ab initio Calculation of 3 3 S Quadrupole Coupling Constants. Reanalysis of the 3 3 S Hyperfine Structure in the Rotational Spectrum of Thiirane

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1 ab initio Calculation of S Quadrupole Coupling Constants. Reanalysis of the S Hyperfine Structure in the Rotational Spectrum of Thiirane B a r b a r a Kirchner, H a n s p e t e r H u b e r, G e r o l d Steinebrunner, H e l m u t Dreizler, Jens-Uwe G r a b o w, a n d Ilona M e r k e b Institut für Physikalische Chemie der Universität Basel, Klingelbergstr., CH- Basel Institut für Physikalische Chemie der Christian-Albrechts-Universität zu Kiel, Olshausenstr., D- Kiel b Institut für Physikalische Chemie der RWTH Aachen, Templergraben, D- Aachen a Z. Naturforsch. a, - (); received January, We present quantum chemical calculations on the MP(SDQ) level with basis sets of high local quality to determine the nuclear quadrupole coupling tensor of S in a series of molecules, which were investigated up to now by microwave spectroscopy. The analysis of the nuclear quadrupole coupling in the rotational spectra provided experimental information on the tensors. As an example for such an analysis, improved values for thiirane, C H S, are given: i a a =.() MHz, X = -.() MHz, * =.() MHz. Introduction Since the advent of microwave spectroscopy after one property, which could be observed, is the hyperfine structure (hfs) of r o t a t i o n a l transitions p r o duced by the interaction of molecular a n d nuclear rotation via the electric nuclear q u a d r u p o l e m o m e n t and the molecular field gradient tensor at the site of the nucleus. The i n f o r m a t i o n provided by the analysis of the hfs is the electric field gradient (efg) tensor in the g = a, b,c principal inertia axis system with the tensor elements dv/dgdg' = qgg., g,g'=a,b,c (V electric potential). This tensor reflects the b o n d i n g situation of an a t o m with a nucleus having a nuclear spin I > and a nuclear q u a d r u p o l e m o m e n t. T h e nucleus acts as a p r o b e for the efg tensor at its coordinates. The technique of analysis of the hfs is described in m a n y publications e.g. []. T h e use of the electric field gradient tensor elements qgg. or the nuclear q u a d r u pole coupling tensor elements xgg e Q gg (e electron charge, Q nuclear q u a d r u p o l e m o m e n t ) to c h a r a c t e r ize chemical b o n d s is discussed in detail e.g. in []. In the last decades the hfs of m a n y nuclei was investigated a n d evaluated, e.g. C, C, Br, B r, I,, N, n B, B, a n d D. Until recently only few molecules could be w o r k e d on c o n t a i n i n g S, as the natural a b u n d a n c e is only.% a n d a p r e p a r a t i o n is sometimes difficult and always expensive. Reprint requests to Prof. Dr. H. Dreizler. T h e sensitivity, resolution, a n d auracy o b t a i n e d by molecular beam Fourier t r a n s f o r m microwave spectroscopy [] allowed us to investigate the hfs of S containing molecules in n a t u r a l a b u n d a n c e. This opens an interesting a n d wide field, as sulfur exists in different b o n d situations. As q u a n t u m chemistry advanced tremendously, it is interesting to c o m p a r e the experimental d e t e r m i n a tion a n d calculation of the efg tensor elements qgg.. These calculations provide the complete tensor with diagonal a n d off-diagonal elements referred to the principal intertia axis system g = a, b, c, whereas the analysis of the experiments results only in exceptional cases in a complete tensor. The usual result is the set of diagonal elements qgg or xgg Sometimes s y m m e t r y forces some off-diagonal elements to b e c o m e zero or considerations using isotopomers with a r o t a t e d principal inertia axis system allow the d e t e r m i n a t i o n of the off-diagonal tensor elements [] f r o m the r o t a t i o n a l spectra. It should be mentioned that experiments a n d q u a n t u m theory determine a slightly different quantity: T h e efg tensor of a molceule in the vibrational g r o u n d state a n d the efg tensor of a molecule with a certain fixed structure, respectively. First, we present a b initio calculations for molecules performed in Basel. Second, as an example of an analysis of S-hfs, results for thiirane will be given. T h e spectra were remeasured in Kiel a n d Aachen to improve former results []. - / / - $. - Verlag der Zeitschrift für Naturforschung, D- Tübingen Dieses Werk wurde im Jahr vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.v. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namensnennung. Lizenz. This work has been digitalized and published in by Verlag Zeitschrift für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution. International License.

2 B. Kirchner et al. ab initio Calculation of S Q u a d r u p o l e Coupling Constants Quantum Chemical Methods Basis Set Evaluation All calculations were performed at experimental microwave gas phase structures, usually restructures, in a few cases restructures []. The calculations are for the rigid structure, i.e. vibrations are neglected. We expect the error due to this approximation to be a few percent (see also discussion below). Hence, high auracy of the structure is of minor importance. MollerPlesset perturbation theory was applied on the M P (SDQ) full level using the Gaussian [] set of programs. Basis sets of high local quality, which had been applied suessfully in the calculation of deuterium[-], lithium- [], nitrogen- [, ] and oxygen[] quadrupole couplings were used (note that Chesnut and Moore [] have recently used the same concept under the name "locally dense basis sets" for the calculation of chemical shifts). Using a quite large basis set on the sulfur yielded results very close to experiment, in contrast to previous calculations of other chemical elements. Hence, we did not use the nuclear quadrupole moment of S as a fit parameter but applied the IUPAC value of -. " m [], Therefore, the results in this paper were obtained fully ab initio (at the experimental structures). We performed a few calculations on H S, H C S and H N C S with distorted geometries to study the influence of the structure on the size of the quadrupole coupling constants x A change of % in the valence angle results in about.% change in the couplings. A change of % in the S-X bond-length(s) yields a change of about % in the coupling with the exception of HNCS, where the change is about % for the large components of the coupling tensor, but about %, i.e. MHz, for the smallest component. In general, the structures used here are more aurate than %, hence the error due to the inauracy of the structures should be negligible. However, in extreme cases, if only an r e s t r u c t u r e is available and the coupling is very sensitive (as in HNCS), such an error might be the origin of a deviation from experiment. With the above test calculations we estimated the vibrational contributions to the quadrupole coupling constants to be of the order of a few percent (probably typically to %). A further test was performed to estimate the intramolecular basis set superposition error of the efg. For H C S this error turned out to be about.%. This is negligible compared to the other inauracies. Whereas for molecular properties balanced basis sets are appropriate, the calculation of local properties (e.g. the efg at a nucleus) can be performed much more efficiently with basis sets which have locally a very high quality, whereas atoms further away are treated with smaller basis sets. Here we use an extremely large basis on sulfur, medium sized basis sets on the nearest (basis A) or nearest and next nearest neighbours (basis B), and a small basis on all atoms further away. The sulfur basis was constructed starting with a primitive regularised even-tempered basis set [] for the oupied orbitals. For H S and H C S the size was increased until the change of the electric field gradient was negligible (here and in the following we call a change or an error negligible, if it is small compared to the expected error due to the neglected vibrations, which we estimate to be a few percent). The resulting basis consisting of s- and p-functions was contracted to s- and p-functions such that the change again was negligible. With the same citeria, d-functions and then f-functions were added to make the electric field gradient converge on the M P ( S D Q ) level in these two molecules. The final basis is given in Table and was used in all further calculations. The medium sized basis set on the hydrogens consisted of Dunning's (s)/[s] basis [] scaled by and enlarged by a set of p-functions with exponent. For the first row elements, Dunning's (s p)/[s p] basis [] was enlarged by two sets of d-functions (exponents and. for C, and. for N,. and. for O, and. and. for F). For the second row elements, the (sp)/[s p] basis by McLean and Chandler [] was supplemented with two sets of d-functions (exponents. and. for P, and and. for S). For the direct neighbours of S, always the medium sized basis was used. In basis B, the medium basis was also used for atoms other than hydrogens if they were one step further away. We expected to improve the results mainly for conjugated systems like thiophene with basis B. On Ge we used the (s p d f)/[s p d If] basis set by Curtiss et al. [, ]. The small basis used for hydrogen was Dunning's (s)/[s] basis [] scaled by a factor of, whereas for first row atoms the (s p)/[s p] basis by Roos and Siegbahn [] was applied.

3 B. Kirchner et al. ab initio Calculation of Table Basis set evaluated for sulfur (different contractions are subdivided by underlining). s-functions p-functions Exponent Coefficient Exponent Coefficient L /-functions Exponent.. <Coefficient d-functions Exponent... Coupling Constants S Quadrupole Coefficient L Results and Discussion of the Quantum Chemical Calculations In Table the results of all calculations are collected a n d c o m p a r e d with the experimental couplings. W h e r e basis A a n d B are identical, the values are t a b u l a t e d under B. Also given are values by P a l m e r [], calculated including electron c o r r e l a t i o n by c o m plete active space scf studies. The i m p r o v e m e n t by the present calculations is shown by the r m s deviations between experiment a n d calculation. T h e rms value of. M H z corresponds to to % relative to the largest c o m p o n e n t, or % of the whole r a n g e of couplings, which is p r o b a b l y very close to the e r r o r due to the neglect of the zero p o i n t vibrations. Figure shows the calculated (basis B) versus the experimental values. Basis B was mainly introduced t o i m p r o v e results for conjugated systems, where a t o m s which are n o t neighbouring the sulfur a t o m are p a r t of the i-system. F o r the coupling elements where basis A a n d B are different, the rms deviation between experimental a n d calculated couplings was reduced f r o m M H z for basis A to M H z for basis B. H o w e v e r, a detailed S-QCC QCC/MHz o Co _o to o experimental QCC/MHz Fig. ab initio calculated (basis B) versus experimental Squadrupole coupling constants for the compounds in Table. The dimers are not included. Where available, all diagonal terms were used; in the case of CH SSCH the off-diagonal terms are included. The line has slope one, i.e. it is not a fitted line. analysis shows t h a t the largest i m p r o v e m e n t s are for isothiazole, thiophene, thiazole, O C S a n d H N C S, whereas, e.g., the substituted thiiranes show only a m i n o r improvement. This is exactly what we expected, a n d it shows t h a t for t-systems the basis h a s to be of reasonably g o o d quality t h r o u g h o u t the t-system. A l t h o u g h basis B improved the results for O C S f r o m -. M H z (basis A) to -. M H z, the deviation f r o m the experimental value of. M H z is still surprisingly large. To check, whether this is due to an unsaturated basis or has an another source like, e.g., vibration, we repeated the calculation with the still larger aug--pvtz basis set by D u n n i n g [] on C and O. T h e calculation yielded a value of. M H z, which proved that the basis set is still not completely saturated. Similarly, replacing the two sets of d-functions on the P of SPF by sets of d-functions (exponents.,. and.) and one set of f-functions (exponent.) changed the coupling to. M H z for basis A a n d. M H z for basis B. This shows that two sets of d-functions might not be sufficient as polarization functions for second row elements. Nuclear Quadrupole Coupling in the Rotational Spectrum of S-thiirane In S h o e m a k e r a n d Flygare [] investigated thiirane with an experimental precision which was

4 B. Kirchner et al. ab initio Calculation of S Quadrupole Coupling Constants Table. Comparison of calculated with experimental S quadrupole couplings in MHz. Molecule Principal axes of the moment of inertia Principal axes of % Ref. of exp. data Axis Exp. Basis A Basis B Ref. [] a Axis Basis A Basis B Structure H S [] [] Hydrogen sulfide ±.... H S HF [] [] ac. CHSSCH [] [] Dimethyl disulfide ab. +. ac be CHSCH [] [] Dimethyl sulfide CHSCN [] [] Isothiocya natomethane ab.. C H S this [] Thiirane work C H S [] [] Methylthiirane ab ac be.. C H S [] [] trans-,-di methylthiirane ac.. C H S [] [],-dimethyl thiirane ac C H S [] [] Thiophene advanced at that time. Our studies on methyl substituted thiiranes, like monomethyl- and dimethyl thiiranes [,, ] convinced us that the S-hfs of thiirane [] itself could presently be investigated with higher precision, as the technique of microwave spectroscopy improved considerably []. Thiirane may be used as reference molecule for substituted thiiranes. For symmetry reasons, all off-diagonal elements of the coupling tensor are zero. Rotation of the coupling tensor from the inertial system of thiirane into the inertial systems of substituted thiiranes may therefore serve as reference for the comparison of changes in the electronic environment due to substitution. The following report may also be taken as an example for many S-hfs investigations.

5 B. Kirchner et al. ab initio Calculation of S Quadrupole Coupling Constants Table. Continued Molecule Principal axes of the moment of inertia Principal axes of % Ref. of exp. data CHNS Thiazole CHNS Isothiazole (CH)so Dimethylsulfoxide HNCS Isothtiocyanic acid SPF Thiophosphoryl fluoride H CS Thioformaldehyde GeS Germaniumsulfide so Sulfurdioxide OCS Carbonoxidesulfide Axis Exp. Basis A Basis B Ref. [] a Axis Basis A Basis B Structure ab ab be ab b. b. b. b."." > [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] (-.) [] [] [] [] SCO HF [] [] rms deviation between exp. and calc. values.. a Calculated from electric field gradients in atomic units using the IUPAC value of. " m quadrupole moment of S. b Values given in the principal axes of the quadrupole coupling (not included in the rms values). for the nuclear Experiment and Analysis Thiirane, C H S, was obtained from Aldrich, Steinheim, and used without further purification. Since for this molecule the transitions with low angular momentum quantum number J are distributed over a wide range, we used molecular beam Fourier transform microwave spectrometers in the range from to. GHz [-] in Kiel and Aachen, and from. to GHz [] in Aachen. The instruments introduce the molecular beam parallel to the resonator axis [], thus increasing resolution, auracy and sensitivity. The sample was introduced as a pulsed supersonic molecular beam with a content of % in argon and a backing pressure of approximately kpa. K to K experiment cycles were necessary for the S transitions. K data points with ns interval were recorded. As the rotational spectra of the S, S, and S isotopomers were known [, ], the low J transitions could easily be identified. Nevertheless we performed a centrifugal distortion analysis for the S isotopomer aording to van Eijck [] with the newly measured lines. The centrifugal distortion constants

6 B. Kirchner et al. ab initio Calculation of were used for a m o r e precise evaluation of the molecular c o n s t a n t s of the S isotopomer. We could not record a sufficient n u m b e r of lines for this rare isotop o m e r in n a t u r a l a b u n d a n c e to determine its centrifugal distortion constants. T h e lines are given in Table, the r o t a t i o n a l a n d centrifugal distortion c o n s t a n t s in Table. F o r m a n y S- a n d S i s o t o p o m e r lines a partially resolved fine structure was observed which is not yet interpreted. Spin-rotation or spin-spin coupling m a y be a source of it. Its analysis needs a still higher resolution. We report in Table for the lines m e a n values averaged over this fine structure a n d the D o p p l e r d o u blets. T h e lines of the S i s o t o p o m e r measured in n a t u r a l a b u n d a n c e are given in Table. T h e measured transitions of Table are splitted by nuclear q u a d r u pole coupling. They were analysed by a H a m i l t o n i a n of a centrifugally distorted r o t o r supplemented with S nuclear q u a d r u p o l e coupling []. T h e p r o g r a m H F S C of G r i p p [] used for the evaluation of the p a r a m e t e r s diagonalises the hamiltonian matrix. T h e results are presented in Table b. With the values xgg, g = a, b, c of the q u a d r u p o l e coupling constants, included also in Table, a reference is available to evaluate substitution effects. A c o m p a r i s o n with [] shows the improved auracy, by a factor of at least ten, of the presented analysis. Table. Measured transitions of S thiirane. J' K'_ K'+ J" K'l K: vobs/mhz v/khz Sv = vobs ^ calc ' vcalc calculated with constants of Table a. S Quadrupole Coupling Constants Table a. Rotational and centrifugal distortion constants of S thiirane. A / MHz B /MHz C /MHz K D'j /khz D; K /khz D'K /khz <; /khz /khz n a /khz. (). (). () -. (). (). (). (). () -. (). K = asymmetry parameter (B A C)/(A C), n = number of components, cr = standard deviation, standard errors in parentheses are in units of the last given digit. Table b. Rotational, centrifugal distortion, and quadrupole coupling constants of S thiirane. A B C /MHz =. () /MHz =. () /MHz =. () K -. () [.] Dj [.] DjK [.] K [.] <; [-.] K /MHz = -. () X ~X j MHz = -. () /MHz = -. () X /MHz =. () N = O. The centrifugal distortion constants were fixed to the values of the S isotopomer, K = asymmetry parameter = ( B A C )/(A C), n number of components, o standard deviation, standard errors in parentheses are in units of the last given digit, fixed values in brackets. Transformation of Coupling Tensors and Discussion To assist the analysis of a r o t a t i o n a l spectrum s h o w i n g hfs, the tensor of the considered nucleus of a similar molecule is t r a n s f o r m e d into the principal inertia system of the molecule u n d e r investigation []. We d e m o n s t r a t e the p r o c e d u r e with thiirane a n d its methyl derivatives included in this w o r k. T h e a s s u m p tion for this p r o c e d u r e is t h a t the structure of the reference molecule a n d that u n d e r investigation is k n o w n at least a p p r o x i m a t e l y. F o r the examples given below, rs- a n d r e s t r u c t u r e s were determined. T h e p r o cedure f u r t h e r neglects different s u r r o u n d i n g of the coupling nucleus d u e to substitution effects.

7 B. Kirchner et al. ab initio Calculation of Table. Measured transitions of J' = Vo b s F' / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / ^calc ^calc S Quadrupole Coupling Constants S thiirane. J" K'L K'i F" vobs/mhz v/khz calculated with constants of Table b T h e q u a n t u m chemical prediction of a c o u p l i n g tensor relies also on an experimental structure, if it was not optimised. In our cases the r e s t r u c t u r e was used. In Table we compile for convenience the d a t a for the thiiranes. T h e rotation of the q u a d r u p o l e coupling tensor of thiirane in Table was p e r f o r m e d with the help of structural d a t a [,,, ]. We give only the m a g n i t u d e of the off-diagonal elements of the coupling tensor as a n analysis of the hfs results in the magnitude of the xgg, a n d the sign of the p r o d u c t n xgg,,g^g' [], T h e individual signs of the three or one n o n zero element is u n d e t e r m i n e d. Consideration of Table shows that the values of the coupling constants calculated by q u a n t u m chemistry are slightly closer to experimental values t h a n the values obtained by tensor r o t a t i o n. But the tensor rotation excludes substitution effects, which are noticeable for the example molecules. Table shows also that experimental a n d calculated values for dimer complexes disagree m o r e t h a n for the stable molecules. T h e reason is that the calculated values are for the rigid structure, whereas the experimental values include a zero point vibrational m o t i o n mainly of the angle defining the relative position of the t w o m o n o m e r s. In S C O HF, Legon a n d Willoughby [] have calculated a zero point vibrational angle of., a s s u m i n g n o change in the electronics, a n d applying the e q u a t i o n Xdimer/Xmonomer = J < C S ~ > If we t a k e the decrease of x due to electronic influences of M H z (Table, basis B) into aount, i.e. increase / d i m e r in the a b o v e equation by this a m o u n t, the a b o v e angle decreases to. N o n l i n e a r complexes, like H S HF, need m o r e detailed experimental work to provide at least all xggw i t h the complete set it m a y be checked if the coupling tensor is changed under complexation. F o r the e x a m p l e m e n t i o n e d, especially X is i m p o r t a n t as it should result f r o m ;c a a (H S) if the tensor is not modified by c o m p l e x a t i o n. An estimate of the electronic influence similar to t h a t for S C O HF, but less aurate, can be m a d e by t a k i n g the decrease of M H z of the largest tensor element x- z of the q u a d r u p o l e coupling in the principal axes of the efg (Table, basis B). Willoughby et al. [] calculated a n angle of, which is increased to using the new coupling constants of Saleck et al. [] for H S. Taking into aount the above decrease d u e to electronic effects, this value decreases to.. This c o n f i r m s t h a t the a s s u m p t i o n was a reasonably g o o d one. F o r complexes, an averaging of the coupling tensor over the large a m p l i t u d e m o t i o n s should be studied in m o r e detail. T h e assumption of a coupling tensor inv a r i a n t to complexation needs verification in each case. W i t h m i c r o w a v e spectroscopy it is only in rare cases possible to determine the complete coupling tensor in the inertia axis system a, b, c. An example is C H S S C H []. In m a n y cases the coupling tensor in its o w n principal axis c a n n o t be determined straight f o r w a r d. H e r e q u a n t u m chemical calculations are superior. We give in Fig. an illustration for selected examples, where the principal inertia a n d coupling tensor axes d o not coincide. The i n f o r m a t i o n results f r o m calculations with basis B.

8 B. Kirchner et al. ab initio Calculation of S Quadrupole Coupling Constants Table. Compilation of quadrupole coupling constants x gg [MHz] in the principal inertia system determined by experiment (exp), by rotation of the quadrupole coupling tensor of thiirane (rot tensor) and by quantum chemical calculations with basis A (QCA) and basis B (QCB). Methylthiirane,-Dimethylthiirane trans-,-dimethylthiirane a Exp. cit a Rot.-tensor < b cit c QCA < b QCB < b X -. () [] -. [] X -. () X. ()... I Xab n.d \Xac\ n.d I Xbc I n.d X. -. () [] -. [] - - X. () () I Xab n.d. - - I Zoe I n.d \Xbc\ n.d. - - X. () []. [].. X -. () X. ().. I Xab n.d \Xac\ n.d IZfI n.d Citation of experimental values, b relative deviation from experimental value in %, citation restructure used for the tensor rotation, n.d. not determined. Thiazole S. bisectrix. Isothiocyanatomethane Isothiazole efg-principal axis,-dimethylthiirane HoC Conclusion It may be stated that the ab initio calculations reproduce the experimental data within the mentioned errors mainly determined by the neglected vibrational contributions. From the still limited number of molecules two groups may be selected, sulfur in a bent bond and sulfur in aromatic systems. Within the groups there are noticeable variations. For other bond types, like sulfoxides and others, the experimental results are very limited. Combination of ab initio calculation and experiment leads presently to the most complete information... Acknowledgements trans-,-dimethylthiirane H,C / HC S CH CH ring plane. c Fig.. Calculated deviations of the efg principal axis from the bisectrix in some molecules of the X-S-Y type. For trans-,-dimethylthiirane the deviation from the vertical to the ring plane is shown. The authors from Basel thank the staff of the university computer centre in Basel for their assistance and the Swiss HLR-Rat for a grant of computer time on the national supercomputer. The investigation is part of the project -. of the Schweizerischer Nationalfonds zur Förderung der Wissenschaften. The authors from Kiel and Aachen thank the members of their groups for help and discussions, the Deutsche Forschungsgemeinschaft, the Fonds der Chemie and the Land Schleswig-Holstein for funds.

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