Calculation of Molecular Constants for the of the NeH + and KrH + Ions

Size: px

Start display at page:

Download "Calculation of Molecular Constants for the of the NeH + and KrH + Ions"

Regina Andrews
6 years ago
Views:

Calculation of Molecular Constants for the of the NeH and KrH Ions Ground States P. Rosmus and E.-A. Reinsch Fachbereich Chemie der Universität Frankfurt (Main) Z. Naturforsch.

1 Calculation of Molecular Constants for the of the NeH and KrH Ions Ground States P. Rosmus and E.-A. Reinsch Fachbereich Chemie der Universität Frankfurt (Main) Z. Naturforsch. a, 66-7 (98); received July, 98 Potential energy and dipole moment functions have been calculated for the ground states of the NeH (. ^ R ^ a. u.) and the KrH (.6 ^ R ^ a. u.) ion from highly correlated SCEP/VAR and SCEP/CEPA electronic wave functions. The following spectroscopic constants have been derived: Ne<>H re = 996± A, we = 896±cm", D(Ne H) =. ± ev; Kr 8 H re = -9 ± Ä, we = 6 ± cm", Z>(Kr H) =.6 ± ev. The Einstein transition probability coefficients of spontaneous emission have been calculated for all transitions of Ne H, Ne D, Kr 8 H and Kr 8 D, respectively.. Introduction Scattering [ ], associative ionization [], ion cyclotron resonance [6], mass [7, 8] and infrared [9] spectroscopic experiments on the strongly bound protonated rare gas atoms have stimulated much theoretical work concerning the potential energy functions (PEF's) for the ground states of the HeH [-], NeH [, -6] and ArH [7 9] ions. There is considerable interest in accurate PEF's for these ions, which have been, for instance, used to interpret the observed HeH quasibound rovibronic states[,] and the scattering experiments [ ]. They also represent an interesting model system for the study of the long-range interactions []. Only recently, molecular parameters of the present work for NeH and our previous results for ArH [9] have been found to agree very well with the electron energy spectra for as- Distance Total energy a Dipole moment SCF SCEP/VAR SCEP/CEPA SCF SCEP/C Table la. The potential energy and the dipole moment functions of the 7 ground state of NeH (all values in a.u.). a The following Gaussian AO basis sets have been employed: s, 8 p, d, f for Ne and 7 s, p, d for H; in the SCEP/VAR calculations all single and double substitutions with respect to the Hartree-Fock configuration have been included and the higher substitutions have been approximately accounted for by the CEPA scheme. Previously, the following total energies at re have been calculated: a.u. (SCF, Ref. []), a.u. (SCF, Ref. []), -8.6 a.u. (SCF, Ref. [6]), a.u. (FO-CI, Ref. [6]). b with respect to the Ne atom as origin. -8,/ 8 / -66 $ / - Please order a reprint rather than making your own copy. Download Date //8 8: PM

2 67 P. Rosmus et al. The x Ground States of the NeH and KrH Ions sociative ionization [] in the collisional processes Ne* ( P), Ar* ( P) H. These experiments yielded so far the most accurate proton affinities of the Ne and Ar atoms and the vibrational spacings for several bound vibrational states of the NeH and ArH ions. In this work we report the ground state PEF's for the NeH and KrH ions, encompassing a large region of internuclear distances, and their infrared transition probability coefficients of spontaneous emmission as calculated from high correlated SCEP/ VAR [] (self-consistent electron pair approach yielding variational results) and SCEP/CEPA [ ] (coupled electron pair approach) electronic wave functions.. Results In Table a the calculated SCF, SCEP/VAR, and SCEP/CEPA total energies and the dipole moments for NeH are listed (for computational details see footnote of Table a). The calculated spectroscopic constants are given in Table. Our SCF results closely parallel those calculated by Peyerimhoff [], which represent near Hartree-Fock limit results for NeH. Comparison of the SCEP/VAR correlation energies at R =. a.u. with the so far best variational calculations for the Ne atom performed by Sazaki and Yoshimine [] demonstrates that we have obtained about 9 per cent of their correlation energy, i. e. about 8 per cent of the valence correlation energy for the Ne atom. Thus, the SCEP/ CEPA potential energy function should reproduce the "true" function quite accurately close to the equilibrium distance. In our recent calculations for the isoelectronic HF, HCl, and HBr molecules [] we used the same size of the basis sets as in the present work and obtained spectroscopic constants which agree within about to cm - for <oe and within ± A for re with the well established experimental values. We therefore expect similar accuracy also for the present values for both NeH and KrH ions. The SCEP/CEPA results for NeH confirm the previously published theoretical coe and Table lb. The potential energy and the dipole moment functions of the ground state of KrH (all values in a.u.). Dis- Total energy a Dipole moment b tance SCF SCEP/CEPA SCF SCEP/ CEPA c a The following Gaussian AO basis sets have been employed: 6s, p d, If for Kr and 7s, p, Id for H. The s and p exponents in the core region have not been fully optimized with respect to the energy, since we were only interested in valence shell properties, with respect to the Kr atom as origin. Near r = 6 an avoided crossing of two states causes convergence difficulties so that the results of the procedure employed are subjected to larger errors. re Be <*e (Oe (Oc xe Do a Ho b (A) (cm" ) (cm- ) (cm" ) (cm- ) (ev) (Debye) Table. Calculated molecular constants (ground state). NeH SCF VAR c CEPA d KrH SCF CEPA d a All values corrected for zero point energies (G() = l/roe l/coe#e)- b vibrationally averaged dipole moment with respect to the center of mass as origin, c SCEP/VAR. d SCEP/CEPA. Download Date //8 8: PM

68 P. Rosmus et al. The x Ground States of the NeH and KrH Ions D values obtained f r o m first order CI calculations scattering experiments by Bandybey et al.

3 68 P. Rosmus et al. The x Ground States of the NeH and KrH Ions D values obtained f r o m first order CI calculations scattering experiments by Bandybey et al. [ 6 ], in which only a small por- NeH is quite well, the theoretical value lies between tion of the correlation energy had been accounted the values for. Our equilibrium distance is calculated to be r e =. Ä of Rich et al. [ ]. For KrH somewhat larger (cf. Table ). empirical values are seen to be t o o long by about [ ]. T h e agreement f o r re =. 9 9 Ä of Weise et al. [] and these In Table b results obtained f o r the K r H ion Ä (cf. Table ). The AG values of NeH has are given. For this molecule no other theoretical been directly measured in the associative ionization results f o r comparison are available. experiments of Lorenzen et al. [ ]. Although the molecular energy resolution in these experiments is smaller are listed in than our estimated error in the S C E P / C E P A value Various theoretical and experimental parameters f o r the ions HeH to XeH Table. From these data one recognizes that, though of about c m -, both values agree nicely relatively small, the correlation contributions to the Table ). The proton affinities of the rare gas atoms PEF's are of considerable interest for the calculation of the are not negligible. The correlation effect (cf. always increases the SCF r e values ( f o r instance, by heat of reaction of a variety of ion-molecule reac- about Ä f o r N e H ), decreases the coe values tions. One would therefore like to know these values ( f o r instance, by about c m - f o r N e H ), and rather accurately. As we have previously demonstrat- increases the values of the dissociation energies ( f o r ed in the calculations of the proton affinites f o r the NeH and A r H by about e V ). For the K r H atoms Li to F and Na to Cl, these quantities can be ion a rather pronounced increase in the correlation calculated f o r the atoms at the right side of the energy has been calculated by going f r o m the Kr periodic system f r o m highly correlated electronic atom to the K r H ion, increasing the SCF proton wave of affinity of the Kr atom by 8 ev. This is due to ±. ev [ 6 ]. This is fully confirmed also by the the strong penetration of the proton into the valence associative ionization experiments of Lorenzen et al. functions within an accuracy about shell of Kr ( f o r the /^-dependency of the calculed [ ] f o r N e H and A r H, which yielded values in a correlation energies cf. Table b ). very g o o d agreement with our theoretical predictions be (cf. Table ). For K r H only a value derived f r o m model model potentials is available f o r comparison. This potentials used f o r the interpretations of the elastic value lies close to our SCF result, but the S C E P / Our calculated compared only equilibrium with those distances can obtained f r o m Table. Comparison of some spectroscopic data of the protonated rare gas atoms. Molecule Method r e ( A) ZK?i/ (cm-i) A)(eV) HeH SCF a CW" c NeH SCF FO-CI d SCEP/CEPA ± 99 e ;.f ± 6 ± ± B ArH SCFh PNO/CEPA.7.86 ±.f;.e 68 6 ± 6 ±.7.89 ±..86 ± 8. KrH SCF SCEP/CEPA..9 ±..7 e ;.f 6 ±.7.6 ±..9 e 8. XeH.7 iil/'/iifseo- ) a Ref. []. from data given in Ref. [] as calculated from the PEF from correlated wave functions (CW) of Ref. []. c Ref. []. d first order CI calculations of Ref. [6. e Ref. [], [] and []. f) Ref. []. g) Ref. []. h) Ref. [9]. b Download Date //8 8: PM

69 P. Rosmus et al. The x Ground States of the NeH and KrH Ions Table. Einstein " A " transition probability coefficients of spontaneous emission (J =, all values in sec - ).

4 69 P. Rosmus et al. The x Ground States of the NeH and KrH Ions Table. Einstein " A " transition probability coefficients of spontaneous emission (J =, all values in sec - ). v' Ne H (lower triangle and Ne D (upper triangle) 76/ 67/ 96/ 96/ 9/ 96/ / 7/ 87/ 67/ / 8/ 6/ / 6/ Kr 8 H (lower triangle) and Kr 8 D (upper triangle) 7/ / 7/ 8/ 6/ 68/ / 7/ 8/ - / / 6/ - 7/- 996/ 7/ - a 6/ 6/ 7/ 7/ / 8/ 7/ 98/ 9/ 76/ - / 86/ 88/ / 69/ 99/ 89/ 77/ / 7/ 7/ / 78/ 88/ 96/ / 86/ 697/ 6/ 97/ defined in terms of rotationless dipole moment matrix elements; the vibrational spacings and eigenfunctions have been obtained from the solution of the radial Schrödinger equation with the fitted SCEP/CEPA PEF as input. For the dipole moment curves the center of mass has been taken as origin. C E P A proton affinity of K r is calculated to larger by 6 ev. be Very frequently the protonated rare gas atoms are produced in excited rovibronic states. Nevertheless, no emission systems c o u l d so far be detected experimentally. From our S C E P / C E P A dipole moment functions we have calculated the Einstein transition probability coefficients of spontaneous emission which are listed f o r all transitions v ^ of Ne H, Ne D, K r 8 H, and K r 8 D in Table. These data give insights into the magnitude of the radiative lifetimes of the vibronic states in this series of molecules, and they might be useful f o r the derivation of the infrared intensities and the populations of the particular rovibronic states in the protonated rare gas atoms. Similar calculations f o r the isoelectronic HF, HCl, and HBr molecules [ ] demonstrated the high reliability of such theoretical [] H. U. Mittmann, H. P. Weise, A. Ding, and A. Henglein, Z. Naturforsch. 6a, (97). [] H. P. Weise, H. U. Mittmann, and A. Henglein, Z. Naturforsch. 6a, (97). [] A. Henglein, J. Phys. Chem. 76, 88 (97) and references therein. [] W. B. Rich, S. M. Bobbio, R. L. Champion, and L. D. Doverspike, Phys. Rev. A, (97). [] J. Lorenzen, H. Hotop, M. W. Ruf, and M. Morgner, Z. Physik A, in press, and references therein. [6] R. D. Smith and J. H. Futrell, Int. J. Mass Spectr. Ion Phys., (976). [7] a) J. Schooman, P. G. Fournier, and J. Los, Physica 6, 8 (97). b) P. G. Fournier, G. Comtet, R. W. values. This investigation allows to estimate an accuracy of about to % f o r the fundamental sequence (Av = l) in the calculated probability coefficients and probably slightly larger uncertainties f o r the first overtone sequence. It is interesting to note that the NeH, A r H, and K r H ions in their electronic ground states emit much better than their isoelectronic neutral counterparts H F, HCl, and HBr. The corresponding A(v' = > v" ) values are: HF 89 [ ], NeH 7. 9 ; HCl.6 [ ], A r H 8. ; HBr.6 [ ], K r H 8. 9 (all values in s e c - ). A chnowledgements W e are indebted to the Hochschulrechenzentren der Universität Frankfurt and Darmstadt f o r providing their computer facilities. [8] [9] [] [] [] [] [] [] Odom, R. Locht, J. G. Maas, N. P. F. B. van Asselt, and J. Los, Chem. Phys. Letters, 7 (976). R. Locht, J. G. Maas, N. P. F. B. van Asselt, and J. Los, Chem. Phys., 79 (976). G. Herzberg and H. Liu, to be published, cf. Ref. []. S. Peyerimhoff, J. Chem. Phys., 998 (96). W. Kolos, and J. M. Peek, Chem. Phys., 8 (976) and references therein. D. M. Bishop and L. Cheung, J. Mol. Spectr. 7, 6 (979). R. I. Price, Chem. Phys., 9 (978). K. Vasudevan, Mol. Phys., 7 (97). E. F. Hyes, A. K. Siu, F. M. Chapman, Jr., and R. L. Matcha, J. Chem. Phys. 6, 9 (976). Download Date //8 8: PM

7 P. Rosmus et al. The x Ground States of the NeH and KrH Ions [6] V. Bondyney, P. K. Pearson, and H. F. Schaefer III, J. Chem. Phys. 7, (97). [7] A. C. Roach and P. J. Kuntz, Chem. Communic. 97, 6.

5 7 P. Rosmus et al. The x Ground States of the NeH and KrH Ions [6] V. Bondyney, P. K. Pearson, and H. F. Schaefer III, J. Chem. Phys. 7, (97). [7] A. C. Roach and P. J. Kuntz, Chem. Communic. 97, 6. [8] R, L. Matcha and M. B. Mileur, J. Chem. Phvs. 69, 6 (978). [9] P. Rosmus, Theor. Chim. Acta, 9 (979). [] W. Meyer, J. Chem. Phys. 6, 9 (976). [] W. Mever, J. Chem. Phvs. 8, 7 (97). [] W. Meyer in Modern Theoretical Chemistry, ed. H. F. Schaefer, Plenum Press, New York 977. [] R. Ahlrichs, H. Lischka, V. Stämmler, and W. Kutzelnigg, J. Chem. Phys. 6, (97). [] F. Sazaki and M. Yoshimine, Phvs. Rev. A9, 6 (97). [] H. J. Werner and P. Rosmus, J. Chem. Phys. in press. [6] P. Rosmus and W. Meyer, J. Chem. Phys. 66, (977). Download Date //8 8: PM

Ab initio study of spectroscopic and radiative characteristics of ion-pair states of the Cl 2 molecule

JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 20 22 NOVEMBER 2001 Ab initio study of spectroscopic and radiative characteristics of ion-pair states of the Cl 2 molecule D. B. Kokh, a) A. B. Alekseyev,