Isotope Effects and Spectroscopy - ACS Publications

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2 Isotope Effects and Spectroscopy CHARLES P. NASH Downloaded via UNIV OF CALIFORNIA SANTA BARBARA on July 11, 2018 at 09:37:20 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Department of Chemistry, University of California, Davis, Calif. 95616

Introduction One of the most valuable techniques available to any kind of spectroscopist i s that of isotopic substitution. This paper w i l l discuss a few applications of the method to problems i n the optical spectroscopy of atoms, diatomic and small polyatomic molecules, the vibrations of transition metal complexes, hydrogen bonding, solvation, and optical a c t i v i t y . We shall not treat either magnetic resonance or microwave spectroscopy. Any review which treats optical spectroscopy must acknowledge at its outset the magnificent series of volumes on this subject by Herzberg ( 1 , 2 , 3 , 4 ) . The textbooks by Walker and Straw (5), and King (6) also treat many of the subjects we s h a l l discuss at a somewhat less advanced l e v e l . Atomic Spectra In the domain of atomic spectroscopy, the f i r s t direct observation of deuterium was made in 1932 by Urey, Brickwedde, and Murphy (7), who observed weak satellites of four of the Balmer lines of hydrogen which were shifted to shorter wavelengths by amounts ranging from 1.79 Åfor H at 6536 Åto 1.12 α

for H

δ

at 4102

Å.

Å

Within experimental error the shifts were i n

exact agreement with the predictions of quantum mechanics for the effect of a mass " 2 " nucleus on the reduced mass of the atom. For multi-electron atoms, isotope effects are manifest not only i n the changes i n hyperfine structure arising from nuclear spin changes (1,8), but also i n small shifts i n the energies of s electrons which may be attributed to changes i n the nuclear dimensions (9)· Hindmarsh, Kuhn, and Ramsden (10) have attributed some of the irregularities found i n atomic isotope shifts to the closing of nuclear shells.

29

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ISOTOPES AND CHEMICAL PRINCIPLES

Diatomic Molecule Spectra When two atoms are combined to form a diatomic molecule, isotope effects appear i n the vibrational, rotational, and electronic spectra. To the extent that the Born-Oppenheimer approximation i s v a l i d , the potential function for a given electronic state i s independent of the masses of the nuclei. The harmonic vibration frequencies of two isotopic variants of a diatomic molecule i n the same electronic state are then related by the equation

where ay i s the harmonic vibration frequency of the j'th isotopic variant, and i s the reduced mass of that molecule; i . e . , μ = M^/^+Mg) Here

(2)

and Mg are the atomic masses of the atoms comprising the

molecule. One obvious source of differences i n the rotational spectra of isotopically-related diatomic molecules arises from the fact that the energy levels of the r i g i d rotor contain an explicit μ " dependence. Another effect also occurs i f one of the isotopic variants i s a homonuclear molecule and the other i s heteronuclear. 1

For a homonuclear diatomic molecule composed of even (odd) mass-number nuclei, the t o t a l wave function, which we assume to be a product of electronic, vibrational, rotational, and nuclearspin functions, must be symmetric (antisymmetric). I f the electronic wave function i s symmetric, and i f the nuclear spin is zero, as i n the ground state of 0 , only even values of J , the rotational quantum number, are allowed. I f the nuclear spin is not zero, both even and odd values of J (i.e., symmetric and antisymmetric rotational wave functions) are allowed, but with different s t a t i s t i c a l weights. These may be determined from the nuclear-spin part of the wave function. 1 6

2

For a nuclide of spin s the nuclear-spin degeneracy i s n

g =(2s +l). n

n

For the molecule a t o t a l of +

nuclear-spin 2

functions are possible, of which S ( g l ) / are symmetric (ortho), n

n

and g ( g - l ) / 2 are antisymmetric (para). n

n

The ortho (or para)

nuclear spin functions then combine exclusively with either even-J or odd-J rotational states to produce overall wave functions which have the proper symmetry.

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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Isotope Effects and

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For H (s =|) the t o t a l wave function must be antisymmetric, the odd-J levels combine with the ortho spin-funetions, and the s t a t i s t i c a l odd-J:even-J ratio i s 3 : 1 . For D or N (s =l) the t o t a l wave function must be symmetric. The even-J levels now combine with the ortho spin-states, and the s t a t i s t i c a l even-J:odd-J ratio i s 6:3=2:1. For heteronuclear diatomic molecules the allowable values of J are not subject to symmetry constraints. 2

n

1 4

2

2

n

In accordance with these considerations, the pure-rotational Raman spectrum (selection rule AJ=±2) of 0 has every second line missing, whereas that of N has a l l lines present, but those arising from even-J states are more intense than those arising from odd-J states (g). Yoshino and Bernstein ( l l ) have observed intensity alternations having s t a t i s t i c a l origins i n both the pure-rotational Raman spectrum of H , and i n the rotational fine-structure (selection rules AJ=0, ±2) of the vibrational band i n the Raman spectra of both H and D . 1 6

2

1 4

2

2

2

2

If a high-resolution infrared spectrophotometer i s available to them, undergraduates can obtain and analyze i n detail the fundamental vibration-rotation spectra of the four common isotopic variants of hydrogen chloride (H,D, Cl, Cl) ( 12,12.). For these molecules the potential curve i s significantly anharmonic, and a dependence of the rotational constant on the vibrational quantum number i s immediately apparent, since the rotational lines are not evenly spaced. From their data our students have confirmed the constancy of the equilibrium internuclear distances i n these four molecules to within ±0,001 Â , and they have confirmed the v a l i d i t y of Eq. 1 to four decimal places. It must be emphasized that when band-origins rather than harmonic frequencies are used i n Eq. 1, disagreements occur i n the second decimal place. Extensive comparison data are available i n the literature for a l l these molecules ( l 4 , 1 5 , l 6 , 1 7 » l 8 ) . 35

37

It i s of some interest to note here also that Connes et a l . (19) have detected 8 lines of the R-branch of the Δν=2 vibrationrotation band of both H C 1 and H C 1 at about 5700 cm" i n the spectrum of Venus. The agreement between the astronomical data and laboratory data was within ±0.01 cm*" for a l l lines. 3y comparing the relative intensities of the Venusian HC1 and C 0 spectra they estimated a p a r t i a l pressure of HCl^lO" torr, and from the relative intensities of the rotational lines they estimated a rotational temperature of 2^0 K. 35

1

37

1

2

4

The electronic spectra of isotopically varied diatomic molecules reflect the effects of changes i n the vibrational and rotational energy levels of both the ground and the excited electronic states. This subject i s of great h i s t o r i c a l importance, since the isotopes 0 , 0 , C , and N were a l l identified in 1929 on the basis of weak bands i n the electronic spectra of diatomic molecules. 1 8

1 7

13

15

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ISOTOPES AND CHEMICAL PRINCIPLES

32

Giauque and Johnston ( 2 0 , 2 l ) identified a weak band i n the solar spectrum of oxygen near 7595 Â as the (θ,θ) band of the b-»X transition of 0 0 on the basis of an isotopic shift of the bank origin of - 2 . 0 7 cm" vs. the band origin of the (θ,θ) band of 0 , as well as the fact that the band envelope of the homonuclear molecule contained 13 lines whereas that of the heteronuclear molecule contained 26. 1 8

1 6

1

1 6

2

There then followed the identification of c C i n the Swan bands of C by King and Birge ( 2 2 ) : 0 0 i n the solar spectrum by Giauque and Johnston ( 2 £ . 2 4 ) 7 ^ N 0 , N 0 , and N 0 by Naudé ( 2 5 ) ; and C N aiiaP- C 0 by King and Birge ( 2 6 ) . 1 3

1 7

1 2

1 6

2

é

1 3

1 4

5

16

1 4

1 8

1 4

1 7

l6

The Spectra of Small Polyatomic Molecules Isotopic substitution has been an important tool i n the solution of an enormous variety of problems i n the spectroscopy of small polyatomic molecules. One such problem i s the structure of the ethane molecule ( 2 7 ) . The eclipsed form of this molecule, having symmetry D , would have three Raman-active vibrationrotation bands, designated v i o v u and v i , for which the selection rule ΔΚ=±1 would predict only one series of Q-branches. The corresponding vibration-rotation bands for the staggered conformation, having symmetry D ^, would obey the selection rules 3n

5

2

3

ΔΚ=±1,±2. Thus two sets of Q-branches would be observed. The CH stretching-region of the C He spectrum contains a complicated admixture of the lines of the νιο fundamental together with those of the v i fundamental and three other combination bands. The νιο fundamental of C D , however, occurs free from any other inter­ ferences. Two well-defined sets of Q-branches were observed, and hence the staggered structure of ethane was confirmed beyond question. 2

2

6

If one wishes to determine the vibrational force constants for a polyatomic molecule, isotopic substitutions are essential. The general valence force f i e l d for a non-linear polyatomic molecule, expressed i n internal coordinates, contains a t o t a l of -|(3N-6)(3N-5) force constants. Some of these may equal others by the symmetry of the molecule, but a maximum of only (3N-6) vibration frequencies may be observed. The well-known Wilson GF-matrix method (28,29) allows one to break down the (3N-6)x(3N-6T~secular determinant for the molecule into smaller blocks, the number and size of which depend on the symmetry of the molecule i n question. Any n x n block of the block-diagonal secular equation obtained by Wilson's method yields, of i t s e l f , an n x n secular equation of the form |GF - A | = 0

(3)

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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33

Isotope Effects and Spectroscopy

The G matrix elements are composed only of structural parameters of the molecule (its masses, bond distances, and bond angles), while the F matrix elements, which are called symmetry force constants, are usually linear combinations of the general valence force constants. The roots, λ^, of the secular equation, Eq. 3 , are related to the harmonic vibration frequencies of the η normal modes of that symmetry type by χ

2

±

= ^TT ^.

2

( ) t

1

where the

are expressed i n cm" and c i s the speed of l i g h t .

Except when n=l, the number of independent F matrix elements, §η(η«ϋ), exceeds the number of observable frequencies, n. Even when n=l the F matrix element may s t i l l be a combination of general force constants. If one or more isotopic substitutions are performed on the molecule, new frequencies w i l l be obtained, as well as new G matrix elements. Within the Born-Oppenheimer approximation, however, the F matrix elements w i l l transfer intact to the new molecule. The amount of new information which can be obtained about the elements i n the F matrix i n this way i s , however, limited by several isotope rules which the sets of harmonic frequencies of each symmetry type must obey. One of these, the form of the Teller-Redlich product rule which applies to two isotopic variants having the same molecular symmetry, may be deduced immediately from the secular equation i t s e l f . When the n x n secular determinant i s expanded i n polynomial form, the constant term, which must be equal to the product of the roots, η ΤΤ λ., i s simply the determinantal product |G|·jF|. Thus, i f i=l we designate with superscript j s and k s the properties of two isotopic variants having the same molecular symmetry, we find 1

T

η j ΤΤ λ, i-Ll _ ]£L_ n k , k, ΤΤλ. > i=l

!

TT u>? i=l 1

(5)

G1

1

i=l

In addition to the product rule, there are also sum rules which further r e s t r i c t the number of independent observables when more than two isotopic variants are available. This subject has been discussed i n d e t a i l by Heicklen (^O). One interesting conclusion he reaches i s that for molecules with symmetry the f u l l F matrix can be determined by substituting for a l l but one of the sets of equivalent atoms. In principle, then, CH4 and CH4, C H and C D , or C 6 H and C6H , should suffice to 12

13

12

6

6

6

6

13

6

6

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ISOTOPES AND CHEMICAL PRINCIPLES

34

determine the force-fields for methane or benzene. In practice, however, such a minimum set of data i s rarely enough. For methylamine, H CM , D CMD , D CNH and H G WH have a l l been studied, but almost half the elements of the general forceconstant matrix are s t i l l undetermined (31). Hirakawa, Tsuboi, and Shimanouchi ( j l ) point out that C substitution would be very helpful i n analyzing this particular molecule. 15

3

2

3

2

3

25

3

2

1 3

The vibration frequencies of a molecule are not the only sources of information about the elements of the symmetry forceconstant matrix. In the vibration-rotation spectra of polyatomic molecules, especially those with degenerate vibrational modes, e.g., symmetric tops, there occur certain anomalies i n the spacings of the rotational lines which may be attributed to the Coriolis interaction ( 3 2 ) . This phenomenon, which i s a coupling between the rotational angular momentum of the molecule and i t s vibrational angular momentum, i s expressed i n terms of coupling constants called zeta constants. The ζ-constants are directly related t o the F and G matrices for the molecule i n question. The ζ-constants for a given molecule must have a sum which may be inferred from the molecular structure, and for a l l symmetric tops, except those which belong to the S 4 and D a point groups, there i s also an isotope rule which they must obey, namely 2

(6)

2

mEcj ( l - f . ) = constant i i 1

Here m i s the mass of the off-axis atom, CD^ i s the harmonic vibration frequency of the i - t h degenerate normal mode, and i s the Coriolis constant for that mode. The 'summation extends over a l l the normal modes belonging to a given degenerate species. The work of Aldous and Mills (33»3^) on the methyl halides provides an excellent example of the determination of force constants. For one of these molecules there are six independent vibrations — t h r e e of class A and three of class E. There are 16 different force constants i n the general valence force f i e l d expressed i n internal coordinates, and 12 force constants i n the symmetrized F matrix, a l l but two of which are linear combinations of the original 16. For CH X and CD X together there are 12 observed frequencies, but the product rule states that within each class only five of the six frequencies are independent observables. For the Ε-vibrations of either CH X or CD X three ζ-constants can be measured. However each molecule must obey a ζ-sum rule, and together they must obey the isotope rule, so that only three of the six ζ-constants are truly independent. ±

3

3

3

3

In addition to the vibration frequencies and the zeta constants, Aldous and Mills included i n their determination of the force f i e l d the data then available on the centrifugal-

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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Isotope Effects and Spectroscopy

35

distortion constants, two of which are possible for one of these molecules. These constants are related to derivatives of the moment-of-inertia tensor and the elements of the inverse of the F matrix for both the A and the Ε vibrations (35^,36) · Thus, up To 22 experimental values for each isotopic pair were used by Aldous and Mills to determine the 12 elements of the F matrices for a l l the methyl halides, together with estimates 6? their probable errors. 1

The effects of isotopic substitution on the vibrational spectra of small polyatomic molecules have resulted i n two recent astrophysical observations of considerable interest. The f i r s t extra-terrestrial detection of deuterium was reported i n 1972 by Beer et a l . (37) , who found 11 lines of the P-branch of the 2200 cm" vibration-rotation band of C H Q D i n the spectrum of Jupiter* More recently Beer and Taylor (38) have examined the intensities of these lines and concluded that the D / H ratio i n the atmosphere of Jupiter i s between l / 2 and l / 6 the t e r r e s t r i a l value. 1

In I969 Young (39) published a high-resolution spectrum (which had actually been obtained earlier by Connes' group) showing a very complete vibration-rotation band comprising the 2v transition of ^C^O^O centered at k508 cm" i n the spectrum of Venus. This molecule, unknown i n the laboratory, could be detected i n spite of the abundance of C0 i n the earth's atmosphere, because for a l l the symmetrical isotopes of carbon dioxide (symmetry D , ) this overtone i s symmetry forbidden. On 1

3

2

00

π

the basis of a painstaking analysis of the intensities of the rotational lines Young deduced a .rotational temperature of 2^5+3 K, i n excellent agreement with the value of 2k0 Κ obtained by Connes e_fc a l . (l£) from the spectra of the HC1 species. While i t i s common knowledge that isotopic substitution alters the vibration frequencies of normal modes, i t may be less well known that the intensity of the corresponding infrared absorption band must be affected as well. Crawford (ho) has shown that within the harmonic approximation the integrated intensity of an infrared absorption band, Γ . , i s given by

band Here η i s the concentration of the absorber, I i s the path length, I and I are the incident and transmitted intensities respectively, i s the harmonic frequency of the i ' t h absorption band, N. i s Avogadro's number, c i s the speed of 0

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

36

ISOTOPES AND CHEMICAL PRINCIPLES

l i g h t , *ft i s the dipole moment of the molecule, and i s the i t h normal coordinate. Now μ i s invariant to isotopic sub­ stitution, but both ω. and are mas s-dependent, and hence the intensity of the band must be mass-dependent as well. f

Crawford (4l) has also shown that the integrated intensities of the infrared absorption bands of isotopically related molecules must obey two sum-rules, one of which, the socalled F-sum rule, may be written Σ Γ . / V · = constant. Here the i summation extends over a l l vibrations of the same symmetry class. Dickson, M i l l s , and Crawford (42) have made an extensive study of the vibrational intensities of the proto and deuteromethyl chlorides, bromides, and iodides. Among other things, they found that the A i vibrations of the methyl bromides and methyl iodides showed excellent agreement with the F-sum rule, but the agreement for the methyl chlorides was less satisfactory. 1

1

In his excellent recent monograph based on his Baker lectures, Herzberg (43) describes the way i n which isotopic studies contributed to the identification of two transient species. In the spectrum of a comet, a band system was found near 4050 a which Herzberg, i n 1942, attributed to the CHg radical. He also found the same bands i n the spectrum of a discharge through methane. In 1949, however, Monfils and Rosen (44) found the identical spectrum from a discharge through CD , and hence the entity responsible for i t could not have been CHg. In 1951 Douglas (45) reported the spectrum of a discharge through an equimolar mixture of ^CE^ and ^CH*. There appeared six bands, and hence the species i n question must have contained three carbon atoms. In 1954 Clusius and Douglas (46) reported the spectrum of a discharge through pure ^CH^. They found an intensity alternation i n the rotational lines having a 3:1 ratio, and they also inferred that i n the spectrum of the ^CH^ discharge every-other rotational line was missing. This kind of behavior, analogous to that cited earlier for diatomic "molecules, is diagnostic for a linear triatomic molecule. Thus the species responsible for the 4050 a band was identified as linear C · 4

3

Herzberg (43_) then describes the actual discovery of the C H 2 radical, which was produced by the flash photolysis of diazomethane. The absorption band, which appeared at 1415 A> shifted when CD^lUg rather than C R 2 N 2 was photolyzed. In sub­ sequent experiments the photolysis of ^ClfeNg confirmed the presence of a carbon atom i n the radical. Very recently Katayama, Huffman, and 0 Bryan (47) have studied the absorption and photo ionization spectra of several isotopic water molecules i n the vacuum ultraviolet. As part of this investigation they used the spectra of H 2 0 and H 2 0 to establish that the f i r s t electronic excited state of HgO" i s linear. 1

1 6

1 8

4

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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Isotope Effects and

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The Vibrational Spectra of Metal Complexes. In recent years Nakamoto (48) has pioneered i n the use of isotopes of the transition metals i n order to make assignments of the vibrational bands of their complexes. 3y studying the spectra of C r ( a c a c ) and C r ( a c a c ) , Nakamoto, Udovich, and Takemoto (4£) were able to assign a band at 460 cm" to a Cr-0 stretching mode and one at 592 cm" to an out-of-plane ring mode. On the basis of 0 -» 0 isotopic substitution, the 592 cm" band had previously been misassigned as the Cr-0 stretch (50). 50

53

3

3

1

1

1 6

1 8

1

For tetrahedral XY species the t o t a l l y symmetric A i stretching mode involves no motion of the central atom, and hence should y i e l d v i r t u a l l y no isotope shift when that atom i s substituted. The triply-degenerate F mode, however, should display an isotope effect. Thus Takemoto and Nakamoto (51) were able to assign bands i n the Raman spectra of Zn(NE ) atT^O cm" and 410 cm" to the Αχ and F modes respectively. In this instance the isotopes Z n and Z n were used. The ordering of these two levels i n this complex i s somewhat unexpected, since in the vast majority of the X E ^ tetrahalogeno, or X0 species which have been examined the F band occurs at the higher frequency (52). 4

2

3

1

4

1

2

6 4

6 8

4

2

As a f i n a l example of the use of isotopic substitution i n the study of metal complexes, we cite the use of N0 as a ligand by Collman, Farnham, and Dolcetti (53), who found what they termed "hybridization tautomerism" i n several cobaltn i t r o s y l complexes. From their infrared spectra they inferred a rapid equilibrium between a trigonal-bipyramidal Co(l) species having a linear Co-nitrosy1 geometry, and a square-pyramidal C o ( l l l ) species, i n which the Co-nitrosyl moiety i s bent. l5

Hydrogen Bonding Studies. Much current interest i n the spectroscopy of hydrogen bonded systems attaches to the question of how one might infer the shape of the potential function from the vibrational spectrum of the entity. In this connection Wood and his collaborators have recently made major contributions. They have examined the infrared and Raman spectra of a great number of cations of the form (BFB ) , where Β and B are nitrogen bases or perdeutero-nitrogen bases, and Ρ i s either hydrogen or deuterium. 7

+

7

When Β and B were both trimethy lamine s (54) the NET" stretching band and the ND stretching band were both singlets. The same behavior obtained also when Β and Β were trimethylamine and pyridine (55)· When B=B =pyridine (56), or sub­ stituted pyridines (57) , and B=H, the NH"" band was s p l i t into a 7

1

+

7

7

1

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

38

ISOTOPES AND CHEMICAL PRINCIPLES

+

broad doublet. The KD stretch, however, was a singlet. Also in these ions the Ν — Ν stretching motion, which was observed i n the infrared spectrum, showed only a small frequency shift when the bridge was deuterated. 7

When Bj^B , but both bases were various pyridines or quinoline, the NIT" band could be characterized as a doublet with an intensity ratio of the components which varied between 1.2 and zero as the pK^ difference of the bases varied between zero and eight (58). The Ν—Ν stretching mode i n these unsymmetrical ions was not substantially more intense than that found when B=B'. Another remarkable feature of the spectra of this set of unsymmetrical ions was the appearance of a new band in the 500-600 cm" region whose frequency increased when the bridge was deuterium substituted. 1

1

Wood (59) analyzed a l l these results i n a semi-theoretical paper i n which may be found, at least schematically, the spectral consequences (including deuterium isotope effects) to be expected for linear or bent Η-bonded systems having potential functions with single minima, or double minima with either low or high barriers. He interprets those of his (BPB') systems which show a s p l i t t i n g of the ΜΓ " band as having low-barrier double-minimum potential functions. Wood also shows that the anomolous frequency shift of the 550 cm" band on deuteration can be explained on the basis of a well-to-well proton transition occurring i n a low-barrier double-minimum potential which i s markedly asymmetric. +

4

1

Laane (60) has made calculations which show that for doubleminimum, symmetric, but possibly anharmonic, potentials the frequency ratio ω^/ω^ varies depending on the relative sizes of the height of the barrier and the energy of the transition. For a high barrier the frequency ratio i s about l.k. As the barrier height decreases the ratio f a l l s , attaining a minimum value of about 1.2 when the upper level i s near the top of the barrier. With a further decrease i n the barrier the ratio increases again, passing through a maximum value of about 1.6 for a f l a t bottomed well. For a s ingle-minimum harmonic potential the ratio becomes l.k again. On the basis of his calculations Laane has questioned the frequency assignments which Berney ejt a l . . ( 6 l ) have made for acetic acid. These authors have correlated two bands for which ω^/ω^ = 0 . 9 3 . "Very recently Bournay and Maréchal (62) have studied the integrated intensities of the infrared absorption bands of the dimers of acetic acid and acetic a c i d - d For these molecules they find that the intensity of the band attributed to the OH—0 antisymmetric stretching mode i s twice that of the corresponding 0D—0 band, whereas the intensity ratio i n the le

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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Isotope Effects and Spectroscopy

39

harmonic approximation should be more nearly /" 2. In their discussion of this anomolous result they conclude that anharmonicity i s not a dominant factor. Rather, they suggest that i n this hydrogen bonded system the Born-Oppenheimer approximation i s invalid; i.e., they propose that the motion of the H atom along the bond induces an electronic transition i n the molecule, and the vibrational spectra have borrowed some intensity from that electronic transition. Ionic Solvation. In recent years isotopic substitution has been used to identify the vibrational modes of cation solvates i n both aqueous and nonaqueous media. Da S i l v e i r a , Marques, and Marques (63 ) obtained the Raman spectra of various salts of Mg"", Zn , and A l i n both H 0 and D 0 . They observed one polarized and two depolarized lines i n each case, which they attributed to the Aig, Eg, and F g vibrational modes of octahedral solvates. The 2

1

3 +

2

2

2

frequencies of the A and E vibrations were decreased by a factor of•1.04-1.05 when D 0 was used as the solvent, whereas that of the F vibration decreased by a factor of 1.08. These values are those which would be expected for species having octahedral symmetry. l g

g

2

2 g

In our own laboratory we have obtained the Raman spectra of aqueous solutions of L i C l and L i C l (64). In addition to three depolarized librational bands of water at 720 cm" , 585 cm" , and 462 cm" , we find two other bands i n the low frequency region. One of these i s a polarized band at 420 cm" , independent of the lithium isotope used, which the other i s a depolarized band which occurs at 355 cm" i n the L i C l solutions or 385 cm- i n the L i C l solutions. We interpret these bands as the Αχ and F modes of vibration of L i tetrahedrally solvated by water molecules. Singh and Rock (65) had earlier noted that i f the lithium ion were tetrahedrally solvated, and i f the F vibration frequencies of the solvates were 384 cm" and 358 cm- for Li(0H )J and Li(CE )î respectively, the experimental value of the equilibrium constant of 1.046 for the exchange reaction L i ( s J + LiCl(aq) = L i ( s ) + LiCl(aq) could be explained. 6

7

1

1

1

1

1

1

7

6

+

2

1

2

1

6

7

2

2

7

e

6

7

In an extensive series of papers Popov and his collaborators have studied the solvation of a l k a l i metal cations i n various nonaqueous media, using N a magnetic resonance shifts ( 6 6 ) , and far-infrared spectroscopy. The ion-solvent vibrational bands which they find f a l l i n the 100-500 cm" range. 23

1

In dimethylsulfoxide the bands were identified by using DMS0-d as solvent (6j). In acetone (68) both L i -» L i and acetone-d substitutions were used. In this solvent the frequencies of the "lithium" vibrations showed an anion 7

+

6

6

6

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

+

40

ISOTOPES AND CHEMICAL PRINCIPLES

dependence, indicative of ion pairing, when the mole ratio of acetone to lithium was less than four. In pyridine and substituted pyridines (6°;) lithium isotopes were again used. In these solvents also, lithium halide contact ion pairing was inferred. Concurrently with Popov's work. Roche and Huong (70) reported the cage vibrations of Ca , Mg , and L i i n acetonit r i l e . These authors employed both L i -> L i and CH CN-»CD CN substitutions to identify the absorption bands of the solvates. 2+

7

+

6

+

+

3

3

Optical Activity Induced by Isotopic Substitution. The f i r s t example of optical activity i n a compound of the type R R CHD was reported i n I9A9 by Alexander and Pinkus (71). They measured a specific rotation for 2,3-dideutero-transmenthane of [ a ] = -O.O9 . They could not, however, establish X

2

2 5

0

the origin of the optical activity, owing to the presence of four asymmetric carbons i n the molecule. In the same year E l i e l (72) reported the synthesis of ethylbenzene with one deuterium i n the a position. The optical activity of this compound ( [ a ] = -O.3O ) clearly derives from 2 5

0

the asymmetry between D and H. Subsequently Streitweiser and Wolfe characterized a number of other benzyl-a-d-derivatives. In I963 S t i r l i n g (jh) reported the preparation of (-)-benzyl-p-tolyl-[ 0i 0]-sulfone, whose rotation ([Œ]^ =-O.I6 ) 16

0

Q

arises from the presence of two different oxygen isotopes bonded to sulfur. A number of other 0 0 sulfones have since been prepared (75,76). 1 6

1 8

Anderson, Colonna, and S t i r l i n g (77) have recently reported (R)-dibenzyl-[ CH CH ]-sulfoxide. In this compound the optical activity ([α] βο =+0.71) originates from having two carbon isotopes bonded to sulfur. 12

13

2

2

2

There have also appeared very recently the studies of Kokke and Oosterhoff ( 7 8 , 7 2 ) . These authors have prepared (lR) - [ 2 - 0 ] -α-fenchocamphoronequinone and (lR) - [ 1 - D ] -afenchocamphoronequinone. In these molecules thes sole source of asymmetry was either an 0 i n the of-diketone function, or a single deuterium atom at a bridgehead. The circular dichroism spectra of these two compounds i n the visible are remarkably different. 1 8

1

8

Literature Cited. 1. 2.

Herzberg, G., "Atomic Spectra and Atomic Structure," Dover Publications, New York, 1944. Herzberg, G., "Spectra of Diatomic Molecules," 2nd ed., Van Nostrand Reinhold, New York, 1950.

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2.

NASH

3. 4. 5. 6. 7. 8. 9.

Isotope Effects and Spectroscopy

Herzberg, G., "Infrared and Raman Spectra of Polyatomic Molecules," Van Nostrand Reinhold, New York, 1945. Herzberg, G., "Electronic Spectra and Electronic Structure of Polyatomic Molecules," Van Nostrand Reinhold, New York, 1966. Walker, S. and Straw, Η., "Spectroscopy," Vol. I I , Chapman and Hall Ltd., London, 1962. King, G. W., "Spectroscopy and Molecular Structure," Holt, Rinehart and Winston, Inc., New York, 1964. Urey, H. C., Brickwedde, F. G., and Murphy, G. Μ., Phys. Rev. (1932), 40, 1. Candler, C., "Atomic Spectra," Ch. 19, Van Nostrand Reinhold, New York, 1964. Wilets, L., Hill, D. L., and Ford, K. W., Phys. Rev. (1953), 91,

10. 11. 12.

13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

41

1488.

Hindmarsh, W. R., Kuhn, H., and Ramsden, S. Α., Proc. Phys. Soc. (London) (1954), A67, 478. Yoshino, T. and Bernstein, Η. J., J . Mol. Spectry. (1958), 2, 213. Daniels, F., Williams, J . W., Bender, P., Alberty, R. A., Cornwell, C. D., and Harriman, J. Ε., "Experimental Physical Chemistry," 7 t h ed., pp. 247-256, McGraw-Hill Inc., New York, 1970. Shoemaker, D. P., Garland, C. W., and Steinfeld, J. L., "Experiments i n Physical Chemistry," 3rd ed., pp. 450-459, McGraw-Hill Inc., New York, 1974. Levy, Α., Rossi, I., and Haeusler, C., J . Physique (1966), 27, 526. Levy, Α., Rossi, I., J o f f r i n , C., and Van Thanh, N., J . Chim. Physique (1965), 6 2 , 601. Rank, D. Η., Eastman, D. P., Rao, B. S., and Wiggins, Τ. A., J. Opt. Soc. Am. (1962), 52, 1. Van Horne, Β. Η. and Hause, C. D., J . Chem. Phys. (1956), 25, 56. Pickworth, J . and Thompson, H. W., Proc. Roy. Soc. (London) (1953), 218, 3 7 . Connes, P., Connes, J., Benedict, W. S., and Kaplan, L. D., Astrophys. J . (1967), 147, 1230. Giauque, W. F. and Johnston, H. S., Nature (1929), 123, 318. Giauque, W. F. and Johnston, H. S., J . Amer. Chem. Soc. (1929), 5 1 , 1436. King, A. S. and Birge, R. T., Nature (1929), 124, 127. Giauque, W. F. and Johnston, H. S., Nature (1929), 123, 831. Giauque, W. F. and Johnston, H. S., J . Amer. Chem. Soc. (1929), 51, 3528. Naudé, S. M., Phys. Rev. (1929), 34, 1499. King, A. S. and Birge, R. T., Astrophys. J . (1930), 72, 19. Weber, Α., i n Anderson, A., Ed., "The Raman Effect," Vol. I I , pp. 637-640, Marcel Dekker, Inc., New York, 1973.

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ISOTOPES AND CHEMICAL PRINCIPLES

42

28. 29.

30. 31. 32. 33. 34. 35. 36. 37· 38. 39. 40. 41. 42. 43.

44. 45. 46. 47. 48. 49. 50. 51. 52. 53· 54. 55. 56.

Wilson, Ε. Β., Decius, J. C., and Cross, P. C., "Molecular Vibrations," McGraw-Hill Inc., New York, 1955. A detailed application of the method to the chloroform molecule has been given by Colthup, Ν. B., Daly, L. H., and Wiberley, S. Ε., "Introduction to Infrared and Raman Spectroscopy," Ch. 14, Academic Press Inc., New York 1964. Heicklen, J., J . Chem. Phys. (1962), 36, 721. Hirakawa, A. Y., Tsuboi, Μ., and Shimanouchi, T., J. Chem. Phys. (1972), 57, 1236. Weber, Α., i n ref. 27, pp. 690-705. Aldous, J . and M i l l s , I. Μ., Spectrochim. Acta (1962), 18, 1073. Aldous, J . and M i l l s , I. M., Spectrochim. Acta (1963), 19, 1567. Kivelson, D. and Wilson, Ε. B., J . Chem. Phys. (1953), 21, 1229. Wilson, Ε. B., J . Chem. Phys. (1957), 27, 986. Beer, R., Farmer, C. B., Norton, R. H., Martonchiek, J. V., and Barnes, T. G., Science (1972), 175, 1360. Beer, R. and Taylor, F. W., Astrophys. J . (1973), 179, 309. Young, L. G., Icarus (1969), 11, 66. Crawford, B., J. Chem. Phys. (1958), 29, 1042. Crawford, B., J . Chem. Phys. (1952), 2 0 , 977. Dickson, A. D., M i l l s , I. Μ., and Crawford, B., J . Chem. Phys. (1957), 27, 445. Herzberg, G., "The Spectra and Structures of Simple Free Radicals," pp. 10-16, Cornell University Press, Ithaca, Ν. Υ., 1971. Monfils, A. and Rosen, Β., Nature (1949), 164, 713. Douglas, A. E. Astrophys. J . (1951), 114, 466. Clusius, K. and Douglas, Α. Ε., Can. J . Phys. (1954), 3 2 , 319. Katayama, D. Η., Huffman, R. E., and O'Bryan, C. L., J . Chem. Phys. (1973), 59, 4309. Nakamoto, K., Angew. Chem. internat. Edit. (1972), 11, 666. Nakamoto, Κ., Udovich, C., and Takemoto, J., J. Amer. Chem. Soc. (1970), 92, 3973. Pinchas, S., Silver, B. L., and Laulicht, I., J . Chem. Phys. (1967), 46, 1506. Takemoto, J . and Nakamoto, Κ., Chem. Commun. (1970), 1017. Nakamoto, Κ., "Infrared Spectra of Inorganic and Coordination Compounds," 2nd ed., pp. 106-112, WileyInterscience, New York, 1970. Collman, J . P. Farnham, P., and Dolcetti, G., J . Amer. Chem. Soc. (1971), 93, 1788. Masri, F. N. and Wood, J . L., J. Mol. Struct. (1972), 14, 217.

Masri, F. N. and Wood, J. L., J. Mol. Struct. (1972), 14, 201. Clements, R. and Wood, J. L., J. Mol. Struct. (1973), 17, 265.

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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57·

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Clements, R. and Wood, J . L., J . Mol. Struct. (1973), 17, 283. 58. Clements, R., Dean, R. L., and Wood, J . L., J . Mol. Struct. (1973), 17, 291. 59· Wood, J . L., J . Mol. Struct. (1973), 17, 307. 60. Laane, J . , J . Chem. Phys. (1971), 55, 2514. 6 1 . Berney, C. V., Redington, R. L., and Lin, K. C., J . Chem. Phys. (1970), 53, 1 7 1 3 . 62. Bournay, J . and Marechal, Y., J . Chem. Phys. (1973), 59, 5077. 63. da S i l v e i r a , Α., Marques, Μ. Α., and Marques, N. M., Mol. Phys. ( 1 9 6 5 ) , 9, 271. 64. Nash, C. P., Donnelly, T. C., and Rock, P. Α., unpublished results. 65. Singh, G. and Rock, P. Α., J . Chem. Phys. (1972), 57, 5556. 66. Greenberg, M. S., Wied, D. Μ., and Popov, A. I., Spectro­ chim. Acta (1973), 29A, 1927, and earlier papers cited there. 67. Maxey, B. W. and Popov, A. I., J . Amer. Chem. Soc. (1969), 91, 2 0 . 68. Wong, M. K., McKinney, W. J . , and Popov, A. I., J . Phys. Chem. (1971), 75, 56. 69. Handy, P. R. and Popov, A. I., Spectrochim. Acta (1972), 28A, 1545. 70. Roche, J.-P. and Huong, P. V., B u l l . Soc. Chim. France (1972), 4521. 71. Alexander, E. R. and Pinkus, A. G., J . Amer. Chem. Soc. (1949), 71, 1786. 72. E l i e l , E. L., J . Amer. Chem. Soc. (1949), 71, 3970. 73· Streitweiser, A. and Wolfe, J . R., J . Amer. Chem. Soc. (1959), 8 1 , 4912. 74. S t i r l i n g , C.J.M., J . Chem. Soc. (London) (1963), 5741. 75· Sabol, M. A. and Andersen, K. K., J . Amer. Chem. Soc. (1969), 91, 3603. 76. Annunziata, R., Cinquini, Μ., and Colonna, S., J . Chem. Soc. Perkin Trans. I (1972), 2057. 77. Andersen, Κ. Κ., Colonna, S., and S t i r l i n g , C.J.M., J . Chem. Soc. Sec. D (1973), 645. 78. Kokke, W.C.M.C. and Oosterhoff, L. J . , J . Amer. Chem. Soc. (1972), 9 4 , 7583. 79. Kokke, W.C.M.C. and Oosterhoff, L. J . , J . Amer. Chem. Soc. (1973), 95, 7159.

Rock; Isotopes and Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 1975.