Electrostatic-Covalent Model Parameters for Molecular Modeling

Chapter 6

Downloaded by UNIV MASSACHUSETTS AMHERST on September 30, 2012 | http://pubs.acs.org Publication Date: February 1, 1998 | doi: 10.1021/bk-1998-0677.ch006

Electrostatic-Covalent Model Parameters for Molecular Modeling 1

2

R. S. Drago and T . R. Cundari 1

Department of Chemistry, University of Florida, Gainesville, FL 32611-7200 Department of Chemistry, University of Memphis, Memphis, T N 38152 2

In molecular modelling o f physicochemical properties, the estimation o f the magnitude o f specific donor-acceptor interactions, e.g., hydrogen bonding, is most difficult. This article presents a compilation o f the most recent set o f parameters that allow prediction o f neutral molecule, intermolecular, donor-acceptor interactions and a set o f parameters that provides bond energies for organic, inorganic and organometallic compounds. Solvent polarity parameters are also discussed that provide a measure o f non-specific solvation. The meaning o f the parameters in the context o f the electrostatic-covalent model are presented and their use illustrated. Examples are discussed to illustrate the value o f these parameters when used in conjunction with quantum chemical calculations. Understanding the trends and predicting values o f bond energies are essential for many problems in chemistry ranging from chemical reactivity, to structure, to physicochemical measurements. The electrostatic-covalent model (7), without question, provides the most general set o f parameters for they encompass enthalpies for neutral donor-neutral acceptor adducts, energies o f gas phase ionmolecule reactions, homolytic bond dissociation energies and solvation energies. The elegance of the model is its simplicity. A s the chemical reaction becomes more complex, terms are logically added, a priori, to account for the new energetic contributions. The purpose o f this article is to illustrate the application o f this model to the area o f molecular modelling and to provide the most recent set o f parameters for incorporation into modelling programs. Neutral Donor-Acceptor Adducts Correlations o f physicochemical properties, like solubility parameter theory, often break down when contributions from specific donor-acceptor interactions exist

© 1998 American Chemical Society

In Computational Thermochemistry; Irikura, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1905.

105

106

COMPUTATIONAL THERMOCHEMISTRY


because these energies are not adequately predicted. The correlation o f over 500 enthalpies o f donor-acceptor interactions in poorly solvating solvents leads to acceptor and donor parameters that can be used to determine the hydrogen bonding and other donor-acceptor contributions, resolving complex physicochemical properties into their energetic components. The electrostatic-covalent model o f Pauling and Mulliken is used to write equation 1. Measured enthalpies, - A H , for donor-acceptor reactions fit equation 1, -AH = E E A

B

+ C CB + W

(1)

A

which consists o f covalent, CACB, and electrostatic, E E , components. Each acid is proposed to have a tendency to undergo electrostatic, E A , and covalent, C A , bonding as is each base ( E and CB). When the empirical E and C parameters (7) in Table I are combined according to equation 1 they produce the reaction enthalpy, that is, the adduct bond strength. In the molecular orbital description, E relates to the tendency o f the acceptor or donor to undergo a charge-controlled reaction while C relates to the tendency to undergo a frontier-orbital controlled reaction. The W term, which is zero for most enthalpies, incorporates any constant contribution to the reaction o f a particular acid (or base) that is independent o f the base (or acid) it reacts with. F o r example, the enthalpy to cleave the Al Cl6 dimer, when a B-A1C1 adduct is formed, would be included in the W term o f the enthalpy fit. The base parameters in Table I and the acceptor parameters in Table II can be used in equation 1 to predict over 8000 enthalpies o f interaction. In those cases where donor-acceptor pairs have been subsequently measured, the predictions agree with experiment to 2%. In molecular modelling, the parameters can be used as a scale o f acid or base strength to correlate physicochemical measurements in energy units, A x , and determine i f the measurements are dominated by the donor- acceptor component. For physicochemical measurements, equation 1 takes the form shown in equation 2. A

B

B

2

3

Ax

=

E *EB + C *CB + W A

(2)

A

Several physicochemical properties besides enthalpies have been correlated (2) to equation 2, the E C W model. In this application, weighted regression analyses with the weights in the tables should be used because the parameters are not all known to the same degree o f certainty. When the measurement is that o f an acceptor molecule studied with a series o f donors whose E and C B are known, the measured property, A x , and the base parameters are substituted into equation 2,. The series of equations, one for each base, is solved for E * , CA*, and W . Asterisks are placed on the acceptor parameters to indicate that they do not refer to enthalpies in poorly solvating solvents and that conversion units leading to A x are included. W is the value o f A x when a donor is attached whose E and C B value is zero. When a base property is measured with a series o f acids, E and C are substituted and E * and B

A

B

A

A


B

6.

DRAGO & CUNDARI

107

Electrostatic-Covalent Model Parameters

CB* determined. The results for correlations to E C W o f physicochemical properties other than enthalpies are summarized in Table III. To illustrate the correlation o f a physicochemical property to E C W , the C O stretching frequencies o f a series o f base, B , adducts o f B-Rh(pfb)4Rh-CO will be employed (pfb is a perfluorobutyrate anion that bridges two R h centers). The question asked is: does the frequency shift parallel changes in the sigma donor strength of B ? Instead o f plotting the shift versus p K , a dual parameter correlation is made to E and C B using equation 2. The independent variable Vco is correlated to the dependent variables E and C B using a linear regression routine (e.g. N C S S , Kaysville, Utah). The E and C parameters are weighted according to Table I and solved for the parameters E \ C * and W . The resulting correlation equation (r = 0.935) and data fit are given in Table I V . Since the E C W model only incorporates sigma bonding effects, one can conclude that the change in the C O stretching frequency is dominated by the sigma bond strength o f the base with stronger bases leading to lower frequencies. Note the excellent agreement o f the intercept, W , with the value o f v o with no base coordinated. B


B

B

B

B

2

A

A

C

The good correlations summarized in Table III provide probes that can be combined with measured enthalpies to add new donors or acceptors to the model. To add a new donor, enthalpies o f reaction with a series o f acceptors whose E ^ C and W are known and other physicochemical measurements with acceptor probes whose E * , C * and W are known are substituted into equation 1. A series of equations results that can be solved for the E and C B parameters for the new donor. Most o f the bases whose statistical weights are l o w in Table I were determined from limited data in this manner. In most instances, the set o f simultaneous equations solved to give these tentative parameters involves types o f acids or bases whose electrostatic and covalent parameters are similar. The C / E ratios indicate the relative importance o f these effects in acids and the C B / E B ratios indicate the base types. When the range o f acids used to determine C and E for a donor is limited, the base parameters will provide a good fit o f new data for similar acids but may not provide good estimates for acids with different ratios (7). When data become available for new acids that extend the ratio, the base parameters should be redetermined. A

A

A

B

A

B

A

B

The E C W parameters provide an estimate o f the sigma bond strength o f the donor-acceptor interaction. The widespread applicability o f these parameters to a variety o f acids and bases and the subsequent use o f these parameters to correlate many new systems (7) leads to confidence in the predictions made with this model. Correlations o f data sets for a series o f bases (or acids) with these parameters will indicate whether or not the physicochemical measurements are dominated by the same base (or acid) properties that determine donor- acceptor bond strengths. When poor correlations result, a systematic pattern in the deviations may reveal an unusual bonding effect. The deviant systems are omitted and the fit redetermined. To confidently omit systems, the deviations o f the omitted system should be 2.5 times larger than the average deviation o f the fit o f well behaved donors. Deviations in data sets have been shown to provide estimates o f the magnitudes o f steric effects and pi-back bond stabilization (2). Unusual entropic effects also have


COMPUTATIONAL T H E R M O C H E M I S T R Y

108

Table I. Base Parameter Weight C E

Bases

B

NH CH NH (CH ) NH (CH ) N C H NH (C H ) NH (C H ) N (CH ) NH HC(C H4) N N-CH Im C H N 3CH C H N 3CIC5H4N 3BrC H4N 3IC5H4N 4CH C H4N 4C H C H4N 4CH OC H4N 4-N(CH ) C H4N 4-CNC5H4N quinoline CH CN n-C H CN C1CH CN (CH ) NCN C H CN 3

3

2

2

3

2

3

3

5

2


2

5

2

2

5

3

2

5

2

3

3

a

5

5

3

5

4

5

3

5

2

5

5

3

5

3

2

5

3

3

7

2

3

6

2

5

CH C(0)CH CH CH C(0)CH 3

3

3

2

(CH ) CO CH C(0)OCH 2

3

4

3

3

CH C(0)OC H (C H )C(0)CH (C H ) CO Propylene Carbonate CH C(0)N(CH ) HC(0)N(CH ) NMP CO[N(CH ) ] (C H ) 0 /-Pr 0 3

2

6

5

6

5

5

3

2

3

3

3

3

2

5

2

2

(C H ) 0 0(C H4) 0 (CH ) 0 (CH ) 0 (CH ) 0 4

9

2

2

2

2

4

2

5

3

2

2

2

2

2

2.31 2.16 1.80 1.21 2.34 1.22 1.32 1.44 0.80 1.16 1.78 1.81 1.66 1.66 1.67 1.83 1.81 1.83 1.92 1.53 2.28 1.64 1.81 1.67 1.92 1.65 1.74 1.67 2.02 1.63 1.62 1.72 2.01 1.51 2.35 2.19 2.12 2.06 1.80 1.95 1.89 1.86 1.64 2.05 1.68

B

2.04 3.12 4.21 5.61 3.30 4.54 5.73 4.93 6.72 4.92 3.54 3.67 3.08 3.08 3.13 3.73 3.74 3.83 4.43 2.94 2.89 0.71 0.54 0.33 0.92 0.75 1.26 1.24 0.88 0.95 0.98 1.15 0.55 1.32 1.31 1.31 1.65 1.87 1.63 1.60 1.67 1.29 2.18 1.38 1.50

CB/E

B

0.88 1.4 2.3 4.6 1.4 3.7 4.3 3.4 8.4 4.2 2.0 2.0 1.9 1.9 1.9 2.0 2.1 2.1 2.3 1.9 1.3 0.43 0.3 0.2 0.48 0.45

1 1 1 1 0.6 0.2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.2 1 0.6 0.6 1 0.4 0.4 1 1 0.2 0.2 0.4 1 1 0.4 0.5 1 0.2

0.72 0.74 0.43 0.58 0.61 0.7 0.3 0.9 0.56 0.60 0.8 0.91 0.91 0.85

1 1 1 0.4 0.6

0.69 1.3 0.67 0.89

0.88


6.

D R A G O & CUNDARI

109


Table I (continued) (C H ) 0 (CH ) (CH) 0 (CH ) S (C H ) S (CH ) S C6H5SCH3 (CH ) S CH3S2CH3 (CH ) SO (CH ) SO (CH ) S0 C5H5NO 4-CH3C5H4NO 4-CH3OC5H4NO (CHJ^CJHSNOCTEMP) QH N0 CH N0 (C H ) PO (CH 0) PO (C H 0) PO [(CH ) N] PO (CH ) P (C H ) P (?-butyl) P (C H )P(CH ) (C H ) PCH (C H ) P (4-ClC H ) P 8

1 7

2

3

2

2

2


2

4

5

2

2

4

2

5

3

2

2

4

2

4

2

5

2

3

2

6

5

3

3

2

3

5

3

3

2

3

b

3

3

2

5

6

5

6

S

6

S

3

3

3

2

2

3

3

6

5

3

(4-CH C H ) P (4-CF C H ) P 3

6

3

6

5

5

3

2

(CH 0) P (C H 0) P cage phosphite /-C4H9OH (CH ) Se 3

2

3

5

3

3

2

(C H ) PS (C H ) As a

6

5

3

6

5

3

1.77 1.45 0.25 0.24 0.26 0.21 0.34 0.55 2.40 2.44 1.61 2.29 2.32 2.34 1.46 1.27 1.09 2.59 2.42 2.51 2.87 0.31 0.28 0.25 0.44 0.57 0.70 0.82 0.65 0.91 0.50 0.56 0.09 2.05 0.05 0.70 0.35 0.90

1.95 2.14 3.75 3.92 4.07 3.13 3.81 2.34 1.47 1.64 1.09 2.33 2.57 3.02 3.20 0.57 0.70 1.67 0.98 1.10 1.52 5.15 5.53 6.08 4.49 3.74 3.05 2.35 3.41 1.52 3.32 3.17 4.85 1.00 4.24 0.45 3.65 2.16

0.2 1 1 1 1 0.6 0.6 0.2 1 1 0.2 0.2 0.8 0.2 1 0.6 0.2 0.8 0.2 1 0.5 1 1 0.5 1 1 1 1 1 0.8 1 1 0.7 0.2 0.4 0.5 0.2 0.2 1

The E and C parameters in units o f (kcal mol" ) B

B

1

1.1 1.5 15 16 16 15 11 4 0.61 0.67 0.7 0.33 1.1 1.3 2.2 0.45 0.6 0.64 0.4 0.44 0.53 17 20 24 10 6.6 4.4 2.9 5.2 1.7 6.6 5.7 54 0.64 83 0.64 10 2.4

for 56 x-substituted pyridines X

X

can be obtained by using reported substituent constants A E and A C (Drago, R . S . Organometallics 1945, 34, 3453) in E

x b

X

= 1.78 + A E and C

X B

= 3.54 +

X

AC . ^Tor parameters for thirty-seven substituted phosphines see Joerg S.; Drago, R . S.; Seles, J. submitted. M o s t o f the phosphines have been studied on systems that utilize only phosphine ligands. See the above reference for limitations on their use.



Table EL Enthalpy Acid Parameters

Acid

E 0.50 2.92 1.20 2.27 2.30 2.37 2.38 2.34 2.23 2.22 2.07 2.89 1.27 1.15 1.14 3.06 0/89 0.58 1.35 1.56 1.38 0.80 0.86 2.85 1.60 3.57 8.28 6.95 6.60 2.87 0.51 1.55 1.82 2.75 2.50 3.15 2.72 2.32 4.70 4.32 A

h ICl IBr C6H OH

fl

5

4-FC6H4OH


3-FC6H4OH

3-CFQH4OH 4-CIC6H4OH 4-CH3C6H4OH 4-/-C4H9C6H4OH

CF CH OH (CF ) CHOH 3

2

3

2

CH3OH C2H5OH

6

/-C4H9OH

(CF ) COH C H OH C6H SH H 0 HCC1 3

3

fe

8

17

5

2

3

C4H4NH

CF (CF ) H CH C1 HNCS HNCO B(CH ) V [A1(CH ) ] Ga(C H ) ln(CH ) (CH ) SnCl S0 [Ni(TFAcCAM) ] Cu(HFAcAc)/ Zn[N(Si(CH ) )] Cd[N(Si(CH ) ] Mo PFB ZnTPP^ CoPPIXDME* V [MeCo(Hdmg) ] V [Rh(CO) Cl] 3

2

2

6

2

3

3

2

3

2

5

3

3

3

2

3

3

3

2

c

2

3

3

3

3

2

2

2

e

2

4

2

2

2

2

2

2

C 2.00 1.66 3.29 1.07 1.11 1.17 1.22 1.14 1.03 1.03 1.06 1.33 0.74 0.67 0.66 1.88 0.87 0.37 0.78 0.44 0.68 0.63 0.11 0.70 0.69 2.97 3.23 1.48 2.15 0.71 1.56 1.32 2.86 2.32 1.83 1.05 1.45 1.34 3.24 4.13

W

A

-0.16

-0.87

-8.46

-5.84 -10.39

Weight 1.0 1.0 0.4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 0.8 1.0 0.2 0.4 1.0 1.0 0.2 1.0 0.6 0.4 0.8 1.0 0.2 1.0 1.0 1.0 1.0 0.8 0.8 1.0 1.0 1.0 1.0 1.0

C /E 4.0 0.57 0.47 0.47 0.48 0.49 0.51 0.49 0.46 0.46 0.51 0.46 0.58 0.58 0.58 0.61 1.0 0.6 0.59 0.28 0.49 0.8 0.13 0.2 0.4 1.2 0.39 0.21 0.33 0.25 3.1 0.85 1.6 0.84 0.73 0.33 0.53 0.58 0.69 0.96 A

A

X

* Values for 56 x-substituted phenols can be obtained by substituting reported A E and A C substituent constants (Drago, R. S. Organometallics 1995, 34, 3453) into E =2.27-0.817AE and C =1.07-0.225AC . Values for several other aliphatic alcohols have been reported: Joerg, S.; Drago, R. S. submitted. bis(3-trifluoroacetyl-d-camphorate)nickel(II)dimer bis(hexafluoroacetylacetonato)copper(II) molybdenum(II)perfluorobutyrate zinc tetraphenylporphyrin cobalt(II) protoporphyrin I X dimethyl ester X

X

A

X

X

X

A

b

c

d

c

f

8


6.

DRAGO & CUNDARI


111

Table III. Probe Parameters E/ w*CA /EA 167 -205 0.65 109 Avo (C6H OH) 189 -220 0.65 122 AvoH(3-F CC H OH) -124 0.61 89.9 55.0 AvoH(/-C4H OH) 150 0.65 96.9 -193 Avo (F CCH OH) 4.40 -2.0 3.3 14.6 Av (ICN) 1.3 4.59 -8.2 6.05 Av (I C ) 1080 -1252 1.0 Av(I ) 1098 0.20 -1.06 4.23 0.211 Av(4-N0 C H4NH ) ' 0.20 -0.683 -0.140 Av(4-N0 C H OH) 1.14 0 0.68 7.23 4.93 -AH(BF /CH Cl ) 4.51 5.70 0.84 1.3 -AH(HS0 F/l,2Cl C H ) Spectral shifts in the JK (cm* ), parameter units cm" /(kcal mol" ) Spectral shifts in the U V - v i s (cm" ), parameter units cm"7(kcal mol" ) Spectral shfts in the U V - v i s (kK; 1 k K = 1000 cm" ), parameter units kK/(kcal mol" )

Acceptor Probe a

H

5

a

3

6

5

a

9

a

H

3

2

a


IC

a

IC

2

2

b

2

c

2

6

d

2

c d

2

6

4

e

3

2

2

e

3

2

2

4

a

1

1

b

1

172

1

1

c

172

1

1

172

d

A v is the 4-nitrophenol minus the 4-nitroanisole transition or the 4-nitroanaline minus the N,N-diethyl-4-nitroanaline transition. Parameter units (kcal mol" ) 1

172

Table IV. E C W Fit of the Carbonyl Frequencies for the Base Adducts of the Acceptor Rh (pfb) CO Base v o(ECW) Vco(EXP) a

2

4

b

C

None CH C(0)OC H (CH ) CO (C H 0) PO CH C(0)N(CH ) (CH ) SO Bridged ether Melm (C H ) N HCtCiHdaN CH CN Cage phosphite (C H ) S 3

2

3

2

5

2

5

3

3

3

3

2

2135.8 2130.8 2128.6 2126.2 2125.4 2126.2 2127.0 2124.7 2121.6 2120.8 2129.0 2125.0 2126.0 2123.0 2122.0

2

2

5

3

5

2

3

2

C5H5N

4-CH C H N 3

5

4

2135.3 2129.0 2128.2 2126.3 2126.4 2125.9 2127.3 2122.8 2120.9 2120.4 2129.5 2125.9 2127.2 2123.7 2123.2

a

Data from Bilgrien, C ; Drago, R.S.; Vogel, G . C . Inorg Chem, 1986, 25, 2864. Frequencies in cm" Calculated with v = -2.751 (±0.829) - 1.892 (±0.147) + 2135.3(±0.8) R = 0.935, x = 1.1, F-ratio 86.56 1

c o

2


112

COMPUTATIONAL

THERMOCHEMISTRY

been detected (2) in the correlation o f free energies o f formation and activation to ECW. In molecular modelling o f properties that are not related to donor-acceptor interactions but are suspected o f having minor contributions from this effect, the E E + C A C B terms are added to the parameters being used to model the property. A n improvement in the data fit would signify a donor-acceptor component. A

B


Ion-molecule Interactions Gas phase energies o f reactions between donor molecules and ions do not correlate to equation 1 and one would not expect that they should in view o f the different expressions for the energies o f dipole-dipole and ion-dipole interactions. Furthermore, there are additional energy contributions to the ion-dipole interaction from the more extensive electron transfer that occurs between the donor and acceptor upon adduct formation to partially neutralize the positive charge on the cation. There also is a significant component to the energy o f the gas phase reaction from the dispersion interaction between the ion and the donor. In solution, solvent molecules are displaced from both the donor and acceptor when an adduct is formed and this displacement cancels out most o f the dispersion contribution in the adduct bond. It is important to remember that solution reactions are invariably displacement reactions and gas phase reactions are combination reactions. The consequences o f these additional energy contributions to the correlation o f gas phase ion-molecule reactions is to require the addition o f a transfer term. In view o f the increased extent o f electron transfer and the increased dispersion interaction energy with an increase in the size o f a donor molecule or ion, a single transfer term can incorporate both effects for the systems studied to date. Equations 3a,b are found to provide accurate estimates o f the energies o f gas phase ion-molecule interactions. F o r reactions between cations and electron donors, the equation is: -AH

= E

M A

E

+

B

C

M A

C

(3a)

M

+ RA T

B

B

The R parameter is called receptance and the T parameter transfer to indicate the direction o f electron density transfer. F o r reactions between anions and electron the equation is: -AH

= E

a n B

E

A

+

C

a n B

C

+ R T

A

A

(3b)

a n B

The E and C or E and C parameters from the neutral donor- acceptor fit (Table I and II ) are used for the neutral molecule. The R and T parameters for the neutral molecules and the cation parameters ( E , C , R ) for cation-donor adducts as well as the anion parameters ( E , C , TB*") for acceptor adducts are given in the literature (7,5). It is particularly significant that the donor and acceptor parameters in Tables I and II can be used to interpret this set o f data in view o f the similar neutral molecule contribution to dipole-dipole and ion-dipole interaction equations. B

B

A

A

A

M

A

a n

B

B

M

A

M

A

a n

B


6.

D R A G O & CUNDARI


113


Bond Energy Parameters The fit o f bond energies can be treated as reactions involving a cation and an anion or as reactions involving atoms. The former requires a knowledge o f the dissociation energies, the ionization energies and electron affinities. Consequently, the decision was made (4) to fit the bond energies, which are dissociation energies with opposite sign. The parameters for an atom will depend on whether the atom becomes the positive or negative end o f the bond dipole in the product molecule. The former are called catimers and described with catimer parameters. The latter are called animers and described with animer parameters. A n excellent fit o f bond energies for a wide variety o f systems including organometallic compounds results (4) by substituting the parameters in Table V into equation 4. The E and C parameters have the same electrostatic and covalent -AH

- EcatE

+

an

CcatC

an

+

RanTcat

(4)

significance as in the E C W equation with subscripts referring to catimers and animers. T^t is the catimer transference parameter and Ra is the animer receptance parameter. The product RanT t indicates the stabilization o f the bond that occurs by electron transfer from the neutral atom catimer to the animer and by the dispersion interaction. For homonuclear diatomic molecules, the bond energy is predicted by combining the animer and catimer parameters for the same atom. F o r a polar molecule,e.g., I C l , an incorrect assignment o f the atoms to animer and catimer results in a smaller calculated bond energy than that for the correct assignment. This difference provides a way o f assessing bond polarity in systems where the choice is not obvious. A s with the neutral adduct fit, deviations from the correlation are found in systems in which steric effects exist or in which pi-bonding exists. n

ca

The electrostatic-covalent parameters provide a much better fit o f bond energies than the estimates o f ionic and covalent contributions to bond energies from electronegativities (4c). The parameters can be used instead o f electronegativities as a reactivity scale to fit physicochemical measurements. Reported correlations include chlorine quadrupole coupling constants in X - C l compounds (7) and C - H coupling constants (4c) in C H X compounds. 1 3

3

Solvation The trends in properties o f the systems treated above are not influenced by solvent polarity contributions. Recent advances have led to a Unified Solvation M o d e l (5) for predicting the non-specific solvation contribution to chemical reactions and spectral shifts. The total specific and non-specific contributions to solvation are predicted by adding a P S ' term to equation 1 to produce equation 5. The P parameter describes Ax = E E A

B

+ C C B + PS' + W A


(5)


Table V . Cafimer and Animer Parameters for use in Equation (4) Catimer Parameters* Catimer (wgt) H-(l) H C-(1) CH CH (l) (CH ) CH(1) (CH ) C-(1) H C>(0.3) C6H CH (l) CH C(0)- (0.3) H Si- (0.3) (CH ) Si-(0.3) Li-(l) Na-(l) K-(0.3) Rb- (0.4) Cs- (0.4) Al- (0.5) In- (0.4) Tl- (0.4) Bi- (0.3) CI- (0.3)

c a

3


3

r

3

2

3

3

5

5

c

E 7.84 4.00 4.27 5.06 4.78 5.77 2.36 4.41 9.13 10.29 10.98 8.03 9.99 9.89 10.65 11.78 9.42 8.07 4.12 0.99

r

3

3

3 3

ca

13.00 11.83 11.45 11.04 10.77 12.92 10.22 9.80 10.12 9.89 2.77 1.48 0.26 0.31 0.17 4.50 3.14 1.81 7.33 14.30

T 0.52 3.37 3.41 2.37 3.16 2.22 4.59 2.63 1.22 1.00 6.43 7.47 8.00 7.74 7.74 5.59 6.81 6.69 4.60 0.73 c a

Catimer Br- (0.4) I-(l) Mn- (0.5) Co- (0.3) Ni- (0.3) Sc- (0.3) Cr-(0.3) Zn- (0.3) Cu-(l) Ag-(0.5) T!-Cp*IrP(CH3)3H-(l) T CpRu[P(CH ) ] -(l) DPPEPt- (1) (CO)sMn- (0.5) T! -CpMo(CO) - (0.5) Ti -Cp2Zr-(0.3) Ti-Cp'3U-(0.5) V-Cp*ThOC(CH ) (0.5) 166-JH - C- (0.6)

E

5

5

1

3 3 2

5

3

5

s

3 3

13

c a

0.78 0.95 7.68 8.37 7.44 12.34 8.55 5.53 7.40 6.30 3.77 2.92 2.90 2.83 0.55 7.63 7.02 0.31 -1.17

b

3

T 1.31 3.37 7.24 5.31 6.57 5.27 5.31 4.03 5.18 5.63 9.96 4.62 5.45 8.82 12.83 8.74 5.54 6.71 0.89

Co 12.25 8.94 1.07 2.88 4.51 1.28 2.05 0.01 5.12 4.11 6.42 3.29 1.02 4.71 5.31 7.06 3.67 11.48 6.50

c >

Animer Parameters* c E Animer (wgt) Ran Can Ean Ran 4.97 1.14 2.10 5.07 6.62 2.36 -OCH (l) -H(l) -CH (1) 5.78 • 0.53 2.36 6.66 3.98 -NH (0.5) 0.60 1.28 3.47 1.77 6.70 4.13 0.20 -N0 (0.5) -CH CH (1) 1.56 3.44 4.78 1.11 -CH CH;CH CH (0.3) 6.51 0.36 -SH(1) 1.08 4.84 0.89 3.64 6.12 -SCH (0.5) 0.18 - H . C Q ^ (0.5) 2.52 1.59 6.64 4.45 -H CSi(CH ) (0.3) 9.81 0.83 -F(l) 3.86 3.41 2.12 7.24 -H CC(0)CH (0.3) 6.23 1.24 •Cl(l) -(0)CCH (0.5) 3.53 0.64 2.91 6.17 1.58 -Br(l) 6.12 3.26 3.43 2.23 6.54 2.63 5.14 -1(1) -CfiHsCl) -CH=CH (1) 1.13 2.71 2.50 6.42 1.96 4.90 -Au(l) -CCCsH, (0.5) 2.53 6.43 5.90 3.12 5.44 1.39 -Ag(l) -CN(1) 2.33 5.52 2.63 6.19 5.87 2.29 -Cud) 1.07 4.18 -CF (0.3) 5.44 5.05 5.88 -Bi (0.5) 1.45 7.18 3.53 5.06 -0.42 -CC1 (0.3) 5.51 4.45 Dc Qq(Cl) (0.5) 1.25 0 7.12 0 4.76 2.55 14eV-IE (0.2) -OH(l) 3.86 4.04 -OCgH, (0.3) 0.77 'Enthalpy parameters in units of (kcal mol* ) The " C - H coupling constant for H C - X derivatives. The quantity calculated is 166-J CH . The value of 166 is for an sp carbon so the larger the number the closer to sp the carbon hybridization. Parameter units H /(kcal mol* ) Animer (wgt)

a n

3

3

2

:

2

3

2

:

3

3

2

3

2

3

3

3

:

3

2

c

c

3

d

1

b

d

172

J

3

l3

2

3

3

1

172

3

c

The chlorine quadrupole coupling constant for M - C l compounds where chlorine is the animer. The e Qq(Cl) value + 109.7 is fit where 109.7 is the value for a free chlorine atom in megahertz. Parameter units MHz/(kcal mol" ) '' 14eV minus the ionization energy in electron volts. Parameter units MHz/(kcal mol' ) 2

1

1

2

d

1

1


6.

D R A G O & CUNDARI


115

the solute response to solvent polarity and S' is a measure o f solvent polarity. Analysis with equation 5, produces the specific ( E E + C C ) and non-specific (PS') contributions to the solvation process. Again, it is important to emphasize that the E and C parameters used in these data fits (for the specific interaction) are those in Tables I and II. The reader is referred to the literature (7,6) for compilations of the solvation parameters, S' and P. A

B

A

B


The E C T Model as a Tool to Accompany Quantum Chemical Calculations The use o f electrostatic-covalent parameters to accompany quantum mechanics in molecular modelling will be illustrated with the E C T model. Since our electrostatic-covalent parameter sets encompass all known sigma bond energies, they can be used in conjunction with molecular orbital calculations, e.g. ab initio quantum calculations, to compare calculated trends from theory against those for all known experimental data, vide infra. Furthermore, a major disadvantage o f high-level calculations is that often a simpler, more chemically intuitive picture o f bonding is sacrificed. N o t only do E C T and E C W provide an intuitive picture, but the use o f these models will be shown to suggest new avenues for inquiry in computational applications. In a recent publication (4c), the C l T i - X and ( C O ) C o - X bond energies calculated (7) with density functional theory were analyzed with equation 4 using the parameters for X in Table 5. Average deviations o f 3.6 and 3.1 kcal mol" , respectively, result between calculated and E C T predictions for bond energies that spanned a range o f - 4 0 kcal mol" . The poor fit indicates that there is no known experimental data set that parallels these calculated trends to a reasonable (~1 kcal m o l ' ) in the predicted bond energies. Either the calculations are at best good to ~10% or there are some unusual bonding effects in some of these compounds. B e l o w an application to organometallic compounds is presented to illustrate data fits to equation 4 and to highlight the E C T model as a valuable tool for the analysis o f quantum chemical calculations. 3

4

1

1

1

Analysis of Metal-Ligand Bonding in Technetium Organometallics Technetium is o f importance as a radiometal in medical imaging (8) and also as a by-product o f nuclear materials processing (9). A major challenge in the study o f technetium compounds results from their wide diversity o f formal oxidation states (from -1 to +7) and coordination numbers (from 4 to 7). Experimental results and theoretical computations point to M ( = N R ) complexes o f d° transition metals as being able to activate the C - H bonds o f hydrocarbons including methane. O n the other hand, d -analogues o f X T c ( = N R ) o f C symmetry are stable enough to be isolated. Hence the strength and polarity o f the interaction between X and M in these complexes is o f interest in the design o f a system to activate hydrocarbons. A s part o f a joint theory-experiment study, Tc-tris(imido) complexes o f the form T c ( = N R ) X , 1, were studied.(10-15) Three-coordinate tris(imido) species are crucial to understanding the bonding in 1.(14) Calculations indicate that d ° - M ( N H ) complexes ( M o and W ) are 3

2

3

3 v

3

3


116


1

2

pyramidal while T c d and Os d analogues are trigonal planar. VSEPR considerations would predict a planar d° configuration instead o f the calculated pyramidal structure. However, the strong 7C-bonding o f the imido ligand is enhanced by going to a pyramidal structure. F o r d and d complexes, the singlyand doubly-occupied d a orbital, respectively, is greatly destabilized by pyramidalization, leading to a trigonal planar ground state. l

2

The geometry o f X T c ( N H ) is sensitive to changes in the X-group. One can fit the X-Tc-Nimido angle determined by quantum calculation to equation 6. F o r X groups o f lower symmetry than C , the average X-Tc-Nimido angle is used. Substituting the E , C and Ran parameters from Table V and the corresponding angles into equation 5 leads to a series o f simultaneous equations o f the form o f equation 6.


3

3 v

a n

a n

e -Tc-N(0) = E ( X ) * k ! + X

an

C (X)*k a n

2

+

Ran(X)*k

+

3

W

(6)

Using parameters for twelve X ligands and their calculated X-Tc-Nimido angles, a least squares best-fit is obtained for k i , k , k and W . The W value corresponds to the 0 value in X T c ( N H ) when E = C = R™ = 0 for X . Six additional X groups in the E C T database ( X = Et, C ( 0 ) C H , vinyl, C = C H , O C H and S C H ) are o f a size to be amenable to calculations on T c ( = N H ) X . The X-Tc-Nimido angles predicted by substituting the parameters from the E C T fit with E , C , and Ra„ for these six groups into equation 6 are consistent with those subsequently determined by quantum methods with an average difference o f 0.7A. The E C T parameters and weights in Table V are used in a fit o f the quantum mechanical angles, 0, leading to the regression equation 7 with r =0.90, an average deviation o f 0.7° and an F-ratio o f 43.6. The E C T angles, 0 CT, and 0 are given in Table V I . 2

3

a n

3

a n

3

3

3

3

a n

a n

2

E

0ECT = 0.77(± 0.11) E

a n

-0.59(± 0.17) C

a n

-0.56(± 0.42) R ^ + 103.6

(7) 5

The parameters suggest that as the X - T c ( = N H ) bond becomes more X ^ - T c * polarized, the electrostatic interaction will increase by increasing the X-Tc-Nimido angle to above 103.6°. A larger electrostatic interaction results as nitrogen lone pair - X repulsions decrease by increasing the angle. A s the X-Tc-bond becomes more covalent, the X becomes less anionic, repulsions decrease and d is populated. Populating d , as in the d complex, leads to a trigonal planar complex decreasing 0. The sign o f the transfer term suggest that as T c becomes more positive, the d-orbitals contract and 7C-bonding to the imido group increases causing 0 to decrease. The X - T c - N i angle is thus an important property for probing the bonding in T c ( = N R ) X (JO). 3

2

z

2

1

z

m i d o

3

High-level calculations are very time consuming for large complexes with heavy metals and it would be very difficult to calculate all animers whose E C T values are known. Thus, the E C T model can not only be used for analysis o f data, but its predictive power provides an efficient tool in the search for new target compounds to study.


6.

D R A G O & CUNDARI


117

Table VI. E C T Fit of Calculated X - T c - N Angles for Tc(=NR) X X group X group OQM OQM OECT 3

H


CF CH CN

3

3

CC1 SH I NH Br a

3

2

98.9 99.7 100.5 101.2 101.5 103.0 103.8

100.1 100.3 101.1 100.9 100.8 102.8 104.4

104.0 104.6

102.9 104.6

CI OH F C2H5

CH C0 3

-C=CH -C^CH SCH

2

2

3

OCH3

6 in degrees calculated with: 9 = 0.77 E

- 0.59 C

a n

a n

OECT

105.0 105.4 106.2 100.3 100.7 101.0 102.4

105.0 104.8 107.1 100.9 99.5 100.8 102.0

102.7 105.2

102.9 103.9

- 0.56 Ra + 103.6 n

Apart from the observations o f good statistical correlations there are several points o f interest which reveal insights from E C T into the chemistry o f the tris(imido) complexes, and their potential as metastable precursors to hydrocarbon C - H activating M ( = N R ) species. First, observation o f a reasonable correlation with animer parameters suggests that, for chemically diverse systems, the dominant description o f T c ( - N R ) X is X"[Tc(=NR) ] , with a d° configuration at the metal. Quantum calculations for methane activation by [2a + 2n] addition across the metal-imido active sites show large kinetic barriers to C - H bond scission when the metal configuration is not d° due to a repulsive interaction between substrate and activating complex in the early stages o f the activation event {11a). Second, the positive coefficient o f E indicates that as the capacity for X to participate in electrostatic/ionic bonding increases so does the X-Tc-lNLido angle. Third, since the E C T model does not include 7t-bonding effects, the existence o f good correlations suggest that the primary influence o f the X group is transmitted to the tris(imido) moiety through the a framework. This is rationalized by the fact that the metal dorbitals in these pseudotetrahedral complexes are monopolized by the strongly 7Cbonding imido ligand. The imido M N a bond is insensitive to changes in the ligand environment (14). Hence, X should have a limited effect on tris(imido) reactivity in a metastable M ( = N R ) X . The X ligand thus quenches the reactivity o f the M ( = N R ) X by engaging the o acceptor orbital o f d ° - M ( = N R ) . Experiments and calculations show the metal-based a acceptor orbital plays a pivotal role in capturing C H bonds prior to scission (11a, 15). 3

+

3

3

a n

3

3

3

The foregoing analysis supports the proposal that it may be possible to design a metastable M ( = N R ) X for hydrocarbon activation by using X as a "place holder" for a methane substrate. Experimental data in support o f this proposal can be found in the work o f Wigley (16) who has shown that C H bonds o f terminal alkynes can be activated by W ( = N A r ) ( P M e ) to yield W ( = N A r ) ( N H R ) ( C = C R ) . It is desirable to find X groups for T c which are weakly bound and can be displaced by methane in either dissociative or associative mechanisms. The E C T analysis allows us to interpret the results o f quantum chemical calculations with these factors in mind. It also provides a valuable tool for predicting systems which have the required electronic and structural characteristics, and hence ligands which engender the desired properties in the resulting organometallic complex. 3

3

3

2


118


Acknowledgments The research by Thomas R . Cundari was supported by the National Science Foundation - CHE-9614346. Literature Cited


1. 2.

3.

4.

5. 6.

7. 8. 9. 10. 11.

12. 13. 14. 15. 16.

Drago, R. S. Applications of Electrostatic-Covalent Models in Chemistry; Surfside Scientific: Gainesville, F L , 1994. a) Drago, R. S. Inorg. Chem. 1990, 29, 1379. b) Drago, R. S.; Vogel, G. C. J. Am. Chem. Soc. 1992, 114, 9527. c) Drago, R. S.; Dadmun, A. P.; Vogel, G. C. Inorg. Chem. 1993, 32, 2473. d) Drago, R. S.; Vogel, G. C. J. Chem. Edu. 1996, 73, 701. a) Drago, R. S.; Ferris, D. C.; Wong, N . J. Am. Chem. Soc. 1990, 112, 8953. b) Drago, R. S.; Wong, N . M . ; Ferris, D. C. J. Am. Chem. Soc. 1991, 113, 1970. a) Drago, R. S. J. Phys. Chem. 1991, 95, 9800. b) Drago, R. S.; Wong, N . M . ; Ferris, D. C. J. Am. Chem. Soc. 1992, 114, 91. c) Drago, R. S. Wong, N . M . Inorg. Chem. 1995, 34, 4004. d) Drago, R. S.; Wong, N . M . J. Chem. Educ. 1996, 73(2), 123. a) Drago, R. S. J. Chem. Soc. Perkin Trans. 2 1992, 1827. b) Drago, R. S. J. Org. Chem. 1992, 57, 6547. a) Drago, R. S.; Hirsch, M . S.; Ferris, D. C.; Chronister, C. W. J. Chem. Soc. Perkin Trans. 2 1994, 219. b) Ferris, D. C.; Drago, R. S. J. Am. Chem. Soc. 1994, 116, 7509. c) Drago, R. S.; Ferris, D. C. J. Phys. Chem. 1995, 99, 6563. d) George, J. E.; Drago, R. S. Inorg. Chem. 1996, 35, 239. Ziegler, T.; Tschinke, V.; Versulius, L . ; Baerends, E . J.; Ravene, W. Polyhedron 1988, 7, 1625. Jurisson, S.; Berning, D.; Jia, W.; Ma, D. Chem. Rev. 1993, 93, 1137. Bunker, B.; Virden, J.; Kuhn, B.; Quinn, R. In Encyclopedia of Energy Technology and the Environment; Wiley: New York, 1995. Benson, M . T.; Bryan, J. C.; Burrell, A. K.; Cundari, T. R. Inorg. Chem. 1995, 34, 2348 and references therein. a) Benson, M . T.; Cundari, T. R.; Moody, E . W. in Aspects of C-H Activation; special issue of J. Organomet. Chem. 1995, 504, 1 b) Wolczanski, P. T. (Cornell Univ.) - personal communication. Anhaus, J. T.; Kee, T. P.; Schofield, M . H . ; Schrock, R. R. J. Am. Chem. Soc. 1990, 112, 1642. Williams, D. S.; Anhaus, J. T.; Schofield, M . H . ; Schrock, R. R.; Davis, W. M . J. Am. Chem. Soc. 1991, 113, 5480. Cundari, T. R. J. Am. Chem. Soc. 1992, 114, 7879. Schaller, C. P.; Cummins, C. C.; Wolczanski, P. T. J. Am. Chem. Soc. 1996, 118, 591. Chao, Y . W.; Rodgers, P. M . ; Wigley, D. E . ; Alexander, S. J.; Rheingold, A. L . J. Am. Chem. Soc. 1991, 113, 6326.


Electrostatic-Covalent Model Parameters for Molecular Modeling

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