estimate the corrections rising from basis set superposition errors, BSSE, a full counterpoise correction w22x was performed for HXe, XeCl, HCl and some linear geometries of HXeCl. For HXeCl the BSSE corrections were determined only for the different dissociation channels. The relative BSSE obtained in this way for HXeCl was found to be close to a constant value. Therefore, the PE surfaces were calculated without explicitly taking BSSE into account. For HXeCl, in order to keep the dimension of the CI space feasible, some virtual orbitals had to be frozen. In the singlet case for C2v symmetry, the

Fig. 1. PE surface for X 1 Sq in linear HXeCl.

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M. Johansson et al.r Chemical Physics 244 (1999) 25–34

number of frozen virtual orbitals was 7 for A1 symmetry, 2 for A 2 symmetry and 4 for both B1 and B2 symmetry, giving a total of 17 frozen virtual orbitals. The number of active orbitals was 31 for A1 symmetry, 6 for A 2 , and 16 for both B1 and B2 . This composition gave a total of 538 641 CSFs. In the singlet C s symmetry, likewise, no explicitly frozen core orbitals were applied. The number of active orbitals was 35 for AX and 14 for AY symmetry. The number of frozen virtual orbitals was 23 and 12, respectively. This composition gave a total of 524 723 CSFs. For the triplet states, the number of frozen virtual orbitals was 13 for A1 symmetry, 3 for A 2 symmetry and 7 for both B1 and B2 symmetry, giving a total of 40 frozen virtual orbitals. The number of active orbitals was 25 for A1 symmetry, 5 for A 2 symmetry and 13 for both B1 and B2 symmetry, giving a total of 56 active orbitals. No explicitly frozen core orbitals were implemented. The PE surfaces for the linear geometries were calculated as a grid, where the bond lengths were systematically varied with a step size of 0.3 bohr Ž16

pm.. The bond lengths for the singlet PE surfaces were varied from 2.8 to 5.8 bohr Ž148 to 307 pm. for R XeH and 4.1 to 7.4 bohr Ž217 to 392 pm. for R XeCl . For the triplet PE surfaces, the bond lengths were varied from 3.4 to 8.8 bohr Ž180 to 466 pm. for R XeH and 4.0 to 8.0 bohr Ž212 to 423 pm. for R XeCl . The singlet PE curve for the bending motion was calculated by varying the bond angle by steps of 108, from 0 to 180 and optimizing the bond lengths for each angle. The numerical CISD fundamental frequencies for the ground state in the harmonic approximation were calculated with the program package GAUSSIAN-94 w23x.

3. Results and discussion The bond lengths and dissociation energies, De , for XeH, HCl and XeCl were calculated for the ground states. In XeH, the calculated R XeH was 393.9 pm and De 0.0069 eV. These compare well

Fig. 2. Minimum PE curve for the bending motion in HXeCl, ground state.

M. Johansson et al.r Chemical Physics 244 (1999) 25–34

with the experimental values of 394 pm and 0.0068 eV, respectively w21x. In XeCl, the calculated values were R XeCl s 317.6 pm and De s 0.01 eV. The corresponding experimental values are 318 pm and 0.03 eV, respectively w21x. In HCl, the calculated values were R HC l s 128.5 pm and De s 4.3 eV. The corresponding experimental values are 127.5 pm and 4.59 eV Žzero point vibration corrected., respectively w21x. The calculated values are BSSE corrected. The values without BSSE correction are approximately the same except for the dissociation energy of XeCl. De for XeCl was found to be too high by 0.4 eV without BSSE correction. The PE surfaces for singlet and triplet HXeCl describing the stretching of the bonds in the ground state and the electronically excited states were calculated. The ground state X 1 Sq linear PE surface is shown in Fig. 1. It has a minimum at R XeCl s 267.4 pm and R XeH s 175.8 pm. The preferred dissociation path, leading to neutral Xe q H q Cl, has a dissocia-

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tion energy of 0.9 eV. These results also compare favorably with the previous theoretical calculations. Pettersson et al. w1x report nonrelativistic large scale ab initio calculations giving a linear equilibrium structure of R XeCl s 285.2 pm and R XeH s 167.4 pm. The BSSE corrected values for De along the various dissociation channels were calculated as 1.0 eV for the HXe–Cl stretch, 1.3 eV for the H–XeCl stretch and 0.9 eV for the linear simultaneous dissociation of both bonds. These BSSE corrected values agree well with the uncorrected ones. These results are in agreement with the assumption, that BSSE correction are more important for weakly bound van der Waals’ type complexes than for more strongly bound molecules. At equilibrium, the molecule can be described as an ion pair ŽHXe.q Cly because the net atomic charges are q0.777 for Xe, y0.157 for H and y0.620 for Cl, calculated from the CISD density. The dipole moment of the molecule is 6.83 Debye.

Fig. 3. PE surface for A1 Sq in linear HXeCl.

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M. Johansson et al.r Chemical Physics 244 (1999) 25–34

Even though the PE surface stretches over a large range of bond lengths, the single reference CISD seems to perform quite well, since the square of the CI coefficient for the reference state was calculated to 0.55 as its lowest value. This was the case for both bond lengths being 320 pm. The molecule is linear. The minimum PE curve for the bending motion, shown in Fig. 2, describes a minimum energy path where both bond distances have been optimized at each bond angle. The curve shows that the dissociation path via bending leads to Xe q HCl, but the process is hindered by an energy barrier of 1.4 eV. The preferred dissociation process is therefore the linear channel with a dissociation energy of 0.9 eV. The optimized bond lengths for each angle are shown in Table 3. The PE curve for bending also shows the formation of a complex, where xenon is bound to HCl.

Adams and Chabalowski w24x have investigated complexes of this type. The dissociation energy for this complex, with respect to the H–Cl bond was found to be approximately 4.0 eV, which is in reasonable agreement with the experimental value of 4.59 eV for pure HCl. The bond length of approximately 143 pm also agree reasonably well with the experimental value of 127.5 pm w21x. The first excited state, A1 Sq, is shown in Fig. 3. It can be qualitatively explained by the single electron excitation 7aX § 6aX , and lies some 5 eV above the ground state at the ground state equilibrium geometry. Some perturbations in the region for the minimum in B1 Sq are clearly visible on the PE surface for A1 Sq. Otherwise, the PE surface is purely repulsive. The second excited state, B1 Sq, presented in Fig. 4, shows a prominent minimum at R XeCl s 249 pm

Fig. 4. PE surface for B1 Sq in linear HXeCl.

M. Johansson et al.r Chemical Physics 244 (1999) 25–34

and R XeH s 267 pm. It dissociates to XeqClyq H with a dissociation energy of 2.0 eV. The vertical excitation energy from the ground state is some 11 eV. The excitation can qualitatively be explained by the double electron excitation 7aX § 6aX . The shape, depth and coordinates of the minimum suggests that this state could be an excited charge transfer state for XeqCly. This exciplex seems to bind the hydrogen atom rather strongly. Some perturbations in the PE surface of the first excited state, A1 Sq Fig. 3 can also be seen at this geometry. The difference in energy between the A1 Sq and B1 Sq states at this geometry is about 0.01 eV. The irregular appearance of the PE surface at the location of the minimum could also be due to these perturbations. One of the possible reasons for these perturbations is an avoided crossing between these two states. The vertical transition energy from the B1 Sq state to the X 1 Sq state is approximately 5.4 eV at the coordinates of the minimum of B1 Sq. It is also

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possible that the X 1 Sq§ B1 Sq transition cannot be seen due to a nonadiabatic A1 Sq§ B1 Sq decay. The PE surface for the a3 Sq state, shown in Fig. 5, is purely repulsive. The b 3 Sq state, shown in Fig. 6, is also repulsive, but it has a shallow van der Waals minimum at approximately R XeCl s 320 pm and R XeH s 360 pm. The depth of the minimum is some 0.02 eV. All studied linear states are shown on the same energy scale in Fig. 7 where the R XeH coordinate is kept constant at its ground state optimized value of 175 pm. The vertical transition energies from the ground state are also shown. The vertical emission energy ŽX 1 Sq§ B1 Sq . is shown in Fig. 8, where the R XeCl coordinate is kept at its optimized value for minimum in the B1 Sq state. The near degeneracy of the A1 Sq and B1 Sq states and the possible avoided crossing can clearly be seen in Fig. 8.

Fig. 5. PE surface for a3 Sq in linear HXeCl.

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M. Johansson et al.r Chemical Physics 244 (1999) 25–34

Fig. 6. PE surface for b 3 Sq in linear HXeCl.

The CISD numerical fundamental frequencies in the harmonic approximation were calculated as 263 cmy1 for n XeCl , 547 cmy1 for d Ždoubly degenerate. and 1788 cmy1 for n XeH . These values are unscaled. With a normal scaling factor of 0.89, the values for n XeCl and d become 234 cmy1 and 487 cmy1 , respectively. A scaling factor of 0.91, typically used for X–H ŽX s C,N,O. stretching vibrations in organic molecules, gives the value 1627 cmy1 for n XeH . The calculated and scaled value for n XeH agrees well with the experimental value of 1649 cmy1 . Other frequencies have not been reported w1x.

Acknowledgements The authors wish to thank the Finnish Academy of Sciences for financial support Žproject a37543..

Thanks are also due to the authors of the program package COLUMBUS, for supplying their programs.

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M. Johansson et al.r Chemical Physics 244 (1999) 25–34

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Fig. 7. The vertical absorbtion energies ŽA1 Sq§ X 1 Sq, B1 Sq§ X 1 Sq . in linear HXeCl. R Xe H is constrained to the equilibrium value of the X 1 Sq state at 175 pm.

Fig. 8. The vertical emission energy ŽX 1 Sq§ B1 Sq .. R Xe Cl is constrained to the equilibrium value of the B1 Sq state at 267 pm.

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