Abbreviations and notations Topological Substituent Descriptors

Issue 1, July-December 2002

ISSN 1583-1078

p. 1-18

Topological Substituent Descriptors

Mircea V. DIUDEA1*, Lorentz JÄNTSCHI2, Ljupčo PEJOV3

1

“Babeş-Bolyai” University Cluj-Napoca, Romania

2

Technical University Cluj-Napoca, Romania

3

“Sv. Kiril i Metodij” University Skopje, Macedonia *corresponding author, diudea@chem.ubbcluj.ro

Abstract

Motivation. Substituted 1,3,5-triazines are known as useful herbicidal substances. In view of reducing the cost of biological screening, computational methods are carried out for evaluating the biological activity of organic compounds. Often a class of bioactives differs only in the substituent attached to a basic skeleton. In such cases substituent descriptors will give the same prospecting results as in case of using the whole molecule description, but with significantly reduced computational time. Such descriptors are useful in describing steric effects involved in chemical reactions.

Method. Molecular topology is the method used for substituent description and multi linear regression analysis as a statistical tool.

Results. Novel topological descriptors, XLDS and Ws, based on the layer matrix of distance sums and walks in molecular graphs, respectively, are proposed for describing the topology of substituents linked on a chemical skeleton. They are tested for modeling the esterification reaction in the class of benzoic acids and herbicidal activity of 2-difluoromethylthio-4,6-bis(monoalkylamino)-1,3,5-triazines.

Conclusions. Ws substituent descriptor, based on walks in graph, satisfactorily describes the steric effect of alkyl substituents behaving in esterification reaction, with good correlations to the Taft and Charton steric parameters, respectively. Modeling the herbicidal activity of the seo of 1,3,5-triazines exceeded the models reported in literature, so far.

Keywords

Steric effect, Substituent descriptors, Molecular topology, Herbicidal activity.

http://lejpt.utcluj.ro

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Topological Substituent Descriptors

Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

Abbreviations and notations

MLR, multi linear regression; SVTI, substituent volume topological index; Es, Taft’s steric parameter; ν, Charton’s steric parameter.

1. Introduction

In the field of chemical reactivity, the first proposal of a substituent steric parameter is due to Taft [1, 2]. He tried to quantify the steric influence of a substituent located on the hydrocarbon part of organic esters in the acid-catalysed hydrolysis of aliphatic carboxylic esters, RCOOR’. His Es steric parameter is defined as:

Es=log(kR/kMe)A

(1)

where log(kR/kMe)A is the ratio of acid-catalysed hydrolysis rate constant of RCOOR’ to that of MeCOOR’. By definition, Es(Me)=0.

The Es parameter has been defined empirically [3]. Taft himself pointed out that Es varies parallel to the atom group radius. Charton also found that Es is linearly dependent on the van der Waals radius of the substituent, thus defining a new steric parameter, ν [4-8].

Murray [9] found correlations between the Taft parameter and the Randić [10] topological index, for a series of substituted alkyls. In this respect, Ivanciuc and Balaban [3] have proposed a topological descriptor, SVTI, which encodes the topological distances (i.e., the number of bonds/edges, Dij, joining the atoms/vertices i and j on the shortest path) in a molecular graph, G.

It is defined on the fragment F (i.e. an alkyl group) attached to the vertex i of G, as:

The summation runs over all NF vertices of F and the distance Dij is limited to 3, in

agreement to the Charton’s conclusion about the limit of the influence of the steric effect beyond the gamma carbon [5-8].

The calculation of SVTI is exemplified for the sec-butyl group (R = H) or higher

homologues (R ≠ H):

2

SVTI(F)=∑Dij;Dij≤3 (2)

j=1

NF

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i

R

SVTI (s-Bu) = 1+ 2 + 2 + 3 = 8

The above authors have tested their descriptors in describing the reaction rates of acid-catalysed hydrolysis of RCOOR' (the Taft's set).

In the present work, two novel descriptors for substituents are proposed. They are now tested in modeling the effector-receptor interaction in the herbicidal activity of 2-difluoromethylthio-4,6-bis(monoalkylamino)-1,3,5-triazines.

2. Substituent Topological Descriptors, XLDS AND Ws

The substituent descriptors XLDS and Ws herein proposed are constructed with the aid Before defining our descriptors, let’s recall some knowledges about the layer matrices [11-17].

A partition G(i) with respect to the vertex i, in a graph, is defined [11, 14, 15] as:

G(i)={G(u)j,j∈[0,ecci]andu∈G(u)j}

of layer matrices.

(3)

where Diu is the topological distance (see above) and ecci is the eccentricity of i (i.e. the largest distance between i and any vertex in G). Figure 1 illustrates the relative partitions for the graph G1.

Let G(u)j be the layer j of the vertices u located at distance j, in the relative partition

G(i):

G(u)j={u:Diu=j}

(4)

The entries in a layer matrix, LM, collect the topological property Pu for all vertices u belonging to the layer G(u)j:

[LM]ij=

u∈G(u)j

∑Pu

(5)

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Topological Substituent Descriptors

Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

j: 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3

521

3G1

4

512

34G1(1,5)

12534G1(2)

43

125G1(3)

1432

5G1(4)

G1(1) = {{1},{2},{3,5},{4}}; G1(3) = {{3},{2,4},{1,5}};

G1(2) = {{2},{1,3,5},{4}}; G1(4) = {{4},{3},{2},{1,5}};

G1(5) = {{5},{2},{1,3},{4}}.

Figure 1. Partitions of G1 with respect to each of its vertices

The matrix LM can be written as:

(6) LM(G) ={[LM]ij;i∈V(G);j∈[0,d(G)]}

where V(G) is the set of vertices in graph and d(G) is the diameter (i.e., the largest distance) of G. The dimensions of such a matrix are N× (d(G)+1).

Figure 2 illustrates the layer matrix of distance sums, LDS [13], the topological property M which collects being the sum of distances joining a vertex i with all the remainder vertices in G. Note that the first column contains just the vertex topological property. (in this case, DSi=∑Dij, marked in the weighted graph, G2{DSi}).

j

159 i \\ j: 0 1 2 3 4 (1) 15 10 24 26 17 (2) 10 39 26 17 0 (3) 9 36 47 0 0 (4) 12 26 24 30 0 (5) 17 12 9 24 30 (6) 15 10 24 26 17 (7) 14 9 22 47 0 LDS(G2) 1510121714 G2Figure 2. Matrix LDS for the graph G2 4Leonardo Electronic Journal of Practices and Technologies

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This matrix and the invariants calculated on (e.g., the well-known Wiener index [18], counting all distances in G) are useful tools in topological description of molecular graphs [13, 14].

Another interesting matrix is the layer matrix of walk degrees [15], LeW. A walk, W, is defined [19] as a continuous sequence of vertices, v1, v2, ..., vm; it is allowed edges and vertices to be revisited.

If the two terminal vertices coincide (v1 = vm ), the walk is called a closed (or self returning) walk, otherwise it is an open walk.

If its vertices are distinct, the walk is called a path. The number e of edges traversed is called the length of walk.

Walks of length e, starting at the vertex i, eW(i), can be counted by summing the entries in the row i of the eth power of the adjacency matrix A (whose nondiagonal entries are 1 if two atoms are adjacent and zero otherwise):

e

W(i)=

j∈V(G)

∑[A]

e

ij

(7)

where eW(i) is called the walk degree (of rank e) of vertex i (or atomic walk count [15, 20] ).

Walk degrees, eW(i), can be also calculated by summing the first neighbours degrees of lower rank, according to an additive algorithm11 illustrated in figures 3 and 4.

Local and global invariants based on walks in graph were considered for correlating with physico-chemical properties [15, 20].

Figure 3 illustrates the layer matrix of walk degrees, LeW, e = 1-4, for G2. Note that the first column in L1W is just the vertex degree or the vertex valency. Note that the matrix LeW was re-invented by Randic in 2001, for e = 1, under the name “valence shells” [21].

The substituent descriptor XLDS is the local “centrocomplexity index”, XLM [14], defined on the LDS matrix:

XLDS(i)=∑[LDS]ij⋅10−zj

j=0

ecci

(8)

where i is the attachment point of the substituent to a given chemical structure (see figure 4)

and z denotes the number of bits of max[LDS]ij in G. Calculation of XLDS is exemplified in figure 4.

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Topological Substituent Descriptors

Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

131

13235

63

4

512126

84

122212

2612

1681325

G2 {1Wi } G2 {2Wi } G2 {3Wi } G2 {4Wi }

i \\ j

L1W L2W L3W L4W

0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4

1 1 3 4 3 1 3 5 9 7 2 5 12 17 14 4 12 22 38 28 8

2 3 5 3 1 0 5 12 7 2 0 12 22 14 4 0 22 50 28 8 0 3 3 6 3 0 0 6 12 8 0 0 12 26 14 0 0 26 50 32 0 0 4 2 4 4 2 0 4 8 8 6 2 8 16 18 10 0 16 34 34 24 0 5 1 2 3 4 2 2 4 6 8 6 4 8 12 18 10 8 16 26 34 24 6 1 3 4 3 1 3 5 9 7 2 5 12 17 14 4 12 22 38 28 8 7 1 3 5 3 0 3 6 9 8 0 6 12 20 14 0 12 26 38 32 0

Figure 3. Layer matrix of walk degrees, LeW for the graph G2(calculated by summing the first neighbor degrees of lower rank)

i122311i

2

354

33

i

3

7

71144

i

1410881212

{1W} {2W} {3W} {DS} (a) Ws (i) = 7+7/2+11/3+8/4 ≈ 16.167;

XLDS(i) = 14·100+10·10-2+8·10-4+8·10-6+12·10-8+12·10-10 = 14.1008081212 ≈ 14.101; (b)

Figure 4. (a) Walk degrees, eW, (calculated by summing the first neighbors degrees of lower rank) and distance sums, DS; (b) Evaluation of Ws and XLDS descriptors

Ws is based on the walks in a connected molecular graph. It is calculated from the layer matrix L3W by:

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ecci

Ws(i)=

∑([L3W]ij/j)

j=1

(9)

where 3W is the walk number, of length 3.

We limited here to elongation 3 by following the Charton’s suggestion about the limit of the influence of steric effect (see above). The calculation of the parameter Ws is exemplified in figure 4.

XLDS descriptor is similar to the SVTI parameter, both of them counting distances The

in the substituent.

Ws describes the branching in the vicinity of the attachment point i.

All these parameters suggest the steric influence of a substituent in the interaction of the skeleton (or a situs of it) with a partner (e.g., a reactant [3, 22] or a biological receptor). They are free of electronic contributions, at least in the variant in which the heteroatom is not considered.

3. Correlating Test

The utility of the substituent descriptors, XLDS and Ws, was proven on a set of thirty

aminoalkyl fragments (table 1) involved in the inhibition of Hill reaction of triazines [23] (figure 5).

In this respect, the fragmental volumes, V, (in cm3/mol) for the considered substituents have been calculated as described below. Other parameter herein considered was the number of atoms different from hydrogen, N.

All these descriptors have been calculated separately for the two sites, A and B (see figure 5).

SCHF2NANNB

Figure 5. Herbicidal bioactive triazines

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Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

Table 1. Topological descriptors and biological activity pI50 for the triazines in figure 5

No A 1 NH22 NH23 NH24 NH25 NHCH36 NHCH37 NHCH38 NHCH39 NHCH310 NHCH311 NHCH312 NHCH313 NHC2H514 NHC2H515 NHC2H516 NHC2H517 NHC2H519 NHC2H520 NHC2H521 NHC2H522 NHC2H523 NHC2H524 NHC3H725 NH-i-C3H727 NH-i-C3H7

B NANBWs, AWs, BNH2NHCH3NHC2H5NHCH3NHC2H5NHC3H7NHC4H9

1 1 1 1 2 1 1 3 1 2 2 5 2 3 5

1 5

XA *XB VA **

VB pI50

1.1 1.1 18.763 18.763 3.821.1 3.23 18.763 32.636 5.201.1 9.06118.763 60.766 5.833.23 3.23 32.636 32.636 6.018.5 1.1 6.44618.763 47.908 5.345

NH-i-C3H71 4 1 13.66

8.5 3.23 6.44632.636 47.908 6.392 4 5 11.753.23 10.07132.636 62.393 6.752 5 5 13.933.23 15.11132.636 76.638 6.74NH-i-C3H72 4 5 13.663.23 9.06132.636 60.766 6.76NH-s-C4H92 5 5 15.163.23 13.09132.636 75.039 6.76NH-t-C4H92 5 5 20.503.23 12.08132.636 74.106 6.78NHC5H11NHC2H5NHC3H7NHC4H9

2 6 5 15.623.23 21.16132.636 88.241 7.123 3 8.5 8.5 6.4466.447.908 47.908 6.823 4 8.5 11.756.44610.07147.908 62.393 6.743 5 8.5 13.936.44615.11147.908 76.638 6.95NH-i-C3H73 4 8.5 13.666.4469.06147.908 60.766 6.NH-i-C4H93 5 8.5 16.166.44614.10147.908 74.497 7.01NH-t-C4H93 5 8.5 20.506.44612.08147.908 74.106 6.97NHC5H11NHC6H13NHC7H15NHC8H17NHC3H7NHC3H7NHC4H9

3 6 8.5 15.626.44621.16147.908 88.241 6.943 7 8.5 17.006.44628.22247.908 102.032 7.213 8 8.5 18.176.44636.29247.908 116.672 7.013 9 8.5 19.186.445.37347.908 128.770 6.814 4 11.7511.7510.07110.07162.393 62.393 6.454 4 13.6611.759.06110.07160.766 62.393 6.754 5 13.6613.939.06115.11160.766 76.638 6.7118 NHC2H5NH-s-C4H93 5 8.5 15.166.44613.09147.908 75.039 6.8726 NH-i-C3H7NH-i-C3H74 4 13.6613.669.0619.06160.766 60.766 6.7528 NH-i-C3H7NH-s-C4H94 5 13.6615.169.06113.09160.766 75.039 6.8829 NH-i-C3H7NH-t-C4H94 5 13.6620.509.06112.08160.766 74.106 6.7030 NH-i-C3H7NHC5H11

4 6 13.6615.629.06121.16160.766 88.241 6.69* The symbol X stands for XLDS (see text); ** Volume, [cm3/mol].

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Table 2. Statistics of multivariable regression (distinct variables on branches A and B)

No.XIbiA r s v(%)F 1 1/N,B-3.7867.5490.870.3114.752117.587 2 1/Ws,B-3.3726.9330.82980.3966.04761.9 3 1/XB-3.806

7.0380.88350.3335.07699.598

4 1/VB-72.2767.7600.750.3134.779115.936

5 1/NA

-1.234 7.8100.95770.2083.175149.557 1/NB

-2.678

6 1/Ws,A-1.335 7.1180.96150.1993.030165.554

1/Ws,B-2.0777 1/XA-1.317 7.2520.96620.1862.8441.755 1/XB

-2.526

8

1/VA-22.9998.0480.94780.2313.519119.237 1/VB-52.514

9 1/Ws,A-1.114 7.6180.97140.1722.619226.162

1/VB-47.19410 1/Ws,A-1.180 7.1590.97290.1672.550239.280 1/XB-2.45811 1/Ws,A-1.120 7.4840.97460.1622.472255.491

1/NB-2.48412

NA-0.385 9.4770.98340.1342.039254.937 1/NA-2.777 1/NB

-2.444

13 Ws,A-0.025 7.3720.96610.1902.903121.327

1/Ws,A-1.594 1/Ws,B-2.05614

XA-0.078 7.8760.98180.1402.132232.401 1/XA-2.047 1/XB

-2.413

15 VA-0.036 10.90.98080.1442.193219.227 1/VA-65.9981/VB-45.367

16

XA-0.155 9.7620.98150.1412.152228.039 1/VA-59.0111/VB-46.244

17

XA-0.154 9.3370.98360.1332.029257.426 1/VA-60.8181/XB-2.399

18

XA-0.153 9.6140.98460.1291.968274.318 1/VA-58.888

1/NB-2.430

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Topological Substituent Descriptors

Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

In table 2 A and bi values are the coefficients of:

Ycalc=a+∑biXi

i

(10)

and leave one out procedure (loo) has the results:

loo(12): r = 0.9768; s = 0.153; v(%) = 2.332;

loo(18): r = 0.9778; s = 0.149; v(%) 2.271. (11)

The inhibitory activities of triazines on Chlorella have been taken from the study of Morita et al [24]. They are expressed as pI50, which represents the negative logarithm of concentration required for 50% inhibition of Hill reaction. The correlating results are listed in table 2.

4. Results and Discussion

=

In single variable regression, the descriptors for the substituents in branch B (table 2) are not satisfactory to model the inhibitory activity of triazines; the correlation coefficient, r, is lower than 0.9 (for those in A, r is still lower) and the coefficient of variance, v, is about 5 %. Note that all these \"steric\" descriptors are taken as reciprocal values, suggesting that the triazine ring fits at the biological receptor as better as the substituent is less sterically involved.

two variables regression, by adding the descriptors for the branch A the correlation In

is improved, as indicates the higher values for r and F (the Fisher ratio) and the drop in the dispersion, s, and v(%) values (entries 5-8, table 2). When the descriptors for the two branches are heterogeneous, the result is still better (entries 9-11).

three variables regression, the correlation is once more improved. Again the In

heterogeneous descriptors model the inhibition reaction better that the homogeneous ones (compare entries 16-18 with 12-15, Table 2).

The best model found (see also entry 18) was:

pI50 = 9.614 – 0.153·XA – 58.888·1/VA – 2.430·1/NB; n = 30; r2 = 0.9694; s = 0.129; v(%) = 1.968; F = 274.3;

(10)

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The cross validation (leave-one-out, “loo”, procedure) test for the equations in entries 12 and 18 are given in the bottom of table 2.

Despite the excellent model offered by equation (10), a brief inspection on the general structure of these triazines showed a rather surprising error: the molecule is symmetric, so that the two branches A and B are interchangeable! In consequence, the two columns of descriptors have no meaning if they are taken as distinct descriptors. Thus, the contribution of the substituents in A and B in modeling the global biological activity must somehow be mixed!

The simple summation (or simple arithmetic mean) of contributions of the two branches, A and B, did not provide satisfactory results. More reliable appeared in other kinds of average: geometric (“geo”) and harmonic (“har”). The best correlating results are included in table 3. The cross validation test, loo, is given for each entry.

From table 3 it appears that, in single variable regression, the descriptor 1/X(LDS)geo provides a rather good (r> 0.95) description of the activity, both in estimation and prediction, \"loo\" (entry 2).

The best prediction is offered by the three variables equation, in entry 6 (r >0.975), all of them as harmonic average of the descriptors of A and B branches:

pI50 = 10.292 – 119.503·1/Vhar – 0.097·Xhar – 0.047·Ws,har; n = 30; r = 0.9807; s = 0.144; v(%) = 2.198; F = 218.158;

(11)

The corresponding arithmetic averaged descriptors used in (11) supplied a correlation of r = 0.955 which is, of course, unsatisfactory.

This equation was chosen for a tempting prediction in the past. The experimental data for the compounds no. 3, 12, 21 and 24 (showing residuals, ycalc-yexp, about two times or larger than the value of standard error of estimate:

s = +0.144; -0.254; +0.236; +0.301 and -0.398, respectively were changed by the values:

5.6209; 6.8778; 6.9073 and 6.8471, respectively calculated by equations:

pI50 = 10.292 – 119.503 1/Vhar – 0.097 Xhar – 0.047 Ws,harn = 26; r = 0.9932; s = 0.086; v(%) = 1.309; F = 530.484

(12)

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Topological Substituent Descriptors

Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

The correlating data, obtained by using the new column of activities, ycor, are included in table 3 as the rows \"ycor\". The improvement in the statistical parameters of the regression equations is obvious for all data of table 3 (where * means \"leave one out\" cross validation procedure; and ** are yi corrected for i = 3, 12, 21 and 24):

Table 3. Statistics of multivariable regression, Ycalc = a + ∑i biXi (averaged variables)

No. Xibia r s v(%)F 1 1/Ws,har

-3.151 7.121 0.95530.2103.204292.215 loo* 0.94670.2293.4

ycor**0.96660.1752.669

398.721 2 1/Xgeo

-3.1 7.253 0.96210.1942.956348.097 loo 0.95580.2093.183 ycor

0.97930.1382.108655.776 3 1/Vhar

-126.80011.0910.97630.1562.387275.063 Nhar -0.541 loo 0.97210.1672.543 ycor

0.99240.0861.307875.466 4 1/Vhar

-113.34010.0100.97770.1522.318292.278 Xhar -0.137

loo 0.97350.1632.480 ycor

0.99070.0951.446

713.286 5 1/Nhar

-5.614 9.4910.97980.1472.247208.342 Xhar -0.056 Ws,har-0.057

loo 0.97420.1602.446 ycor

0.99180.0911.380

523.336 6 1/Vhar

-119.50310.2920.98070.1442.198

218.158 Xhar -0.097

Ws,har-0.047

loo 0.97520.1572.397 ycor0.99380.0791.204

690.328 7 1/Vhar

-105.1319.0580.98240.1412.144172.608 Xhar -0.232 Ws,har -0.081 Nhar0.673

loo 0.97420.1602.444 ycor

0.99380.0801.226

499.253 8 1/Nhar

-4.724 7.8580.98250.1402.139173.400 Xhar -0.228 Ws,har -0.070 Vhar0.052

loo 0.97510.1572.401

ycor

0.99240.01.358

405.773

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More over, among the 24 descriptors (N, V, Ws, XLDS , 1/N, 1/V, 1/Ws, 1/XLDS, taken as \"ari\improvement of the statistics was recorded. Again the equation in entry 6 was the best model. This test suggested that the experimental data for the compounds, above mentioned, are \"in error\".

From eq 11 and table 3, it comes out that the inhibitory activity of triazines is controlled by the possibility of the triazine ring (i.e., the pharmacophor) to accommodate at the receptor situs.

This opinion is supported by the reciprocal values and the negative regression coefficient, and negative partial correlation index of these \"steric\" descriptors involved in an eq. of type 11. It suggests that the triazine ring fits at the biological receptor as better as the substituent is less sterically involved.

A plot of the observed vs. calculated (by eq 11) pI50 values is given in figure 6. For comparison, the plot for the same descriptors and “ycor” is given in Figure 7.

7.576.56pI505.554.543.53345y calc678y = 0.9999x + 0.0009R2 = 0.9618

Figure 6. Plot of experimental biological activity (VAR1) vs. ycalc. (cf. eq 11) values

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Topological Substituent Descriptors

Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

7.576.56pI50 cor5.554.543.53345y calc678y = 0.9746x + 0.1709R2 = 0.9863

4. Computation of Fragmental Volumes

Figure 7. Plot of experimental biological activity (VAR1) vs. ycor values

The geometries of the hydrocarbon fragments (in fact, the corresponding radicals)

were fully optimized at the Unrestricted Hartree-Fock (UHF) level of theory, using the 6-31G** basis set (of DZP quality), which contains a single set of d polarization functions on carbons, and a single set of p polarization functions on hydrogens for better description of the radical wavefunctions.

The Berny's optimization algorithm was used (the energy derivatives with respect to nuclear coordinates were computed analytically [25]), along with the initial guess of the second derivative matrix.

Standard harmonic vibrational analysis was applied to test the character of the optimized geometries (stationary points at the potential energy hypersurfaces - PES). All stationary points corresponded to real minima on the explored PES.

Molecular volume calculations were performed for the optimized structures, by the Monte-Carlo method. Since Monte-Carlo method for calculating molecular volume (defined

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as the volume inside a contour of 0.001 electrons/Bohr3 density) is stochastically based algorithm, it often leads to results accurate up to several percents.

Therefore, 11 volume calculations per fragment were performed for each fragment, and the arithmetic average value was taken as the closest approximation to the real one (at the level of theory employed).

In order to increase the density of points for a more accurate integration, the \"Tight\" option of the Gaussian \"Volume\" keyword was used. All calculations were performed with Gaussian 94 suite of programs [26].

5. Conclusions

The Ws descriptor, based on the walks in graph, satisfactorily describes the steric effect of alkyl substituents in the esterification reaction.

It is a pure steric parameter, not affected by the electronic effects. Ws correlate well to the fragmental volumes (over 0.92) and show a lower degeneracy in comparison to the SVTI,

ν and Nc parameters.

It is also well correlated18 to the Taft, Es, (0.9637), and Charton, ν, (0.9587), parameters, which makes from Ws a promising alternative in describing the steric effect of alkyl substituents.

6. Acknowledgment

The work was supported in part by the Romanian GRANT CNCSIS 2002.

References

[1] R. W. Taft, Linear free energy relationships from rates of esterification and

hydrolysis of aliphatic and ortho-substituted benzoate esters. J. Am. Chem. Soc. 1952, 74, 2729-2732.

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Topological Substituent Descriptors

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Topological Substituent Descriptors

Mircea V. DIUDEA, Lorentz JÄNTSCHI, Ljupčo PEJOV

Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, C. Y. Peng, P. Y. Ayala, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez, and J. A. Pople, Gaussian 94 (Revision B.3), Gaussian, Inc., Pittsburgh PA, 1995.

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