A nuclear magnetic resonance study of acetone in various solvents

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A NUCLEAR MAGNETIC RESONANCE STUDY OF ACETONE

A NUCLEAR MAGNETIC RESONANCE

STUDY OF ACETONE

IN VARIOUS SOLVENTS

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT,

OP GEZAG VAN DE RECTOR MAGNIFICUS DR. IR. C. J. D. M. VERHAGEN, HOOGLERAAR IN DE AFDELING DER TECHNISCHE NATUURKUNDE, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN

OP WOENSDAG 2 JULI 1969 TE 16.00 UUR DOOR

WILHELMUS HENDRIKUS DE JEU NATUURKUNDIG INGENIEUR GEBOREN TE LEERSUM ïchiijc •^\

m

^^7^^i/.

Dit proefschrift is goedgekeurd door de promotor Prof. Dr. Ir. J. Smidt.

Aan allen die een bijdrage tot dit proefschrift geleverd hebben.

TABLE OF CONTENTS

Concise list of symbols 8 Chapter I General introduction 11

Chapter II Basic theory 13 1 Molecular orbital theory 13

1.1 Hartree-Fock-Roothaan SCF theory 13 1.2 Approximate LCAO-SCF theory 14 1.3 Independent electron LCAO theory 15

2 Theory of the chemical shift 17 2.1 Perturbation expression for the screening constant . . . . 17

2.2 MO theory of localized contributions to the screening . . \9

3 Theory of the nuclear spin-spin coupling 22 3.1 Perturbation expression for the coupling constant . . . . 22

3.2 MO theory of the coupling constant 23 Chapter III NMR properties and electronic structure of acetone 27

1 Introduction 27 2 Experimental results 29

3 Theoretical calculations 30

4 Discussion 31 Chapter IV The influence of hydrogen bonding 34

1 Introduction 34 1.1 Hydrogen bonding 34

1.2 Acetone in other spectroscopic methods 35

2 Experimental results 37 3 Theoretical calculations 39

4 Discussion 41 Chapter V The influence of protonation 46

1 Introduction 46 1.1 Protonation and the basicity of carbonyl compounds . . . 46

1.2 Protonated acetone in other spectroscopic methods. . . . 48

2 Experimental results 49 3 Theoretical calculations 51

4 Discussion 53 5 Conclusions concerning the theoretical methods 56

Appendix A Numerical 57 1 Solution of the eigenvalue equations 57

1.1 General procedure 57 1.2 Population analysis 58 2 CNDO calculations 59 3 Independent electron calculations 61

Appendix B Experimental 62 1 Proton resonance 62 2 Carbon-13 resonance 63 3 Double resonance 64 4 Chemical materials 66 Summary 68 Samenvatting 70 References 72

C O N C I S E L I S T O F S Y M B O L S

A magnetic vector potential A electron affinity

«0 Bohr radius (5.29167 x 10 " ^ ^ m) C(c^j) matrix of MO coefficients (coefficient) E energy

e electronic charge (1.6021 x 10-^' C) F{F^y) Hartree-Fock matrix (element) Jff Hamiltonian operator

H magnetic field strength H(H^y) Hückel matrix (element) HQ acidity function

h Planck's constant (6.6256 x 10"^* Js) h /i/27r (1.0545x10-3"^ Js)

/ nuclear spin angular momentum; unit matrix I ionization potential

/ nuclear spin-spin coupling constant I electron orbital angular momentum m electronic mass (9.1091 X 10"^'kg) P{Pft,) charge and bond order matrix (element) P(P^y) Mulliken population matrix (element) q (excess) charge

r distance

S electron spin angular momentum S (Spv) overlap matrix (overlap integral) .5^(0) electron density of j-type AO for r = 0

V potential energy Z nuclear charge

a^ diagonal element Hückel matrix P Bohr magneton (9.2732 x 10"^* Am^) P^ constant in CNDO theory

^^^ off-diagonal element Hückel matrix y Coulomb integral; magnetogyric ratio J methyl öC^C)- carbonyl öC^C) for acetone Ö chemical shift

5^^ Kronecker delta ö(r) Dirac delta function

e{ei) diagonal matrix of MO energies (element) C exponent of STO

V ff(<7) <P X permeability of vacuum (4n x 10"^ H m " ' ) frequency atom-atom polarizability

nuclear magnetic screening tensor (screening constant)

molecular orbital; Latin indices, occupied i,j,..., unoccupied a, b, atomic orbital; Greek indices ii, v, Q,(T, ...

Abbreviations A O C N D O EH lEH I N D O IR LCAO MO N D O N M R PS S C F STO T M S

uv

complete neglect of differential overlap extended Hückel

iterative extended Hückel

intermediate neglect of differential overlap infra-red

linear combination of atomic orbitals molecular orbital

neglect of differential overlap nuclear magnetic resonance Pople-Santry self-consistent field Slater-type orbital tetramethyl silane ultra-violet valence bond

Energy conversion table

joule kcal mole" eV _a.u.

joule kcal mole-^ eV cm-> a.u. 1 6.9x10-" 1.6x10-'» 1.99x10-" 4.35x10-1» 1.44x101» 1 23.06 2.86x10-' 627.4 6.24x101» 4.34x10-2 1 1.24xl0-« 27.211 50.34x10" 350 8068 1 21.95X10* 2.29x10-1* 1.59x10-' 3.67x10-2 4.55x10-» 1

C H A P T E R I G E N E R A L I N T R O D U C T I O N

During the last decade nuclear magnetic resonance (NMR) has appeared to be a powerful experimental tool for gaining insight into the structure of molecules. In this thesis an NMR study of acetone in various solvents is presented. The parameters obtained from the NMR spectra of acetone contain valuable information about the electronic structure of the molecule. From the changes in the parameters from one solvent to another, information can be obtained about the amount of interaction and about accompanying electronic displacements. Therefore we shall first summarize some basic concepts of NMR.

A nucleus with angular momentum Ih has a magnetic moment ft coupled to the angular momentum vector by

/I = ylh (I-l) y is called the magnetogyric ratio. In an external magnetic field H, /x has different

components along H with associated energy levels (Zeeman levels), according to the possible values of /. In NMR transitions between these energy levels are induced and detected.

For the interpretation of NMR spectra two effects are important: the magnetic shielding and the nuclear spin-spin coupling. The magnetic shielding of the nucleus by the electrons gives rise to the chemical shift. The moving electrons produce a sec-ondary field at the nuclear position. So the local magnetic field at the nucleus is given by

ƒƒ,„, = 7 / ( 1 - a ) (1-2) where a represents the nondimensional screening constant, a is independent of H but

depends on the chemical (electronic) environment. In fact «r is a tensor, but in the liquid state only the rotational average is observed. The chemical shift S is measured relative to some reference compound and is defined by

^ = ^ " ^ " ^ 1 0 ^ (1-3) "ret

where the irradiation frequency is thought to be constant. Ö is expressed in parts per million (ppm). Approximately

Ö = CT-o-„f (1-4) So a positive chemical shift corresponds to a higher field or enhanced screening.

interaction between the nuclear magnetic moments. Here we are interested only in the liquid state where this effect practically averages to zero. We still have indirect nuclear spin-spin coupling via the electrons (electron coupled nuclear interaction). The interaction energy is of the form hJ^gl^-ls, where / ^ B represents the coupling constant between the nuclei A and B (expressed in Hz).

The complete spectrum can be described by the spin Hamiltonian operator

^ = - ft X 7i«(l - ^f)^z(0 + /» Z JiAi) • KJ) (1-5)

i i<J

The direction of the external magnetic field H is chosen along the positive z-axis. For a more detailed discussion of NMR we refer the reader to the literature (Pople, Schneider and Bernstein, 1959; Emsiey, Feeney and Sutcliffe, 1965).

Nuclei with an even mass number and an even charge number have zero spin, and consequently no magnetic moment. Among these are the isotopes ^^C and ' * 0 . So the ^ H spectra of organic molecules are mainly due to the proton magnetic moments (ƒ = ^). Nevertheless satellites occur because of the 1.108% ^^C (I = ^) present in natural abundance. In this thesis we shall use these satellite spectra. Moreover use will be made of ^'C resonance and ^'O resonance. The natural abundance of *^0 is 0.037% (/ = I).

Chemical shifts and coupling constants have received an increasing amount of attention from theoretical chemists. As we do not intend to perform a theoretical study, we restrict ourselves to some relatively simple molecular orbital (MO) calcu-lations of coupling constants and of '^C and ^'O screening constants.

In chapter II the necessary basic concepts of MO theory and its application to the theory of chemical shifts and coupling constants are summarized. For a more gen-eral discussion of magnetic properties of molecules we refer the reader to Davies (1967). In chapter III the NMR properties of pure acetone are discussed in relation to the electronic structure. Both chemical shifts and coupling constants are sensitive to changes of solvent (Laszlo, 1967). We shall not discuss these solvent effects in general, but restrict ourselves to the stronger interactions. The effect of solvents capable of forming hydrogen bonds with the carbonyl group of acetone is discussed in chapter IV. The extreme form of this effect is considered in chapter V where we look at acetone in acidic solvents which have such strong proton donating properties, that protonation of the acetone molecules occurs. Here als the various theoretical approaches used in this thesis are compared.

Some concepts in the interpretation of the numerical results and details of the methods of calculation are given in appendix A. Experimental information can be found in appendix B.

C H A P T E R I I B A S I C T H E O R Y

1 Molecular orbital theory *

1.1 Hartree-Fock-Roothaan SCF theory

The basis of most of the MO calculations of the last fifteen years is the Roothaan-version of Hartree-Fock self-consistent field (SCF) theory (Roothaan, 1951a; Parr, 1964). We consider a closed-shell molecule. The MO's (pi are written as a linear com-bination of atomic orbitals x^ (LCAO)

The determination of the optimum MO's is accomplished by determining the coeffi-cients from the matrix eigenvalue equation

{F-Ss)C = 0 (II-2) where C represents the matrix of linear expansion coefficients, s represents the

diag-onal matrix of orbital energies, and S represents the overlap matrix with elements

S,v = </i|v> (11-3) The elements of the matrix F of the Hartree-Fock operator have the form

The A^, are core attraction integrals

V = <Ml)|-i(^' + Z|^|v(l)> (11-5)

A ' l A

where the summation A runs over the atoms. The (i.iv\Qa) are electron repulsion integrals

(/iv|e<7) = </i(l)e(2)|rr;|v(l)a(2)> (II-6)

In the most general case all the AO's are centred on different atoms (4-centre integral).

1-i'.. = 2 Z c„c„, (11-7)

is an element of the charge and bond order matrix.

Because of the large number of integrals the application of this type of theory is restricted to relatively small molecules. For a molecule such as acetone we have to look for more approximate methods.

1.2 Approximate LCA 0-SCF theory

All possible simplifications of (II-4) mean that we have to ignore certain of the less important electron repulsion integrals. Pople and coworkers (Pople, Santry and Segal, 1965; Pople and Segal, 1965, 1966; Santry and Segal, 1967; Pople, Beveridge and Dobosh, 1967) effected these simplifications by applying the neglect of differential overlap (NDO), i.e. they assumed

ZM(1)ZV(1) = 0 IX ^v (II-8) The NDO approximation can be applied to different extents. As a form such as

(II-8) occurs twice in three- and four-centre electron repulsion integrals, these are always disregarded. Applied to its fullest extent also many two-centre, and even one-centre integrals are eliminated. Nevertheless Coulomb integrals are still included, and therefore the charge distribution in the molecule is properly described. In re-ducing the full calculations with the NDO approximation, certain quantities may be estimated from experimental data on atomic systems. So an element of empirism is brought in, which can compensate partly for the crude approximations.

The Hartree-Fock equations have certain transformation properties, such that the results are (a) invariant to rotation of the local atomic coordinate system, (b) inva-riant to hybridization of the atomic functions of any constituent atom. In applying the NDO approximation to (II-4), one should consider only those levels of approxi-mation which do not disturb these invariance properties (Pople, Santry and Segal, 1965). We restrict ourselves further to the theory with complete neglect of differential overlap (CNDO), as this is the most simple SCF method for all valence electrons.

In the CNDO method differential overlap is neglected in all electron repulsion integrals. In the literature the approximations involved are discussed systematically (Pople, Santry and Segal, 1965). Further applications are given to several molecules, and some modifications of the original method are described. (Pople and Segal, 1966).

The elements of the Hartree-Fock operator are now given by

F,, = - W, + K) + {(^AA - ZA) - 4(^.„ - 1)}7AA + Z (^BB - ZB)yAB (11-9) B(#A)

7^ and A^ are the valence state ionization potential and electron affinity associated with the atomic orbital x^- So the first term of F^^ represents the Mulliken electro-negativity. PAA represents the total valence electron density on atom A

i'AA = Z ^ . . ("-11) f

and Z^ represents the core charge of atom A (nuclear charge less the number of inner shell electrons). y^B represents the average Coulomb integral between two electrons in valence orbitals on the atoms A and B. We take for this average the Coulomb integral involving valence .y-orbitals:

VAB = <SA(l)sB(2)|rr2'|sA(l)sB(2)> (11-12) F^^ reduces to —W^ + ^f) if the orbital /^ has a population of one electron (7*^^ = 1)

and all atoms have zero excess charge (7'AA = Z^, PBB = ^B)- SO the second term of (II-9) shows how the electronegativity is modified by the excess charge on atom A. The final term gives in the same way the Coulomb potential at Xn due to the excess charge on ail other atoms in the molecule.

The off-diagonal elements F^^ given in (11-10) use an empirical resonance integral proportional to the overlap integral S'^v» the constant of proportionality depending on the nature of the atoms A and B. The final term is a correction due to electron repulsion. The J?AB'S are obtained by calibrating the CNDO eigenvalues and eigen-vectors to accurate Hartree-Fock calculations on some small molecules (Pople and Segal, 1965, 1966; Sichel and Whitehead, 1967, 1968.) Although the overlap matrix is used in forming the off-diagonal elements F^^, overlap is disregarded in evaluating (II-2).

One should realize that very crude approximations are made in the CNDO method: even the one-centre exchange integrals are disregarded. Despite the semi-empirical adjustments the method still has some ab initio character, contrary to the methods described in the next section. It is possible to retain the one-centre exchange integrals: intermediate neglect of differential overlap (INDO) (Pople, Beveridge and Dobosh,

1967). Applications of both methods appear in an increasing number in the literature (Pople and Gordon, 1967; Pople, Beveridge and Dobosh, 1968; Bloor and Breen, 1967; Ditchfield and Murrell, 1968a; Kroto and Santry, 1967).

1.3 Independent electron LCAO theory

In the independent electron theories (Hückel-type methods) the Hamiltonian operator is no longer specified. The matrix F of the Hartree-Fock operator is replaced by a Hückel matrix H, which is constructed in an empirical way. These types of methods should be seen as fitting formulas (Clementi, 1965) and can be very useful in so far that they reproduce the trends of the Hartree-Fock results.

Writing (II-2) with a Hückel matrix H we get

{H-Se)C = 0 (11-13) The diagonal elements TT^^ or a^ are usually chosen as the negative valence state

ionization potential (Hinze and Jaffé, 1962)

a, = -I, (11-14) For the off-diagonal elements 77^, or )S^, various formulas can be used. In the

sim-plest theory (Pople and Santry, 1964a, 1965a) overlap is ignored in (11-13) by setting ^nv = ^iiv Nevertheless the overlap integrals are used for constructing the jS's:

P,, = kS^, (11-15) with usually k = —10 eV. In the theory of Hoffmann (1963) (called extended Hückel

theory) overlap is taken into account in evaluating (11-13). Here the Wolfsberg-Helm-holtz formula for P is used:

P,, = kS,, ° ^ (11-16)

with usually k = 1.75.

Note that (11-15) and (11-16) give quite different P values. For hydrocarbons (11-16) with k = 0.75 is about equivalent to (11-15) with k = - 1 0 eV.

The theoretical justification of Hoffmann's method has been discussed by several authors (Boer, Newton and Lipscomb, 1964; Allen and Russel, 1967; Fukui and Fujimoto, 1967; Blyholder and Coulson, 1968). According to Blyholder and Coulson (1968) the method can be derived from the Hartree-Fock equations assuming (a) the Mulliken approximation for overlap charge distributions, (b) a uniform charge distribution in calculating the two-electron integrals.

The rotational invariance of (11-16) has been established by Newton, Boer and Lipscomb (1966). Cusachs and Cusachs (1967) proposed a modification of (11-16) taking k = 2 —15^,|. This formula has the virtue of having the right behaviour for ^ = V, thus Sf,, = I, but the results are not generally better.

In fact the ionization potential depends on the charge on the atom. So the diagonal elements a^ are a function of the charge. Several relations have been proposed (Cu-sachs and Reynolds, 1965; Hinze and Jaffé, 1962), both linear and quadratic in the charge, e.g.

a, = a° + J a ^ A (11-17) where p. refers to an AO x^ on atom A with gross excess charge ^^ (see appendix

output are consistent with the ionization potentials at the input. The results for hydro-carbons are in general not much better with this iterative method (Duke, 1968). When hetero atoms are present the method seems to be of more value (Rein, Fukuda, Win, Clark and Harris, 1966). Recently the theoretical justification of these iterative pro-cedures has been questioned (Harris, 1968).

2 Theory of the chemical shift

2.1 Perturbation expression for the screening constant

The interaction energy of a nucleus with magnetic moment /*, surrounded by electrons, in a uniform magnetic field H can be represented by

£,„. = -n-H + iirrH (11-18) where a represents a tensor describing the magnetic screening of the nucleus by the

electrons. In a liquid only the rotational average a can be observed

ff = iTr(ff) (11-19) In order to get a theoretical expression for a, we set up the Hamiltonian operator for

the electrons in presence of a magnetic field.

^ = ^'£(-ihF,-i-eA,y+V (11-20) V is the potential energy in absence of the magnetic field; the summation k runs over

all electrons. The vector potential A,^ due to the external magnetic field H and the nuclear magnetic moment n is given by

A, = iHxr, + f^f^ (11-21)

4nri

We take as the origin the nucleus in question. The gradient of an arbitrary function can always be added to A, and is chosen here such that div A = 0 (Coulomb gauge). For diamagnetic molecules the total electron spin is zero. Therefore the electron spins do not contribute to the chemical shift and need not be included in M'.

Here we shall follow Ramsey (1950, 1952); a somewhat different treatment of the chemical shift using the current density operator can be found in Slichter (1963). We substitute (11-21) in (11-20) and write J^ as

where

h'

3^''"=-^l.Vu+V (11-23)

^ - = ^z(iH-'..'g^) ("-24)

where the angular momentum operator of the unperturbed system /^ = — ih{r^ x F») has been introduced.

Jf'^^ and Jf^^^ can be considered as perturbations on .?f*°\ By comparing the perturbation energy with the form fta-H v/e can derive a theoretical expression for a. To get these kind of terms linear in ft and H ,we have to go up to the second order of perturbation theory for .?f <'* and to the first order for Jif^^\

£per. = < 0 | ^ * ' ' + .?r*'^|0>+ Z (£o-£J"'<0|^<"l«><n|.?f''>|0> (11-26) « ( # 0 )

|0> and |«> stand for the Slater determinants describing the ground state and excited states of the unperturbed system. As J^^^^ contains the angular momentum operator, we find

<0|^<*'iO> = 0 (11-27) (quenching of the angular momentum). The excited states which are usually

un-known occur in the second part of Ej,^„. By replacing E„ — EQ by an average excitation energy AE, we can carry out the summation over the excited states. Using also (11-27) we arrive at

£p.r. = < 0 | . ? f ' ' ' | 0 > - ( J £ ) - ' < 0 | ( J f < ' y | 0 > (11-28) The difficulty is now included in the estimation of AE.

We shall now consider the first part of Ep^^ which contains only ^'•^\ There is only one term linear in ft and H, which can be compared with fi-a-H. The other terms are quadratic in H (which gives part of the magnetic susceptibility), or can be disregarded because of the dependence on p.^. The result is

„2

(1) _ / f o ^ V /ftirr2j_...v.-3 ff' ' =

%nm Z <0|(r,^/-r,r,)r,-^|0> (11-29)

r^r^ is a tensor (direct product of a column and a row vector); / is the unit dyadic. For the rotational average

'''"•ffi^?<''l^'"'l''> ("•»'

This is a diamagnetic contribution (<T*^^ > 0). The form is similar to the classical

formula of Lamb (1941) for an isolated atom.

Next we shall look at the second part of Ep^^t which contains only .Jf ^''. Again we have to consider only the term linear in /i and H. Finally we arrive at

'^"' = - 7 ^ ^ ^ <0\hh.r;'\0} (11-31)

4nm A E k,k'

IJi^. is again a tensor. It is not possible to give a simple closed foimula for the

rota-tional average o-^^\ If only AO's of spherical symmetry are present, then tr^^' = 0; otherwise this is a paramagnetic contribution (o-*^' < 0).

The total expression for a is given by (11-29) and (11-31). The summations run over all the electrons in the molecule. Consequently these formulas are not very useful for calculations except in the case of small molecules. The total result is the difference between two large quantities of opposite sign which almost cancel.

For a more complete general theory we refer the reader to the literature, where also variational formulations can be found (O'Reilly, 1967; Lipscomb, 1966; Musher, 1966). We further restrict ourselves to a simple breakdown in localized contributions to a. This makes a general qualitative understanding of the chemical shift possible in terms of MO theory.

2.2 MO theory of localized contributions to the screening

A discussion of a in terms of localized contributions was first given by Saika and

Slichter (1954), and was later extended by several authors (Karplus and Das, 1961; Pople, 1962a). We can expand the determinantal wave function |0> in terms of the MO's (jOj and take these MO's as a linear combination of AO's. With a^^^ written as (7j (11-30) now becomes

To get a tractable expression we restrict the summation by the following assumption:

</i|r"V> = 0 if ^ and V not both on A (11-33) Thus only the diamagnetic precession on the atom A under investigation is considered;

interatomic currents and currents on neighbours are neglected. Using this simplifica-tion and taking orthogonality into account we get

, 2 A

t^oe V D / . - I

'^. = i l ^ Z ^ . / ' - - ' > . (11-34) 127tm _/•

For a Slater-type orbital (STO) with exponent C^:

<r-'\ = ^ (11-35) " 0

When we expand the determinantel wave function in the paramagnetic term (11-31) in the same way, we get («r'^' written as ffp):

i^oe^ _{Z 2 P , / / i | / / r - ^ | v > + X P,.P,Mlr-'Wy<Q\l\vy] (11-36)}

c.v »i.v,e,iT J Snm A E In,

Spherical symmetric AO's need not be included as they give zero matrix elements. In order to make a tractable expression we make the following assumptions in evaluating the integrals (Alger, Grant and Paul, 1966); A is the atom under investigation.

<;<|l|v>=0 if/x and v on different atoms (11-37)

ip\lr-'\v}=0 '

</i|nr-3|v> = 0

if fx and v not both on A (11-38)

The first assumption corresponds to the neglect of differential overlap. The other ones are consistent with this if /i and v are on different atoms. If /i and v are on the same atom which is not A, the rapid attenuation of r" •^ can be given as the rationale for disregarding these integrals.

We introduce STO's and use the well-known relations for the angular momentum operator. When the radial part of STO x^ is denoted by R(ji) we find for the re-maining radial integrals between the AO's of one atom (Alger, Grant and Paul, 1966):

R,, = <,R(p)\r-'\R(v)} = f f-^ (11-39)

ƒ,, = <R(/i)|R(v)> = ^^^^"^ (11-40)

C^ is the effective nuclear charge of STO Xn- Using a simple Slater screening concept C^ is defined, for instance for a carbon atom by

C^ = 3.25iS-0.35 Z («v-1) (11-41)

q, is the electron density in ;(,;)? is a parameter describing the contraction of an STO

in a molecule (Coulson, 1942). p is given the value 1.05 for a n electron and 1.15 for a <T electron.

With all these substitutions and taking the rotational average, (11-36) reduces to (Pugmire and Grant, 1968)

^P ~ ~ Z: iTE- 1 • ^ 'iiAti\"fifi + i ZJ 2 J ( °MAVB °VA^B ~ °M>iB°VAVB) °Mv^Mv f

OTim AE (. ii = x,ji,z ii,v = x,y,z B J (11-42)

The summation B runs over all atoms, including the atom A under investigation; the index fiA refers to an STO x^ on A.

A further simplification can be made by taking all C's equal for the 2p orbitals on one atom. That means that in (11-41) all electron densities q^ are assumed to be equal. The radial integrals (11-39) and (11-40) now reduce to

24a.^

R,. = <'•"'> = ~ (n-43)

/M. = 1 ("-44) Inserting this in (11-42) gives the well-known formula of Karplus and Pople (1963)

for the chemical shift. However, we shall not use these simplifications.

So the total screening is found by use of (11-34) and (11-42). A more general break-down is localized contributions is given by Pople (1962a), where the approximations involved are also discussed more systematically; see also Memory (1968). The total screening constant for an atom A in a molecule can be written as (Pople, 1962b, 1964):

ffA = ^AA^^AA^ ^ ^ B ^ ^ r i n g (jj.45^

B(*A)

The first two terms are those discussed here. <T'^^ is a contribution to the screening of A by electronic currents on neighbours B (neighbour anisotropy effect). This contri-bution involves the local anisotropy of the susceptibility on atom B, and does not exceed about 10 ppm. This part has disappeared in our expressions because of the assumptions (11-33) and (11-38) for p and v both on B. ^H chemical shifts are deter-mined by Oj^ and 0"^° (Pople, 1957). In this case the paramagnetic contribution can be disregarded as the occupation of the 2/>-orbitals of a proton is negligible. Con-trary to this for the second-row elements in which we are interested here (^^O, ''C), the paramagnetic part is dominant. Finally a'^ "•'"* is a contribution from ring currents in the molecule (if present).

3 Theory of the nuclear spin-spin coupling

3.1 Perturbation expression for the coupling constant

The isotropic part of the hyperfine interaction energy of two nuclei A and B can be represented by

^hyp = hJ^^I^-U ("-46) JAB is the nuclear spin-spin coupling constant. A preference for some spin orientation

means that this situation is energetically favourable. Therefore JE'^yp is negative. Thus /AB is negative for parallel spins and positive for anti-parallel spins.

In order to get a theoretical expression for /AB> we set up the Hamiltonian operator for the electrons.

^ = ^^{-ihV^+eA,f + V + 2pY^S,-H, (11-47) where P is the Bohr magneton, S^ the spin anugular momentum of electron k and

Hj = curl A^. As Ey^yp is independent of the external field, we can use as vector potential

^ , = Z ^ ^ 5 ^ * ^ ^ (11-48) w 4nr^^

On substituting Ak'm (11-47) we arrive at (Ramsey, 1953)

^ = ,?^(i' + ^(^> + ^(3> (11-49)

^''' = ^i:(-it^Vk + ^ ^ h x r , ^ + V (11-50) 2m k,N \ 4nrtf^ )

The only parts of .?f *^* that depend on the nuclear spins are

and

^'"" = ^ Z y^?^''•^^'•^^n('^•^iV')('•.^•'•*ivO-(/^•r»^.)(/^'•'•*iv)} ("-51) ^ " k,N,N'

^ ( 1 . ) = 1 ^ ^ y,r;:,X-(r,, X F,) (11-52) • ' " ' k,N

The other terms .?f ^^' and J f *^^ arise from the spin part of the Hamiltonian operator.

_j^(2) ^ 1 ^ ^ 7iv{3(Sr'-*iv)(/N-'-,^)r,^=-(S,-/^)r,-/} (11-53) • ^ " k,N

This is the normal dipole-dipole approximation for the interaction between the mag-netic moments of the electrons and the nuclei, which is valid for r^jv ¥" 0.

JÈ'^^) = hp^ph X l^KrkN){S,-U^ (11-54)

k,S

This term describes the interaction between the magnetic moments of the electrons and the nuclei for r^^j^ = 0 when the dipole-dipole approximation breaks down. Thus only 5-electrons contribute to this part of the Hamiltonian operator. Jf'-^^ is usually called the Fermi contact term (Fermi, 1930; Blinder, 1965).

We treat .;f<i">, jf*"», ^<^> and .?f<^> as perturbations. By comparing the pertur-bation energy with Ey^yp we can derive an expression for J. We restrict ourselves to

Jt^^\ as this term is known to be dominant for coupling constants involving carbon

and hydrogen (Murrell, 1969; Barfield and Grant, 1965). Similar expressions for the other terms can be found in these two review articles.

If we take J^'^^^ for two nuclei A and B, and include it in the expression for the perturbation energy up to second order, we get

Êpcrt = ^Mo^'fi'yA7B Z {(£o-£»)~'<0|Z^('-*A)S*-/Al"><nlZ«5(r,B)5;-7BiO>}

^ " C O ) k J

(11-55) This expression is not of the form (11-46). On evaluating the various terms we come across /^ • S^Sj • /B in which the direct product of S^ and Sj is present. This is a second-order tensor which averages in a liquid to its isotropic part ^(S^ • Sj). Now (11-55) can be brought in a form linear in /^ and I^. The resulting coupling constant is

^AB = ^filP'fiyAyB Z {(Eo-En)-\0\ X ö(r,^S,\n} <n\ Z ^('•,B)S,|0>} (11-56)

• ^ ' " n ( * 0 ) k J

If desired the average energy approximation can be made.

To evaluate (11-56) one needs knowledge of the excited states. As these are usually unknown this gives rise to many difficulties. Recently another approach has been devised, where the excited states do not occur (Pople, Mclver and Ostlund, 1968). Here we shall restrict ourselves to the application of MO theory to (11-56). For the use of valence bond (VB) theory and for variational calculations we refer the reader to the review paper by Barfield and Grant (1965).

3.2 MO theory of the coupling constant

In agreement with Pople and Santry (1964b, 1965b) we shall take (11-56) as our starting point. The normalized Slater determinant |0> describing the ground state is denoted by

$ 0 = \<Pi(Pi(P2<P2-(p„(P„\ ("-57)

where (pi has spin a and (Pi spin p. We can construct excited states by promoting an electron from an occupied MO (pi to an unoccupied MO (p^. By taking the fact that the electrons are indistinguishable into account we get the following four excited states (singlet and triplet):

'^1 = -^{\9i-<Pi^a-\ + \(pv-Mi-\} ("-58) \(Pi-(Pi<Pa-\ —-{\(Pi...(Pi<p„...\-\(Pi...(p„^i...\} (11-59) v 2 3 A "

$? =

Other than single excitations do not occur as the Fermi contact term is a one-electron operator. As this operator contains a spin and an orbital part, the ground state is mixed with the triplet states and the singlet excited states give zero matrix elements. After the evaluation of the remaining matrix elements

8 occ unocc

JAB= -:^lxlP'hy^y,,Y Z CE''i-Eo)-\cp,\S(r^)\<p,y<cpMrB)\9i> ("-60)

The summations i and a run over the occupied and unoccupied MO's, respectively. (^E° — EQ) represents the triplet excitation energy when (pi is replaced by <p„. For the sake of simplicity we shall further use an independent electron model. Then (^E' — EQ) is given by the difference in orbital energies (e„—e,). In SCF models we have to use (e„ —£,) —7,„. On writing the MO's as a linear combination of AO's:

occ unocc

^AB = - oZt^oP^'^yAJB Z Z (e<.-£i) ^ Z Ci^c„,c„jCi,<^|^(rA)|v><e|(5(i-B)|(T> (11-61) Because of the ^-function only the .y-orbitals among the AO's contribute to the coupling. We retain only one-centre integrals, i.e. AO's on neighbours of A are supposed to give a negligible value for matrix elements with 5(rjiJ. Then

j^(0) represents the electron density of the relevant j-orbital at the nuclear position. These quantities are often calculated from the best available SCF functions for the atom. As there is no reason to believe that this gives the correct values for molecules they can also be treated as parameters. Furthermore the atom-atom polarizability n has been introduced:

occ unocc

JTJASB = - 4 Z Z (s«-ei)~''^i.A'^".A'^«.BCi.B ("-63)

i a

Finally, the calculation of 7^8 is reduced to an MO calculation of 7t,A,B'

•^AB = CAB^ISASB (11-64)

where C^B is a constant for a specific pair of nuclei AB. On making the average energy approximation, we get

A B = C A B ( ^ E ) " ' ^ L B ("-65)

This equation has been derived by McConnell (1956) who made the average energy approximation at an earlier stage. It shows clearly the failure of this approximation in LCAO-MO theory: (11-65) predicts all coupling constants to be positive (VA and y^ assumed to be positive), contrary to the experimental results. As TTJASB can have either sign, this failure is not inherent to (11-62).

(11-62) has been extensively applied in the literature, using Pople-Santry type in-dependent electron theory (Pople and Bothner-By, 1965; Van Duijneveldt, Gil and Murrell, 1966; Murrell and Gil, 1966; Ditchfield, Jones and Murrell, 1968) and extended Hückel theory (Fahey, Graham and Piccioni, 1966; Amos, 1967). The difference between these two approaches has been investigated by De Jeu and Beneder (1969). The application of MO theory other than the Hückel-type theory is still rare; notable are some CNDO calculations by Ditchfield and Murrell (1968a). Recently Murrell (1969) has written a review on MO calculations of coupling constants.

Despite the success of these calculations, especially in predicting the influence of substituents, it is open to severe criticism. As a single determinantal wave function is used, correlation between electrons with anti-parallel spin is ignored. Therefore it has been argued that configuration interaction is essential to MO calculations of spin-spin coupling (Barfield, 1966; Armour and Stone, 1967).

Finally, we wish to draw attention to the fact that in the model described here, the n electrons do not contribute to the coupling constant. When (T-K interaction is present, this is not correct. The n electrons can carry over the spin information more effectively than the a electrons. Consequently n electron contributions could be of importance, especially for long-range coupling constants. This problem has been investigated by Karplus (1960) who used electron spin resonance (ESR) hyperfine

constants to estimate the amount of a-n interaction. The a bonds are assumed to be localized. For a detailed discussion we refer the reader to Murrell (1969). For HH long-range coupling:

JSH- ~ aH«H(^£J"' ("-66) an and a.^^• represent the ESR hyperfine constants of the corresponding radicals, and

AE^ represents the triplet excitation energy for the n electron wave function. Recently

the theory has been extended and improved upon (Cunliffe and Harris, 1967; Ditch-field and Murrell, 1968b).

CHAPTER III NMR PROPERTIES AND ELECTRONIC STRUCTURE OF ACETONE

1 Introduction

For acetone the CH, CC and CO distances are 1.09, 1.56 and 1.23 A, respectively. The methyl carbon atoms and the carbonyl carbon and oxygen lie in one plane (xy-plane). The protons of the methyl groups can have different orientations with respect to the carbonyl bond (figure III-l). The difference in free energy between the two rotational isomers is only 0.78 kcal mole"^ Therefore at room temperature the methyl groups can be considered as freely rotating. As usual in cases like this, the situation with a CH bond eclipsing the carbonyl group is the most favourable. As the CCC angle is 120° the carbonyl carbon can be expected to be sp^ hybridized. Assuming no hybridization of the oxygen, an MO diagram of the carbonyl group can be given as in figure III-2. Many specific properties of acetone are due to the presence of the carbonyl group.

0 H

Figure III-l

Eclipsed and staggered rotational isomer of acetone. 2Pz / ; _{/ /} \ / I \ SP^ \ \ 2 P y N 2 p , ^ V ^Px n ^• 0 / 2s Figure III-2 Schematic MO diagram for the carbonyl group of a ketone.

Carbonyl groups have a characteristic ultra-violet (UV) absorption in the frequency region of 30,000 cm"^. This corresponds to a transition from the non-bonding « orbital to the anti-bonding n orbital (Murrell, 1963). With respect to the symmetry of the CO bond the transition is forbidden, and so the absorption is rather weak. As a result of this excitation electron density is transferred from the oxygen to the carbon atom. For acetone (pure liquid) v„^„. is 36,700 cm" ^ (De Jeu, 1969). The other transi-tions have been studied much less extensively. Only the n^n transition has been assigned with certainty to the region of 50,000 c m ~ \

The carbonyl group has further a characteristic stretching frequency in infra-red (IR) and Raman spectroscopy. For acetone v/CO) is 1715 cm"^ (Bellamy and Wil-liams, 1959).

Due to the large electronegativity of oxygen, the CO bond is highly polar. Con-sequently a negative charge is present on oxygen and a positive one on carbon. As a result acetone has a dipole moment of 2.90 D (Swalen and Costain, 1959). Moreover the ionization potential 7 (which is that of the lone pair 2py electrons on oxygen) is smaller compared with a neutral oxygen atom (Walsh, 1947). It is clear that the polarity of the CO bond will also influence the '•'C and ^'O screening constants in NMR.

The polarity of the carbonyl group can be described in various ways. In VB termi-nology the polarity (or amount of ionic character) is nlqr, where fi represents the dipole moment, q the charge of the complete polar bond, and r the CO distance. Acetone has 46% ionic character (Walsh, 1947). For a more detailed discussion of the

Table III-l Experimental chemical shifts for pure acetone (ppm) chemical shift carbonyl i' carbonyl " methyl " C methyl iH O C

a) Christ and Diehl,

Table III-2 exp. PS EH lEH CNDO -572») - 12.4 162.9 - 2.03 1963 relative to water carbon disulfide carbon disulfide TMS

Experimental and theoretical coupling constants for pure CH 126.8 86.7 67.2 67.3 55.6 CC 40.6») 26.1 27.5 26.5 11.2 CO - 6.7 -31.0 -26.4 - 3.5 HCH -14.9") 0.1 -21.0 -21.3 0.4 HCC -5.9 c) 1.2 -5.4 -5.1 0.1 acetone (Hz) HCCC 2.2'J) 2.0 0.4 0.4 1.2 HCCCH 0.561) 0.8 0.6 - 0 . 1 - 1 . 8 ») Weigert and Roberts, 1968

") Gutowsky, Karplus and Grant, 1959 ") Karabatsos and Orzech, 1964

various properties of the carbonyl group we refer the reader to the review paper by Berthier and Serre (1966).

Most simple MO theories of the carbonyl group assume a non-polar non-polariz-able core of localized a bonds and a polar n bond. The polarity is now given by the coefficients of the AO's in the it bond wave function. As many properties depend on the polarity, they can be related to these coefficients or to each other. Nagakura (1952) and Sidman (1957) studied v„_,i. and other electronic transitions in relation to the 7t bond polarity. Maciel (1965) did the same for (5('^C). Cook (1957) established two linear relations between Vj(CO) and 7 for conjugated and unconjugated carbonyl compounds, respectively. Figgis, Kidd and Nyholm (1962) found a general linear relation between ^('^0) and v„^^., which was extended to solvent effects on these two quantities by De Jeu (1969). Finally Savitsky, Namikawa and Zweifel (1965) tried to correlate 5('^C) and v„_„.. However, in this case there is no strict linearity (De Jeu, 1969).

General calculations on all valence electrons of a molecule with a carbonyl group, that in principle take all properties into consideration, are still rare. Often the mole-cules are too large for ab initio calculations, while the semi-empirical methods some-times present difficulties because of the presence of a hetero atom (oxygen). There is a notable non-empirical calculation on formaldehyde by Foster and Boys (1960), which was found to be reliable in a more recent investigation (Newton and Palke, 1966). Contrary to general opinion about the carbonyl bond, they find a polar a bond as well as a polar % bond. For a further discussion we refer the reader again to Berthier and Serre (1966). Cook and McWeeney (1968) recently made also an inte-resting calculation on formaldehyde. They get a flow of a electrons in the direction of oxygen, accompanied even by a back donation of n electrons in the direction of car-bon.

2 Experimental results

The ^^O, '^C and ^H chemical shifts of acetone, relative to some reference com-pound, are given in table III-l. The methyl ^^C is much more shielded than the car-bonyl *^C. Without calculations on the reference compounds the only chemical shift accessible to numerical calculation is the difference between methyl and car-bonyl '^C. We shall denote this quantity by A.

The coupling constants are given in the first line of table III-2. Nowadays the direct-ly bonded CC and CH coupling constants are well-known to be positive. We assume the negative signs of the two-bond HH and CH coupling constants in analogy with the same coupling constants in methane (Pople and Bothner-By, 1965) and acetal-dehyde (Sackman and Dreeskamp, 1965), respectively. The signs of the long-range coupling constants were determined by means of double resonance experiments (appendix B-3).

3 Theoretical calculations

Calculations are done using the four types of theory mentioned in chapter II: Pople-Santry theory (PS), the extended Hückel theory of Hoffman (EH), the iterative extended Hückel method (lEH) and the CNDO method. In this order there is an in-creasing degree of sophistication. By combining the two possibilities for each methyl

Table III-3 Energies for the various conformations of acetone (eV)

staggered/staggered eclipsed/staggered eclipsed/eclipsed PS EH lEH CNDO 445.949 450.058 429.477 1201.837 - 446.465 - 450.640 - 430.179 -1201.895 - 446.786 - 451.015 - 430.738 -1201.935

Table III-4 Theoretical I'O and I'C screening constants for pure acetone (ppm) carbonyl O carbonyl C methyl C

exp. PS EHLÖ) EH (Mu) lEH (LÖ) lEH (Mu) CNDO Cd 426.7 430.9 433.0 419.9 421.2 420.0 "p - 853.5 - 531.6 - 454.3 - 1 2 3 8 . 6 - 1 1 9 4 . 2 - 1 2 8 7 . 3 Cci 260.2 255.9 253.8 266.4 266.2 264.6 •fp - 6 0 7 . 6 - 6 0 4 . 0 - 5 0 3 . 3 - 5 2 6 . 2 - 4 5 8 . 4 - 5 8 0 . 1 "d 265.9 269.9 271.0 268.8 269.4 269.7 "T, - 5 1 2 . 0 - 4 7 4 . 4 - 4 3 9 . 1 - 4 8 2 . 2 - 4 8 8 . 4 - 4 7 3 . 5 A 175.3 101.3 143.6 81.5 46.4 13.2 111.8

Table III-5 Theoretical excess charges for pure acetone (a.u.)

carbonyl methyl PS EH (LÖ) EH (Mu) l E H (LÖ) lEH (Mu) CNDO O - 0 . 7 5 1 - 1 . 0 6 3 - 1 . 2 1 6 - 0 . 2 4 0 - 0 . 3 1 4 - 0 . 2 6 3 C 0.635 0.985 1.134 0.093 0.116 0.251 C 0.240 - 0 . 0 9 1 - 0 . 1 7 6 0.003 - 0 . 0 4 3 - 0 . 0 7 1 H - 0 . 0 6 1 0.043 0.072 0.024 0.048 0.026

Table III-6 Theoretical populations for the carbonyl group of pure acetone (a.u.) carbonyl O carbonyl C PS EH (LÖ) EH (Mu) lEH (LÖ) lEH (Mu) CNDO 2s 1.702 1.636 1.743 1.587 1.663 1.739 2Px 1.513 1.696 1.723 1.619 1.620 1.331 2Py 1.955 1.964 1.969 1.946 1.947 1.952 2p, 1.580 1.767 1.781 1.087 1.084 1.242 2s 1.066 1.026 1.093 1.093 1.197 1.037 2Px 0.797 0.715 0.578 0.814 0.716 0.930 2Pv 0.947 0.919 0.857 1.001 0.965 0.964 2P. 0.555 0.355 0.337 0.999 1.006 0.818

group (figure III-l) we get four rotational isomers of which two are equivalent. The energies are given in table III-3. For the CNDO method this is the real theoretical energy (electronic energy and nuclear repulsion energy); for the other methods twice the sum of the orbital energies with a correction for the differences in nuclear repulsion energy. All further numerical result are averages over the four rotational isomers.

The results for the coupling constants by use of (11-62) are given in table III-2. One should realize that absolute agreement with experiment depends to a great extent on the values chosen for s^(0), the electron density at the nucleus. We used atomic SCF values of 0.550 for hydrogen, 2.767 for carbon and 7.638 for oxygen (a.u.). Furthermore n electron contributions are not yet included, which may be of impor-tance for the long-range coupling constants.

In table III-4 the diamagnetic and paramagnetic contributions to the screening constant are given according to (11-34) and (11-42). The average excitation energy is chosen equal to 7 eV. As overlap is disregarded when deriving these formulas, they are consistent with the PS and the CNDO method. The EH and lEH wave functions, which include overlap, are a priori unsuitable for calculating the chemical shift from (11-34) and (11-42). Nevertheless we made two attempts at overcoming this difficulty: (a) In the line indicated by (LÖ) the charge and bond order matrix over the Löwdin orbitals (appendix A-1.2) is used. The integrals 7?^, and 7^, are calculated by means of the normal basis of STO's, hoping that these form a reasonable approximation to the Löwdin orbitals. (b) In the line indicated by (Mu) the normal bond order matrix elements are retained, but the diagonal elements are replaced by the Mulliken gross AO populations (appendix A-1.2).

In table III-5 the excess charges on the various atoms are shown. For the EH and lEH calculation both the charges according to Löwdin and the gross charges according to Mulliken are given. In the iteration procedure for the lEH calculation the Löwdin charges are used. Thus the calculation is not consistent with respect to the Mulliken charges (Cusachs and Politzer, 1968).

Finally, table III-6 shows a population analysis of the carbonyl group. For the EH and lEH method both the populations of the corresponding Löwdin orbitals and the Mulliken gross AO populations are given.

4 Discussion

All the four methods reproduce the energetical order of the three rotational isomers (table III-3). The conformation with both methyl groups eclipsed to the CO bond is the most favourable; with both methyl groups staggered it is the least favourable. The CNDO calculation also predicts very well the barriers to rotation: for one methyl group 0.92 kcal mole"' (experimentally 0.78 kcal mole"'), for both methyl groups together 2.26 kcal mole"'. In the last case there is no experimental information, but some classical empirical calculations give 2.18 kcal mole"' (Allinger, Hirsch, Miller and Tyminsky, 1969). The other calculations predict barriers that are too high by a factor 10.

The expected polarity of the CO bond is reproduced by all calculations (table III-5). As usual in such cases the independent electron methods (PS, EH) give a highly exaggerated polarity. This arises because excess charge on an atom does not prevent the attraction of more electrons in these methods. In the lEH method a correction is made in a semi-empirical way, while the CNDO method includes Coulomb repul-sions explicitely. Thus the latter methods give more realistic charge distributions. The CNDO calculation also predicts the right dipole moment (Pople and Gordon, 1967). One might expect the methyl carbon to be slightly positive, because of the electron attracting properties of the CO bond. This is not reproduced by the calculations (except PS). Generally spoken the excess charges on methyl carbon and hydrogen are negligible.

For a more careful account of how the charges arise we consider the orbital popu-lations (table III-6). In all calcupopu-lations the 2py lone pair on oxygen is clearly present; the 2s lone pair is more mixed up with the other AO's. From the 2p^ and 2p^ popu-lations we can gain an impression about a and n bond polarity. The lEH calculation gives an almost non-polar n bond and a highly polar a bond. The other calculations give both a polar a and a polar n bond, the latter being usually the most polar. Thus all our calculations disagree with the idea of a non-polar a bond and a polar n bond, used so often in simple theories.

Next we shall discuss some details of the wave functions not mentioned in the tables. The highest three occupied MO's in the CNDO calculation strongly resemble a localized CO a bond (2/7^ coefficients 0.4 and 0.6), a localized CO n bond (2/?^ coeffi-cients 0.4 and 0.7) and the 2py lone pair {2py coefficient 0.7). Using Koopman's theorem the orbital energy of the last one equals the ionization potential. The value is

13.3 eV (experimentally 9.7 eV). In the lEH calculation the highest three occupied MO's show the same resemblance, but with the a and n bond interchanged in ener-getical position.

When we look at the coupling constants (table III-2) we see that the sign and order of magnitude of the directly bonded CC and CH coupling constants are rather well reproduced. Recent calculations (Pople, Mclver and Ostlund, 1968) seem to indicate that the atomic SCF value we used for s%{()) is too low for molecules. Consequently agreement in absolute magnitude with experiment is probably better than is apparent from table III-2.

The PS and CNDO method are not very successful for the prediction of the two-bond coupling constants. For the PS method this is a well-known feature (Murrell,

1969; De Jeu and Beneder, 1969). Nevertheless substituent effects from one molecule to another are often well reproduced (Pople and Bothner-By, 1965). The same is true for the CNDO results. Here probably the inclusion of the one-centre exchange inte-grals (INDO method) is essential to get the negative sign (Pople, Mclver and Ost-lund, 1968).

n electron contributions which are not included in the calculations may be of importance for the long-range coupling constants. As the protons in both methyl

groups are coupled to the same n electron, a possible contribution to ^Jaa of acetone is necessarily negative. In the application of (11-66) to acetone and 2-butene the same hyperfine constants occur. Using a VB formalism Holmes and Kivelson (1961) found

*JSH (acetone) x -t}^ VHH (2-butene) (III-l) where vi^ represents the coefficient of the covalent part of the VB carbonyl wave

function. For pure acetone t]^ = 0.5. For ^JHH of 2-butene several values can be chosen. Karplus (1960) calculated 2.0 Hz which was corrected to 0.65 Hz by Ditch-field and Murrell (1968b). A VB calculation by BarDitch-field (1968) gives 1.2 Hz which is also the experimental value for some substituted 2-butenes. The theoretical values depend on the dihedral angle between the CH bond and the z-direction, and are given here as the averages for freely rotating methyl groups. Taking 1.2 Hz as a reasonable average we can expect a n electron contribution to VHH of acetone of about —0.6 Hz. The contribution decreases in absolute magrdtude with increasing n bond polarity (decreasing t]^). To obtain the experimental value of +0.56 Hz we have to postulate a positive contribution through space and/or through the a bonds of about 1.2 Hz. By now there is not much ground to postulate a specific through-space effect, as has been done earlier (De Jeu, Deen and Smidt, 1967). The PS and EH calculations in-deed give a value of the right order of magnitude, but the lEH and CNDO methods give a negative value. As the differences between the results of the various calculations are rather small, we cannot attach too much importance to these figures. In analogy with the two-bond coupling constants we may hope that substituent effects can be predicted with more reliability.

Looking at the chemical shifts (table III-4) we see, as expected, that the major part of the difference in shielding between carbonyl and methyl '^C arises from variations of ffp. Both the PS and the CNDO method give the right order of magnitude for A, although the values are somewhat too low. The EH and lEH calculations give much poorer results. The apparent reasonable values from the EH calculation cannot be taken seriously, as they are due to the exaggerated carbonyl polarity. On using the lEH method this exaggeration disappears. We see that the carbonyl '^C screening increases while the methyl '•'C screening does not change very much. This is in ac-cordance with the corrections in the positive excess charges. Thus the wave functions including overlap are not very suitable for calculation of Op from (11-42) which is obtained while ignoring overlap.

A discussion of the relative merits of the various theoretical methods (PS, EH, lEH, CNDO) is given in section V-5.

CHAPTER IV THE INFLUENCE OF HYDROGEN BONDING

1 Introduction 1.1 Hydrogen bonding

As several reviews on H bonding are available we shall restrict ourselves to a brief summary of the theory. A coverage of the whole subject can be found in the book by Pimental and McClellan (1960), while a review of the electronic theories is given by Bratoi (1967). Further reviews are by Sokolov (1965) and by Murthy and Rao (1968a). From the first of these references we quote the following definition: "An H bond exists between a functional group A—H and an atom or group of atoms B when (a) there is evidence of bond formation, (b) there is evidence that this new bond linking A—H and B specially involves the hydrogen atom already bonded to A". It is (b) that differentiates the H bond from other types of association. It is (a) that makes the difference with other types of solute-solvent interactions which do not involve some kind of bonding. As these latter types of interaction have interaction energies much less then the H bond energies of 5-10 kcal mole"', they can often be ignored when the effects of H bonds are studied. B possesses a concentration of electron density (e.g. lone pair electrons); A—H is called the proton donating or electron accepting group.

The classical electrostatic model of the H bond was made by Pauling. He states that as the bonding properties of hydrogen depend on the 1^ orbital, the hydrogen atom cannot form more than one purely covalent bond. Therefore the H bond must be ionic in character. This idea is supported by the fact that the strongest H bonds A—H- • 'B are formed when A and B are both fluorine ions, the H bonds involving oxygen are second strongest, and N—H acids usually from relatively weak H bonds. Calculations can be based on this electrostatic model in which the four relevant electrons (two A—H, two B) are represented by point charges on the line AHB. This is done in such a way that the dipole moments of the A—H bond and the B lone pair have the correct values. Now the interaction energy can be calculated with elementary electrostatics. The results have the right order of magnitude. In discussions of the electrostatic model more sophisticated than the point charge calculations, the charge distribution of the B electrons is taken into account using the concept of orbital hybridization. A notable succes of the model is that on this basis the structure of ice can be explained. For carbonyl bases the H bond is predicted to make an angle of 120° to the CO bond direction. Experimentally 100-120° is found.

Despite the success of the electrostatic model there are some serious defects. We mention two: (a) There is no correlation between H bond strength and dipole moment of the base, as would follow from the theory, (b) The AB distances are always much smaller than the sum of the Van der Waals radii of the atoms involved. Thus strong repulsions arise and the electrostatic forces cannot be the only forces present.

It is clear that a more elaborate quantum theory is necessary.

The essential feature of all quantum theories of H bonding is that some covalent character is attributed to the H bond. That means that charge is transferred from B to A. The simplest qualitative picture can be given in a VB description. The H bond is represented by

<P = C,0, + C,02 + C3^3 (IV-1) where the $f refer to the following mesomeric structures:

"^A—H | B / " ^ A " H + | B / \ A - H — B + /

(1) (2) (3) The resonance between (Pj and 02 represents the ionic interactions between acid and base; $3 gives the charge transfer. Calculations indicate that the weight of «Pj is small for long H bonds, but can be about 20% for shorter H bonds.

For quantitative calculations an MO description is most useful. The H bonded complex is treated in one complete calculation which is compared with calculations on the two separate molecules. Semi-empirical methods are, of course, necessary for most complexes of interest; e.g. the CNDO method has been used by Pullman and Berthod (1968), Murthy and Rao (1968b) and Schuster and Funck (1968). We shall not go into the details of calculations on the H bond itself. The main purpose of our calculations on the H bond between acetone and water is to get a model to predict the changes in the NMR properties of acetone.

1.2 Acetone in other spectroscopic methods

The most significant influences of H bonding on the spectroscopic properties are often found in the proton donating molecule. For example the A—H stretching mode shows a frequency shift, increase in band width and enhancement of intensity. Here we shall restrict ourselves to the effects in acetone as the proton accepting molecule. IR studies of acetone in various proton donating solvents have been carried out by several authors (Bellamy and Williams, 1959). With increasing proton donating properties of the solvent Vj(CO) decreases, indicating the expected decrease in strength of the CO bond. However, Vs(CC) and Vj(CH) shift to higher frequencies. Thus the effect is accompanied by an increase in strength of the CC and CH bonds. These conclusions are confirmed by a Raman study by Puranik (1953) on acetone/water. Here the concentration is varied, and the same effects occur for decreasing molar fraction acetone, thus for increasing H bonding (figure IV-1).

In UV spectroscopy both hypsochromic (blue) and bathochromic (red) shifts are observed, depending on whether the H bond is stronger in the ground state or in the

i : I I 2950 810 1720 29M) 800 1710 2930 790 1700 2920 780 1590 • molar % acetone _L J 0 25 50 75 100 Figure IV-1

Raman frequencies of acetone in water (Puranik, 1953);

I CO bond; II CC bonds; III CH bonds

excited state (figure IV-2). The n^n frequency of acetone and other ketones is known to shift to higher values (blue shift) in solvents with increasing proton donating properties. For acetone see Balasubramanian and Rao (1962) and Hayes and Timmons (1965). When an n--*n transition occurs there is only one n electron left to form the H bond. Furthermore the dipole moment decreases as charge is trans-ferred from the oxygen atom to the CO bond. Thus the H bond energy is much less in the excited state than in the ground state. The situation corresponds to figure IV-2a, and the blue shift is as expected.

The n-*n transitions in a base generally show a red shift when an H bond is formed. This shift can be attributed to an electron redistribution with enhanced electron density in the more peripheral parts of the molecule, which is just the effect of going from a bonding to an anti-bonding orbital. Thus the electrons are more accessible for H bond formation in the excited state, and the situation is as in figure rV-2b (Besnaïnou, Prat and Brato^, 1964). It is not yet clear that the n^n transition of acetone confirms this general pattern (Campbell and Edward, 1960). In practice blue and red shift are used for identification of the transitions.

Ito, Inuzuka and Imanishi (1960) established a linear relation between the increase of v„_„. and the decrease of Vs(CO) for ketones in various solvents. Furthermore there is the same kind of linear relation between the increase of v„_„. and the shift to higher field of the carbonyl '^O of acetone, while a small deviation from linearity occurs for the carbonyl " C chemical shift (De Jeu, 1969).

Figure IV-2 Energy curves for ground state and excited state indicat-ing the origin of UV frequency shifts; (a) blue shift; (b) red shift.

(a) • ' A B (b)

•<AB

2 Experimental results

The two coupling constants that can be obtained directly from the proton spectrum are 'TCH and */„„ (see appendix B-1). To measure the other coupling constants la-borious double resonance methods or isotopic substitutions are necessary. Therefore the attention will be focussed on '/CH and '^J^H- In table IV-1 these coupling constants are given for 20 molar % acetone in various solvents. Both increase with increasing proton donating properties of the solvent. There is no correlation with dielectric constant or dipole moment of the solvent. For the purpose of comparison the car-bonyl '^C chemical shifts of Maciel and Natterstad (1965) are also given. A few points were tested and about the same values were found.

In table IV-2 the concentration dependence is shown for '/CH and ^/HH of acetone in water. Both increase with increasing H bonding (decreasing molar % acetone). Below 5 molar % acetone further dilution is no longer very important. The chemical shifts of methyl and carbonyl '^C are also given. With increasing H bonding the carbonyl '^C is shifted to lower field (deshielded), while the methyl '^C is hardly affected. For the purpose of comparison the carbonyl '^O chemical shifts of Christ and Diehl (1963) are given too.

A plot of '/cH or "^JfiH against the carbonyl '^C chemical shift gives within the experimental errors a straight line, both for 20 molar % acetone in various solvents and for acetone at various concentrations in water. In figure IV-3 the plot for acetone in water is shown. In figure IV-4 the carbonyl '^C and '"'O chemical shifts for acetone in water are plotted against each other. There is a slight but definite deviation from linearity.

Table IV-1 solvent

Coupling constants (Hz) and carbonyl " C chemical shifts (ppm) for 20 molar % acetone in various solvents •^CH ) •'HH / Ö(1'C)6) cyclohexane carbon tetrachloride carbon disulfide acetone dimethylformamide acetonitrile chloroform ethanol methanol formamide water formic acid trifluoroacetic acid 126.6 126.5 126.6 126.7 126.6 126.9 127.1 127.5 127.3 127.2 127.5 127.9 128.2 0.48 0.50 0.56 0.56 0.55 0.58 0.59 0.61 0.60 0.66 0.66 0.68 0.74 2.4 1.3 0.0 - 0.7 - 2.1 - 2.3 - 2.9 - 3.7 - 9.1 - 9.1 -14.1 *) standard deviation 0.1 Hz •>) standard deviation 0.01 Hz

6) ± 0.5 ppm (Maciel and Natterstad, 1965)

Table IV-2 Concentration dependence of coupling constants (Hz) and I'O and I'C chemical shifts (ppm) for acetone in water

molar % acetone 100 65 35 20 10 5 2.5 1.0 0.5 0.2 0 couphng constants • ' c H ) •'HH ) 126.7 0.56 127.1 0.62 127.3 0.64 127.5 0.66 127.6 0.69 127.8 0.70 127.9 0.71 127.8 0.71 127.8 0.70 127.9 0.72 127.96) 0.726) chemical shifts carbonyl I'O») 0.0 12.0 25.5 37.1 45.7 51.16) 53.86) 57.06) carbonyl i'C<i) 0.0 - 3.3 - 6.0 - 8.0 - 9.4 -10.0 -10.4 -10.96) methyl "C-i) 0.0 - 0 . 4 - 0 . 4 - 0 . 6 - 0 . 9 - 0 . 9 - 1 . 3 -1.26) a) ") 6 ) •J) «) standard deviation 0.05 Hz standard deviation 0.005 Hz ± 1.0 ppm (Christ and Diehl, 1963) standard deviation 0.2 ppm

extrapolated from the higher concentrations

In figure I V-5 we give the data of Satake and coworkers for the ' H chemical shifts of the acetone/water solutions. A few points were tested and the same values were found. The water protons undergo a considerable shift to lower field with increasing water concentration (about 2 ppm). The methyl protons of acetone are relatively unaffected (about 0.1 ppm to lower field).

-15 -15

Figure IV-3

Coupling constants versus carbonyl " C chemical shift for acetone at various concentrations in water.

5 ( 0) ppm pigureIV-4

1 I I " C versus "O carbonyl chemical shift for 5 0 acetone at various concentrations in water.

3 Theoretical calculations

We need a model to describe the H bond in order to do theoretical calculations on the NMR parameters of acetone in water. Therefore we start with some CNDO calcula-tions on a model of the acetone-water complex. Using the acetone conformation with both methyl groups eclipsed (lowest energy), a water molecule (ron = 0.96 A, HOH angle 104°) is allowed to approach the carbonyl group with an OH bond making an angle of 120° with the carbonyl bond:

4 . 5 0

--J.OO

Figure IV-5

•H chemical shifts of acetone/water as a function of the concentration;

I water (Satake, Arita, Kimizuka and Matuura, 1966);

II acetone (Satake, 1967).

c=o

H

V"

Thus we assume a linear H bond, while the water molecule is put in the plane of the acetone skeleton. Without changing the molecular geometries the energy is calculated for various OO distances. The total energy of the complex is shown in figure IV-6a; a minimum occurs for 7?oo = 2.50 A. Keeping this distance fixed the next step is to vary the water OH distance (figure IV-6b). A single minimum is found for TOH = 1 -05 A. Rotation of the other water OH bond does not affect the energy very seriously.

The distances obtained from the model calculation are used for calculations with the lEH and the CNDO method. As the influence of the H bond in the acetone cal-culations is seen via a change of the atomic charges and electron repulsion is not included in the PS and the EH method, these two will not reflect these changes. There-fore we shall not give the results of the PS and EH calculations (see also section V-5). The results of the lEH and CNDO calculations are again averages over the four rotational isomers.

In table IV-3 the excess charges on the atoms are shown. Although the methyl groups are no longer equivalent, the differences in the charges are very slight and