Chromatostructural Analysis (Chromatoscopy) A New Method of Determination of Molecular Structure BY ANDREJV. KISELEV Chemistry Department Lomonosov State University of Moscow and Institute of Physical Chemistry U.S.S.R. Academy of Sciences Moscow U.S.S.R. AND DIONISAS P. POSHKUS Institute of Chemistry and Chemical Technology Academy of Sciences of the Lithuanian S.S.R. Vilnius U.S.S.R. Received 1 lth July 1980 The intermolecular interaction of an isolated adsorbed molecule with a homogeneous flat solid surface and thence the thermodynamic characteristics of adsorption and adsorption chromatography at low (zero) surface coverage depend significantly on the molecular geometry of the adsorbate. Graphitized thermal carbon black (GTCB) is such a homogeneous solid and so may be used to deter- mine some parameters of molecular structure.Use is made of the gas-chromatographically obtained Henry’s constant for adsorption on GTCB with a semi-empirical molecular statistical theory of ad- sorption based on an atom-atom approximation for the potential function for intermolecular adsor- bate-adsorbent interaction. The method is shown to be successful in determining first structural parameters for molecules of hexamethylbenzene indane 2-and 5-methylindanes tetralin and secondly potential-function parameters for internal rotation in the molecules ethylbenzene and diphenyl and its methyl derivatives. By extension of the technique experimentally obtained Henry’s constants for adsorption on ion adsorbent-zeolite (NaX) have been used to determine the quadrupole moment of the cyclopropane molecule.The macroscopic property of a molecule most dependent upon its geometry is its adsorption on a homogeneous flat surface of an inert adsorbent since the molecule is subject only to the molecular field effect of the solid from one side in contrast to the situation in a gas a liquid or within a crystal lattice where effects from all sides are experienced. Hence adsorption on a flat homogeneous surface of a solid body can be an important source of information relating to the structure of adsorbed molecules. This fact has been largely overlooked first because of the inhomogeneity of the porous adsorbents so commonly used for adsorption and secondly because typically adsorp- tion has been measured in experiments starting from rather high surface coverages when intermolecular adsorbate-adsorbate interaction contributes considerably.In recent decades however technical developments have emerged which eliminate any difficulty. Graphitized thermal carbon black (GTCB) which is a dispersed non- porous solid body with a totally homogeneous surface [see reviews (1) and (2)] is now freely available while chromatographs with sensitive detectors can be used to study adsorption at very low surface coverages when adsorbate-adsorbate intermole- cular interaction is negligible. Hence in gas-adsorption chromatography the reten- tion volume for zero sample size from essentially non-adsorbed carrier gas is a mea- sure of the Henry’s constant K, a quantity demonstrably sensitive to the geometry of adsorbate molecules.In capillary columns filled with GTCB for example all the ten isomers of para-dibutylbenzene are easily fully separated. The isomer with the CHROMATOSTRUCTURAL ANALYSIS most branched substituents i.e. para-di-tert-butylbenzene is the first to leave the column and the isomer with most extended substituents i.e. para-di-n-butylbenzene leaves last.3 All five isomers of perhydroanthracene (fig. 1) are also separated as a consequence of the progressive flattening of the m~lecule.~ Ions (ionic crystals and specifically zeolites) and dipoles (hydroxylated surfaces of silica etc.) on the surface of the adsorbent make the Henry’s constant sensitive not only to the geometric structure of the adsorbed molecule but also to specific features of its electron structure such as rigid multipole moments ability for donor-acceptor interaction and proton transfer.Y 4 m 2,a5 Y J ~ -1 ;I L 2 4 6 81012 timelmin FIG.1.-Chromatogram4 of perhydroanthracene isomers on capillary packed column with GTCB for 513 K. Length of column 1.4m internal diameter 0.5 mm; particle size 0.1-0.12mm; carrier gas is hydrogen. 1 cis-syn-cis; 2 cis-anti-trans; 3 cis-anti-cis; 4,trans-anti-trans; 5 trans-syn-trans. Hence we can formulate two strategic appro ache^.^-^ (1) Given the structure of adsorbent and adsorbate we may determine the Henry’s Law constant and related thermodynamic quantities for adsorption at zero surface coverage using the molecular-statistical method.In the following diagram this corres- ponds to moving from left to right. (2) Using the same adsorbent and having measured Henry’s constant for adsorb- ate of an unknown or insufficiently known structure we may conversely determine parameters relating to the adsorbate molecule structure. In the diagram this cor- responds to moving from right to left. A. V. KISELEV AND D. P. POSHKUS structure of molecular-statistical Henry’s molecule and theory of adsorption for constant adsorbent zero surface coverage With a non-specific adsorbent like GTCB the method can thus be used to deter- mine certain geometric molecular parameters whilst with ion adsorbents or adsor- bents with polar groups on their surface the method can alternatively be used to determine some parameters relating to the electronic structure of the molecules.MOLECULAR-STATISTICAL CALCULATIONS OF HENRY’S CONSTANT FOR ADSORPTION OF HYDROCARBONS ON GTCB A semi-empirical molecular-statistical theory of adsorption at zero coverage of hydrocarbons on GTCB2*6-10 has been developed. It is based on molecular statistics and an atom-atom approximation for the potential function @ for intermolecular interaction of the adsorbate molecule to adsorbent. According to molecular statistics the relationship of Henry’s constant to potential energy Q depends on the structure of both the adsorbate molecule and the adsorbent. For adsorption of a three-dimensional (non-linear) quasi-rigid molecule on the basic face of graphite to a good approximation the following equation holds where Qoand Qy are values of @ and its second derivative at an equilibrium distance zo between the molecule’s centre of mass and the surface for fixed Eulerian angles 8 and ty which determine the molecular orientation relative to the mathematically homo- geneous surface.Adsorption on GTCB is undoubtedly non-specific as is indicated for example by the fact that the initial heat of adsorption of ethyl alcohol on GTCB is much lower than is its heat of condensation.2J1 Besides both Henry’s Law constants and the heats of adsorption on GTCB,at low surface coverages decrease in the adsorbate series ethane ethylene and acetylene,” i.e. the reduced number of hydrogen atoms in molecules of ethylene and acetylene compared with the molecule of ethane has greater influence than has the change in electron configuration of the carbon atoms from alkane to alkene and on to alkyne.Non-specific adsorption on GTCB and the linear dependence of heats of adsorp- tion of isolated flat molecules on their polarizability2 indicate an atomic or bond addi- tivity of the energy of intermolecular interaction of molecules with GTCB. Thus to determine the potential function Q one can use the atom-atom approximation @ = CA C VM. . . A (2) where q is the potential energy of intermolecular interaction of an atom of the mole- cule M with an atom of adsorbent A. Our published work shows that the form of atom-atom potential function adopted for the intermolecular interaction is of little consequence in the context of molecular- statistical calculations of although the selection of parameters for these Kl,2p8*12 functions is important.Theoretical and combinatorial expressions allow the deter- mination of q from the properties of adsorbent and adsorbate considered sepa- 16 CHROMATOSTRUCTURAL ANALYSIS rately,2,9,13-15 and values of Kl calculated from the relevant atom-atom potentials q differ but slightly from the corresponding experimentally obtained values. Compari-son of the calculated and experimentally obtained constants (Kl) for a few reference adsorbates then allows one to refine the parameters of the atom-atom potential functions In this way atom-atom potential functions were determined for p.299910 intermolecular interactions of the GTCB carbon atom with the hydrogen atom pH.. . C(GTCB) and the carbon atoms of a hydrocarbon molecule for two of their electron configurations pc(sp3). . . C(GTCB) and q+(sp2) . . . C(GTCB). The possibility of extrapolating the atom-atom potential functions obtained for reference molecules of a given class to other molecules of the same class was subsequently checked. The potential functions p obtained by the above procedure were finally used to calculate Henry’s constants which were in good agreement with the experimental values obtained for adsorption of hydrocarbons of different classes (alkanes cyclanes alkenes aromatic alkylaromatic and other hydrocarbons) on GTCB.2p9*10J”18 Molecular-statistical calculations of thermodynamic characteristics of adsorption for some molecules in other approximations have also been gi~en.’~-~~ DETERMINATION OF GEOMETRIC STRUCTURE PARAMETERS FOR QUASI- RIGID MOLECULES The inverse problem i.e.the determination of some geometric structure para- meters of hydrocarbon molecules using experimentally obtained Kl values for the adsorption on GTCB can now also be solved. To do this values of Kl are calculated as above for the molecule under consideration using a range of values of the unknown structural parameters and preference is then given to those which correspond best to the experimental Kl for different temperature^.^*^'-'^ By this procedure one can determine especially those structural parameters of the molecule upon which the constant Kl is strongly dependent.Specifically this technique can be used for deter- mining valence angles and potential barriers of internal rotation of large fragments of a molecule. Some results obtained by this chromatostructural (chromatoscopic) method are considered below. The detailed structure of tetralin and indane molecules is not well known. The tetralin molecule can be represented as a combination of the benzene and cyclohexene molecules in which case it can be assumed that the common bond has the length of the C ...C bond in benzene and that the C atoms of the cyclohexene ring which are the closest to this bond are located in the plane of the benzene ring. This structural model of the tetralin molecule however does not offer any guidance as to the valence angles of the cyclohexene ring and the extent of deviation of the remaining two C atoms of the cyclohexene ring from the plane of the benzene ring.The best agree- ment of theoretical with experimental values of Kl for tetralin adsorption on GTCB was obtained for the valence angles and deviations h given in table 1 (the two C atoms deviate in different directions from the benzene ring plane).17 Similarly to tetralin the indane molecule can be represented as a combination of benzene and cyclopentene molecules along the C ..C bond. We can also assume that the two carbon atoms of the cyclopentene ring which are the nearest to this bond are located in the plane of the benzene ring. This model however leaves uncertain the position of the fifth carbon atom (dihedral angle cc in fig.2) of the cyclopentene ring. Fig. 2 shows the depend- ence of the calculated value of Kl on this angle cc. Agreement between calculated and experimental values of Kl for indane adsorption on GTCB is obtainedI8 for a = A. V. KISELEV AND D. P. POSHKUS 19 & 3" and this value was used to solve the reverse problem i.e. to calculate Kl for 5-methylindane. The calculation shows good agreement with gas-chromatographic measurements (fig. 3).19 Fig. 4 illustrates results of a similar chromatostructural determination of a for TABLE l.-STRUCTURAL PARAMETERS OF TETRALIN MOLECULES (ATOMS 1 AND 2 FORM THE BOND COMMON TO BOTH RINGS) assumed bond lengths and obtained values of h and valence angles valence angles ~~ C=C in benzene ring 1.399 8 h 0.409 A cZ-c3 Cl-c6 1.504 A (ciC,c, czc1crj 122.5" c3-c4 cs-c 1.515 (c2c3c4,c,c6cs 111.0" c4-c5 1.550 A (C3C4C5 C6C5C4 109.5" C-H in cyclohexene ring 1.093 bi C-H in benzene ring 1.101 A (HCH for C3 and C 108" (HCH for C4 and C5 109.5" (CCC in benzene ring 120" 2-methylir1dane.~~ From the two possible structures for 2-methylindane we now have that one with an axial methyl group may be rejected at once since it yields values for Kl that are far too low to be acceptable.The structure with the equatorially located methyl group in contrast shows good agreement with the experimentally obtained Henry's constant for M. = 11 & 3". The experimental value of Henry's constant Kl for adsorption on GTCB was also used to determine the angle of deviation of the carbon atoms of the methyl groups from the benzene ring plane in hexamethylbenzene (fig.5).7*20The angle determined by this method (ca.10') is in agreement with that obtainedvia the electronographic method (9.9 & 2").21 Having successfully determined the structure of molecules of decalin and tetralin I 4t I I I I I I 5 10 15 20 25 30 FIG.2.-Full curve is for the calculated dependence of Kl for indane adsorption on GTCB (450 K on dihedral angle u. Horizontal dashed line shows the corresponding experimental CHROMATOSTRUCTURAL ANALYSIS w/ 01 I I 0.0020 0.0025 KIT FIG.3.-Dependence of In Kl on l/Tfor 5-methylindane on GTCB. Line is theoretical calculation; dots are experimental and of perhydr0phena:ithrene on the one hand and indane indene and hydroindane on the other we are now working on the important problem of applying chromato- scopy to the determination of the structures of isomers of the carbon skeleton of steroids.Clearly determination of the potentials of intermolecular interaction of oxygen atoms with the C atom of GTCB in different electron configurations would allow extension of the chromatostructural method to steroids proper for aglycone parts of glycosides prostaglandins and many other biologically active substances and their metabolites. The substances available normally contain components which are difficult to identify. Hence the initial problem is to know to which substance or at least set of isomers the Henry's Law constants taken from the chromatogram belong.In the preliminary stages therefore the chromato-mass-spectrometric method is necessary 16 c 5 10 15 20 25 30 ddeg FIG.4.-FulI curve is for the calculated dependence of Kl for 2-methylindane adsorption on GTCB on dihedral angle u for 450 K. Horizontal dashed line is for the corresponding experimental Revised data give u = 11 f3. A. V. KISELEV AND D. P. POSHKUS though it of course meets difficulties when substances have similar mass spectra e.g. isomers of polycyclic hydrocarbons. The distinct difference in the intensities of the peaks of basic fragments and in the spectra of metastable ions has been observed in our laboratory in the case of perhydroanthracene and perhydrophenanthrene isomers.Other methods have to be invoked. r 5 n .5 d W -4 5 10 15 Bideg FIG. 5.-Full curve is for the calculated dependence of Kl for hexamethylbenzene adsorption on GTCB for 500 K on the angle B of deviation of C atoms of methyl groups from the benzene ring plane. Horizontal dashed line is for the corresponding experimental value^.^*'^^*^ DETERMINATION OF THE STRUCTURE PARAMETERS FOR MOLECULES WITH INTERNAL ROTATION Many molecules exhibit internal rotation and in most cases this rotation is hindered. The structural quantities characterising the potential function of inner rotation W of such molecules are an equilibrium angle and the potential barrier or barriers to rotation. These quantities can in fact also be determined from experi- mentally measured values of Kl and their temperature dependence.6 For molecules with internal rotation the Henry’s Law constant is given by where a is the angle of internal rotation K,(a) being Henry’s constant calculated for fixed a.W may have one or more minima and maxima (potential barriers) but for ethyl- benzene for example there is a single barrier Wo. To compare the calculated and experimental Kl values the deviation S is used where Klexpand KIcalcare the experimental and calculated values of Henry’s constant for the column temperature Ti, n being the total number of these temperatures. 6 is CHROMATOSTRUCTURAL ANALYSIS thus the root-mean-square deviation of the experimental from the calculated Kl for different values of W,.Evidently the least 6 corresponds to the best agreement of calculated and experimental Kl values. Fig. 6 shows the dependence of 6 on W for ethylbenzene. The minimum of this curve corresponds to Wo= 1.7 kJ mol-1.20 Fig. 7 illustrates the results of a similar analysis for an isolated molecule of 2,6-dimethykliphenyl which has an equilibrium angle between the planes of the benzene 0.02 h E -5 3 -0.01 I I I 1 1 2 3 W,/kJ mol-' FIG.6.-Dependence of 6 for ethylbenzene on barrier to internal rotation Wo. rings aminand two barriers to internal rotation W, and W,,.*O The method yields amin= 68" Wol> 200 kJ mol-' and W, = 5 kJ mol-I. For diphenyl,6 determination of aminhas proved difficult since the calculated dependence of 6 on aminover a large range of amindoes not show a clear cut minimum.However the value amin= 42"has been obtained by the electronographic method,, and with this value the chromatostructural method then yields for diphenyl W, = 7 and W, z 0.1 kJ mol-I. The controversy aroused by the determination of these parameters by other methods is largely resolved by these results.6 The chromatostructural method described here yields the parameters of W for iso- lated molecules (in vacuo). Knowing these parameters we are clearly now in a posi- tion to calculate molecular conformations in different media particularly in the adsorbed state. CALCULATION OF HENRY'S CONSTANT FOR ADSORPTION IN ZEOLITES AND ESTIMATION OF THE ELECTRIC MOMENT OF A MOLECULE BY THE CHROMATOSTRUCTURAL METHOD The atom-atom (atom-ion) approximation can also be applied to calculate the potential energy of the molecule-zeolite intermolecular interacti~n.~.~~-~~ However in the case of adsorption of non-polar molecules in zeolite one has to take extra account of interaction of the induced dipoles of the admolecule and the electrostatic field of the zeolite.Parameters of the relevant potentials q are first estimated from the properties of the adsorbate and adsorbent taken separately. As in adsorption on GTCB the parameters of the functions 9 are corrected by comparing Henry's constant Kl (referred to 1 g of zeolite of the given composition) calculated via an approximate A. V. KISELEV AND D. P. POSHKUS function p with experimental Kl values for a reference molecule (of the given class of adsorbate in zeolite of the given composition).Corrected atom-ion potential functions for intermolecular interaction with ions I of zeolite NaX of H and C atoms of molecules of alkanes pH. . . I and q9c(sp~)I . . . I are then found using ethane as a reference molecule. Then these potentials are used to calculate Kl for other alkanes and cyclanes on the same zeolite NaX.24-26 Kl amin= 68" I I I J (b) 20: 100 60 70 80 90 umin/deg FIG.7.-Values of dminfor 2,6-dimethylphenyl for different fixed values of the equilibrium angle of benzene ring rotation umin(a) and the corresponding values of internal rotation barriers for flat W, (b),and for perpendicular WO2 (c) location of benzene rings.values calculated as above for methane propane n-butane n-pentane neopentane and for weakly strained cyclanes like cyclopentane and cyclohexane (fig. 8) agree with the corresponding experimental values to within experimental error. Significant disagreement of experimental and calculated values of K has been observed only for cyclopropane. This is obviously associated with the distribution of electron density in this highly strained molecule. When molecules with permanent multipoles adsorb in zeolite their electrostatic orientational interaction with the electrostatic field of zeolite must be taken into CHROMATOSTRUCTURAL ANALYSIS account. In the case of adsorption of ethylene and benzene with large quadrupole moments in NaX orientational electrostatic interactions are calculated with the point quadrupole appr~ximation,~"~~ from the equation (9Q= 2pi Q(3 COS' 8 -l)~-~ (5) I where Q is the.point quadrupole moment of the molecule 0 is the angle between the radius-vector connecting the centre of mass of the molecule with ions of zeolite I and 2 3 lo3K/T FIG.8.-Dependence of In K1on 1/Tfor adsorption of cyclohexane cyclopentane and cyclopropane on zeolite NaX.Lines are calculated results using atom-ion potential (~~(~~3) . . . dots arc experi-mental values. the vector determining orientation of the molecule in the large cavity of zeolite pI being the charge of ion I. Total potential energies of intermolecular interaction of unsaturated and aromatic hydrocarbons with zeolite are then calculated from the equation 28329 where (DA .. . is the potential function for intermolecular interaction of atom A of the molecule with zeolite estimated via the atom-ion approximation from the pro- perties of the adsorbate and zeolite taken separately. Kl calculated as above for ethylene agrees with e~perirnent.~**~ There are no experimental values of Kl for ben- zene but the calculated heat of adsorption of benzene by zeolite NaX is close to the experimental initial heat of adsorption with a zeolite of similar composition. Satisfactory agreement of the calculated and experimental values of Kl for adsorp- tion in zeolites of molecules of known structure obviously then allows extension of chromatostructural analysis to molecule-zeolite systems in general.As already noted in discussing fig. 8 calculation of Kl for cyclopropane using the atom-atom potential v for the sp3 electron configuration of carbon atoms in n-alkanes yielded too low re- sults. The considerable strain in the cyclopropane ring probably makes the electron configuration of the carbon atoms closer to the sp2 configuration a view supported to some extent by results for adsorption on GTCB.2*9 Hence the cyclopropane mole- A. V. KISELEV AND D. P. POSHKUS cule should have multipole moments. If these moments are approximated by a point quadrupole moment located in the centre of the cyclopropane ring then eqn (5) can be used for (DQ. One can in fact define a value for the quadrupole moment of the cyclopropane molecule Q such that molecular-statistical calculation yields Kl coinciding with the experimental value.The relevant value Q 4.10-26 esu slightly exceeds the quadrupole moment of ethylene. PROSPECTS FOR DEVELOPMENT OF CHROMATOSTRUCTURAL ANALYSIS Further development of chromatoscopy with GTCB but more particularly zeolites demands first that the accuracy of experimental Kl must be considerably enhanced. Then we will have access to more accurate parameters for the semi- empirical atom-atom potential functions needed for the molecular-statistical cal- culations of Henry’s constants. Such data will also reveal with greater clarity the influence of molecular structure on intermolecular interaction (e.g. for isomers like anthracene and phenanthrene naphthalene and azulene).Secondly a wider range of atom-atom potential functions should be determined via studies of adsorption on GTCB of not only hydrocarbons but also their derivatives containing halogens oxygen nitrogen sulphur and other elements in different valence states. More specific forms of intermolecular interaction such as the formation of hydro-gen bonds charge-transfer complexes and the like are usually only weakly revealed30 by gas chromatography because of the relatively high temperatures needed to elute large molecules. Liquid chromatography can be helpful in this ~ituation,~’ and the application of chromatoscopy to liquid chromatography thus presents great interest. There are however many problems in developing such a method.First the mole- cular-statistical theory of adsorption from infinitely dilute solutions is as yet insuffi- ciently developed. Secondly Henry’s constants obtained by liquid chromatographic methods are not sufficiently accurate. However the liquid chromatography method can already be applied to find rather simple quantitative correlations of the thermo- dynamic characteristics of adsorption from solution with the change of molecule structure.32 Such empirical correlations must help in the development at the mole- cular level of both semi-empirical calculations of Henry’s constant for liquid chroma- tography of complex molecules and solution of the inverse chromatostructural prob- lem i.e. finding parameters of molecule structure via experimental determination of Henry’s constant by liquid chromatography.N. N. Avgul and A. V. 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