nearest neighboring code and hydrogen bond index in labeled hydrogen-filled graph and graph of...

Nearest neighboring code and hydrogen bond index in labeled

hydrogen-filled graph and graph of atomic orbitals:

application to model of normal boiling points of haloalkanes

Andrey Toropova,*, Alla Toropovab

aScientific Research Institute Algorithm-Engineering, F. Khodzhaev Street, 25, 700125 Tashkent, UzbekistanbInstitute of Geology and Geophysics, A. Abdullaev Street, 15, 700125 Tashkent, Uzbekistan

Received 8 May 2004; accepted 1 October 2004

Abstract

Nearest Neighboring Code (NNC) of given vertex in molecular graph is a topological and chemical invariant. Numerical value of the

NNCk of given kth vertex is mathematical function of both number and composition of vertices which are neighbors of the kth vertex in

molecular graph. Hydrogen Bond Index (HBI) is global invariant of a molecular graph. Descriptors calculated with optimal correlation

weights of the NNC and HBI have been studied. The optimal correlation weights have been obtained by Monte Carlo method. This approach

is named as Optimization of Correlation Weights of Local and Global graph Invariants (OCWLI). Two categories of molecular graph have

been used. First category is a Labeled Hydrogen-Filled Graphs (LHFGs). Second category is a Graph of atomic orbitals (GAO). Types of

vertices in the LHFG are chemical elements (i.e. H, C, F, and Cl). Types of vertices in the GAO are atomic orbitals (i.e. 1s1, 1s2, 2s2, 2p2, 2p5,

2p6, 3s2, and 3p5). Comparison of series of models based on extended connectivity, NNC, and HBI in the LHFG and GAO has shown, that

best OCWLI model is one based on optimized correlation weights NNC and HBI in the GAO. Statistical characteristics of this model are the

following: nZ138; r2Z0.9897; sZ7.87 (8C); FZ13094 (Training Set), nZ138; r2Z0.9871; sZ6.94 (8C); FZ10374 (Test Set), nZ276;

r2Z0.9886; sZ7.41 (8C); FZ23863 (all compounds)

q 2004 Elsevier B.V. All rights reserved.

Keywords: QSPR; Haloalkalanes normal boiling points; Graph of Atomic Orbitals

1. Introduction

Halogen-containing organic compounds are an important

class of chemicals, with numerous industrial and laboratory

applications. They are used as solvents, plastics, anesthetics,

foaming agents, refrigerants, and pesticides. A high interest

in predicting physical, chemical, and biological properties

of halogenated compounds is generated by the urgent need

to develop alternatives to chlorofluorocarbons, new com-

pounds with low ozone depletion potential and a low global

warming potential [1].

Quantitative Structure–Property/Activity Relationships

(QSPR/QSAR) are tools of modeling property/activity

0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2004.10.003

* Corresponding author. Address: Sergeli 8-A, Home 4, Room 6, 700085

Tashkent, Uzbekistan. Tel.: C998 71 162 9596; fax: C998 71 162 8772.

E-mail address: [email protected] (A. Toropov).

(biological properties) as defined by mathematical functions

of molecular structure [2–25]. The QSPR can be used to

predict physicochemical properties of halogenated com-

pounds by using theoretical descriptors [24,25]. Optimal

descriptors of Labeled Hydrogen-Filled Graphs (LHFG)

calculated by Optimization of Correlation Weights of Local

Invariants (OCWLI) [2–18] can be used to predict

physicochemical and/or biological properties of haloge-

nated compounds. However, the LHFGs have reflected no

information on structures of atoms. Recently, Graph of

atomic orbitals (GAO) has been suggested [13,15,17]. The

GAO is an attempt to take into account structures of atoms

in QSPR/QSAR analyses. Thus as an interesting alternative

of the LHFG in QSPR/QSAR studies the GAO can be used.

Intermolecular hydrogen bond influences physicochem-

ical and biological properties of substances [19–23]. Hence

development of molecular descriptors reflecting ability of

Journal of Molecular Structure (Theochem) 711 (2004) 173–183

www.elsevier.com/locate/theochem

http://www.elsevier.com/locate/theochem

Table 2

The adjacency matrix, numbering in the LHFG and local invariants under

consideration on fluoroethane

A. Toropov, A. Toropova / Journal of Molecular Structure (Theochem) 711 (2004) 173–183174

substance to formation of hydrogen bond is an important

problem of theoretical chemistry. Aim of the present study

is comparison of optimal descriptors generated by the

OCWLI technique based on the LHFG and GAO in QSPRs

of normal boiling points of 276 haloalkanes taken from

Ref. [25]. As tool of taking into account ability compounds

to formation of hydrogen bond special hydrogen bond

indices are suggested.

C1 H2 H3 H4 C5 F6 H7 H7

C1 O 1 1 1 1 O O O

H2 1 O O O O O O O

H3 1 O O O O O O O

H4 1 O O O O O O O

C5 1 O O O O 1 1 1

F6 O O O O 1 O O O

H7 O O O O 1 O O O

H8 O O O O 1 O O O0ECk 4 1 1 1 4 1 1 11

2. Method

The GAO is constructed on the basis of the LHFG. The

conversion of the LHFG into the GAO replaces each chemical

element by group of atomic orbitals. Table 1 lists such groups

on all chemical elements under consideration. Example

of such conversion of the LHFG adjacency matrix into

GAO adjacency matrix is demonstrated by Tables 2 and 3.

The OCWLI concept is sequence of four steps:
ECk 7 4 4 4 7 4 4 4
2ECk 19 7 7 7 19 7 7 7
(1)
Tabl

Atom

Atom

H

C

F

Cl

NNCk 413 110 110 110 412 110 110 110
Definition of list of all local invariants which takes
place in molecular graphs (i.e. LHFG or GAO) of the

Training Set of haloalkanes under consideration;

(2)
Calculating by Monte Carlo Technique such numerical
values of correlation weights of the local invariants which

produce as large value of correlation coefficient as

possible between the normal boiling points (NBP) of

haloalkanes of Training Set and a descriptor calculated as

DCWðTVk;LIkÞ ZXn

k

CWðTVkÞCXn

k

CWðLIkÞ (1)

where the TVk is type of vertices in molecular graph, i.e.

TVk is representing of chemical elements in the LHFG

(i.e. H, C, F, and Cl) and TVk is representing of atomic

orbitals in the GAO (i.e. 1s1, 1s2, 2s2, 2p2, 2p5, 2p6, 3s2,

and 3p5); LIk is numerical value for given kth vertex of one

of the following local topological invariant types.

– Morgan extended connectivity of mth order [26]

(mZ0,1, and 2). Morgan extended connectivity of

zero order is number of neighboring vertices

connected to given kth vertex; calculating Morgan

extended connectivity of xth order based on

numerical data on (xK1)th order, and this topologi-

cal local invariant on given kth vertex calculated

with recurrent formula

xECk ZX

ðk;jÞ

ðxK1ÞECj (2)

e 1

s o
f the LHFG and their presenting by atomic orbitals in GAO
Group of AO

1s1

1s2 2s2 2p2

1s2 2s2 2p5

1s2 2s2 2p6 3s2 3p5

where summation should be carried out over all

edges (k,j).

– Nearest Neighboring code (NNCk) [11,12]. In the

present study NNCk are defined separately, for case

of the LHFG, this invariant is calculated as

NNCk Z 100Nt C10Nc CNh (3)

where Nt, Nc and Nh are total number of neighbors,

number of neighbors which are carbon atoms, and

number of neighbors which are hydrogen atoms on

given kth vertex in LHFG, respectively; for case of

the GAO this invariant is calculated as

GAONNCk Z 100Nt C10Nð2p2ÞCNð1s1Þ (4)

where Nt, N(2p2) and N(1s1) are total number of

neighbors, number of neighbors which are images of

2p2 atomic orbital, and number of neighbors which

are images of 1s1 atomic orbital on given kth vertex

in GAO, respectively.

CW(LIk) is correlation weight of presence in LHFG

given numerical value of the LIk. Table 2 contains an

example of numerical values of the LIk under consideration

for the LHFG. Table 3 contains examples of numerical

values of the LIk under consideration for the GAO.

(3)
Obtaining by the Least Squares method of NBP model
for haloalkanes of the Training Set as

NBP Z C0 CC1 !DCWðTVk;LIkÞ (5)

(4)
Validation of predictive ability of Eq. (5) with halo-
alkanes of the Test Set.

Table 3

Adjacency matrix and local invariants under consideration on GAO of fluoroethane

C1 H2 H3 H4 C5 F6 H7 H8

1s2 2s2 2p2 1s1 1s1 1s1 1s2 2s2 2p2 1s2 2s2 2p5 1s1 1s1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

C1 1s2 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0

2s2 2 0 0 0 1 1 1 1 1 1 0 0 0 0 0

2p2 3 0 0 0 1 1 1 1 1 1 0 0 0 0 0

H2 1s1 4 1 1 1 0 0 0 0 0 0 0 0 0 0 0

H3 1s1 5 1 1 1 0 0 0 0 0 0 0 0 0 0 0

H4 1s1 6 1 1 1 0 0 0 0 0 0 0 0 0 0 0

C5 1s2 7 1 1 1 0 0 0 0 0 0 1 1 1 1 1

2s2 8 1 1 1 0 0 0 0 0 0 1 1 1 1 1

2p2 9 1 1 1 0 0 0 0 0 0 1 1 1 1 1

F6 1s2 10 0 0 0 0 0 0 1 1 1 0 0 0 0 0

2s2 11 0 0 0 0 0 0 1 1 1 0 0 0 0 0

2p5 12 0 0 0 0 0 0 1 1 1 0 0 0 0 0

H7 1s1 13 0 0 0 0 0 0 1 1 1 0 0 0 0 0

H8 1s1 14 0 0 0 0 0 0 1 1 1 0 0 0 0 00ECk 6 6 6 3 3 3 8 8 8 3 3 3 3 31ECk 33 33 33 18 18 18 33 33 33 24 24 24 24 24

NNCk 613 613 613 310 310 310 812 812 812 310 310 310 310 310

Table 4

Statistical characteristics of model based on DCW(TVk,LIk), without taking into account correlation weights of the HBI

Probe LIs Training Set, nZ138 Test Set, nZ138 All haloalkanes, nZ276

R2 S (8C) F R2 S (8C) F R2 S (8C) F

LHFG OCWLI based on the DCW(Ak,0ECk), number of optimized parameters is 6

1 0EC 0.9558 16.34 2939 0.9373 16.37 2033 0.9465 16.32 4851

2 0.9558 16.34 2939 0.9374 16.36 2037 0.9466 16.32 4855

3 0.9558 16.34 2939 0.9373 16.37 2033 0.9465 16.32 4851


1 1EC 0.9579 15.95 3092 0.9371 15.69 2026 0.9491 15.79 5105

2 0.9579 15.95 3092 0.9369 15.67 2019 0.9491 15.78 5106

3 0.9579 15.96 3092 0.9373 15.68 2032 0.9491 15.78 5111


1 2EC 0.9579 15.95 3093 0.9370 15.67 2024 0.9491 15.78 5108

2 0.9579 15.95 3093 0.9370 15.67 2024 0.9491 15.78 5109

3 0.9579 15.95 3092 0.9369 15.67 2021 0.9491 15.78 5108

LHFG OCWLI based on the DCW(Ak,NNCk), number of optimized parameters is 18

1 NNC 0.9805 10.86 6829 0.9851 7.58 9018 0.9819 9.35 14904

2 0.9805 10.86 6828 0.9851 7.59 9007 0.9819 9.35 14898

3 0.9805 10.86 6828 0.9851 7.60 8990 0.9819 9.35 14885

(continued on next page)

A. Toropov, A. Toropova / Journal of Molecular Structure (Theochem) 711 (2004) 173–183 175

Probe LIs Training Set, nZ138 Test Set, nZ138 All haloalkanes, nZ276

R2 S (8C) F R2 S (8C) F R2 S (8C) F

GAO OCWLI based on the DCW(AOk,0ECk), number of optimized parameters is 17

1 0EC 0.9738 12.58 5053 0.9783 9.93 6130 0.9742 11.31 10345

2 0.9738 12.58 5052 0.9784 9.90 6164 0.9742 11.30 10363

3 0.9738 12.58 5053 0.9783 9.92 6140 0.9742 11.31 10350

GAO OCWLI based on the DCW(AOk,1ECk), number of optimized parameters is 46

1 1EC 0.9829 10.16 7815 0.9713 10.30 4605 0.9784 10.21 12427

2 0.9823 10.33 7555 0.9708 10.43 4520 0.9778 10.36 12078

3 0.9822 10.36 7508 0.9707 10.47 4500 0.9777 10.40 12003

GAO OCWLI based on the DCW(AOk,GAONNCk), number of optimized parameters is 42

1 NNC 0.9841 9.80 8416 0.9854 7.39 9206 0.9845 8.66 17360

2 0.9841 9.80 8416 0.9854 7.39 9165 0.9845 8.66 17351

3 0.9841 9.80 8417 0.9854 7.40 9179 0.9844 8.67 17343

The Ak denotes chemical elements in the LHFG, the AOk denotes atomic orbitals in the GAO.

Table 4 (continued)


In order to define descriptor which is able to reflect

ability of substances to formation of hydrogen bond

descriptor calculated with Eq. (1) may be modified by

adding correlation weights of Hydrogen Bond Index (HBI).

Table 5

Statistical characteristics of model based on DCW(TVk,LIk, HBI), with taking in

Probe LIs Training Set, nZ138 Test Set,

R2 S (8C) F R2

LHFG OCWLI based on the DCW(Ak,0ECk,HBI), number of optimized parameter

1 0EC 0.9672 14.08 4005 0.9427

2 0.9672 14.08 4005 0.9429

3 0.9672 14.08 4005 0.9428


1 1EC 0.9688 13.72 4224 0.9416

2 0.9688 13.72 4224 0.9415

3 0.9688 13.72 4224 0.9413


1 2EC 0.9688 13.71 4230 0.9418

2 0.9688 13.71 4230 0.9419

3 0.9688 13.71 4229 0.9417

LHFG OCWLI based on the DCW(Ak,NNCk,HBI), number of optimized paramete

1 NNC 0.9852 9.45 9049 0.9851

2 0.9852 9.45 9051 0.9852

3 0.9852 9.45 9048 0.9850

GAO OCWLI based on the DCW(AOk,0ECk,

GAOHBI), number of optimized param

1 0EC 0.9801 10.97 6683 0.9789

2 0.9801 10.97 6684 0.9788

3 0.9801 10.97 6683 0.9788

GAO OCWLI based on the DCW(AOk,1ECk,

GAOHBI), number of optimized param

1 1EC 0.9867 8.97 10060 0.9732

2 0.9855 9.35 9250 0.9718

3 0.9860 9.19 9570 0.9727

GAO OCWLI based on the DCW(AOk,GAONNCk,

GAOHBI), number of optimized p

1 NNC 0.9897 7.87 13117 0.9870

2 0.9897 7.87 13117 0.9870

3 0.9897 7.87 13094 0.9871

The Ak denotes chemical elements in the LHFG, the AOk denotes atomic orbital

Such formula is the following

DCWðTVk;LIk;HBIÞ

Z CWðHBIÞCXn

k

CWðTVkÞCXn

k

CWðLIkÞ (6)

to account correlation weights of the HBI

nZ138 All haloalkanes, nZ276

S (8C) F R2 S (8C) F

s is 16

15.40 2238 0.9564 14.726 6005

15.36 2247 0.9565 14.706 6020

15.37 2242 0.9564 14.714 6013

s is 18

14.94 2195 0.9580 14.320 6250

14.96 2189 0.9579 14.328 6242

14.97 2182 0.9579 14.334 6234

s is 22

14.90 2201 0.9581 14.291 6271

14.89 2204 0.9582 14.287 6275

14.92 2196 0.9581 14.302 6261

rs is 28

7.51 8978 0.9850 8.523 17960

7.47 9061 0.9850 8.503 18037

7.50 8951 0.9850 8.517 17967

eters is 27

9.82 6310 0.9784 10.394 12404

9.86 6271 0.9783 10.413 12364

9.87 6268 0.9783 10.417 12358

eters is 56

10.23 4944 0.9812 9.602 14278

10.57 4687 0.9798 9.959 13296

10.38 4842 0.9805 9.787 13758

arameters is 52

6.96 10332 0.9886 7.414 23841

6.95 10320 0.9886 7.412 23842

6.94 10374 0.9886 7.411 23863

s in the GAO.

Table 6

Experimental from Ref [25] and calculated by Eq. (9) values of the haloalkanes normal boiling points on the Training Set

ID Structures DCW NBP (8C) expr. NBP (8C) calc. ExprKcalc.

1 Carbon tetrachloride 12.74 76.70 77.46 K0.76

2 Trichloromethane 11.73 61.20 60.99 0.21

3 Dichloromethane 10.44 39.80 39.96 K0.16

4 Trichlorofluoromethane 9.43 23.70 23.45 0.25

5 Dichlorofluoromethane 8.54 8.90 8.92 K0.02

6 Chlorofluoromethane 7.44 K9.10 K9.01 K0.09

7 Chloromethane 6.51 K24.30 K24.18 K0.12

8 Dichlorodifluoromethane 6.06 K29.80 K31.56 1.76

9 Chlorodifluoromethane 5.49 K40.80 K40.88 0.08

10 Difluoromethane 4.83 K51.70 K51.49 K0.21

11 Fluoromethane 3.22 K78.30 K77.77 K0.53

12 Chlorotrifluoromethane 2.96 K81.30 K82.04 0.74

13 Trifluoromethane 2.97 K82.20 K81.92 K0.28

14 Carbon etrafluoride 0.13 K128.10 K128.12 0.02

15 Hexachloroethane 18.13 184.40 165.23 19.17

16 1,1,2,2-Tetrachloro-1-fluoroethane 14.70 116.60 109.45 7.15

17 1,2-Dichloro-2-fluoroethane 12.21 73.80 68.70 5.10

18 1,1-Dichloro-1-fluoroethane 10.17 32.00 35.55 K3.55

19 2-Chloro-1,1,1-trifluoroethane 8.41 6.90 6.86 0.04

20 2,2-Dichloro-1,1,1,2-tetrafluoroethane 8.70 3.60 11.58 K7.98

21 1,1,2,2-Tetrafluoroethane 6.87 K22.80 K18.27 K4.53

22 Fluoroethane 7.01 K37.80 K16.06 K21.74

23 1,1,1,2,2-Pentafluoroethane 5.45 K48.30 K41.51 K6.79

24 Octachloropropane 24.39 259.00 267.39 K8.39

25 1,1,1,2,2,3,3-Heptachloropropane 22.95 247.00 243.93 3.07

26 1,1,1,2,2,3,3-Heptachloro-3-fluoropropane 22.06 236.80 229.32 7.48

27 1,1,1,2,2,3-Hexachloropropane 21.48 218.00 220.00 K2.00

28 1,1,1,2,2-Pentachloro-3,3-difluoropropane 18.45 175.00 170.47 4.53

29 1,1,3,3-Tetrachloropropane 18.36 161.90 169.07 K7.17

30 1,1,2,3,3-Pentachloro-1,2,3-trifluoropropane 17.44 154.70 154.03 0.67

31 1,1,2,2,3-Pentachloro-1,3,3-triflouropropane 17.26 152.30 151.06 1.24

32 1,1,2,2-Tetrachloro-3,3-difluoropropane 17.36 147.60 152.76 K5.16

33 1,1,2,2-Tetrachloro-1,3,3-trifluoropropane 16.11 134.60 132.39 2.21

34 1,1,3-Trichloro-2,2-difluoropropane 15.76 127.30 126.68 0.62

35 1,1,2-Trichloro-2-fluoropropane 15.05 116.70 115.10 1.60

36 1,1,2-Trichloro-1-fluoropropane 14.92 113.50 112.90 0.60

37 1,1,2,2-Tetrachloro-1,3,3,3-tetrafluropropane 14.97 112.30 113.74 K1.44

38 1,2,2,3-Tetrachloro-1,1,3,3-tetrafluoropropane 14.79 112.20 110.88 1.32

39 1,1,1-Trichloropropane 14.83 108.00 111.50 K3.50

40 1,3-Dichloro-2,2-difluoropropane 14.07 96.70 99.03 K2.33

41 1,2,3-Trichloro-1,1,2,3-tetrafluoropropane 13.66 90.00 92.35 K2.35

42 1,2,3-Trichloro-1,1,3,3-tetrafluoropropane 13.27 88.00 86.06 1.94

43 1-Chloro-3-fluoropropane 12.48 81.00 73.17 7.83

44 2,3,3-Trichloro-1,1,1,2,3-pentafluoropropane 12.69 73.40 76.53 K3.13



47 1-Chloro-2,2-difluoropropane 10.92 55.10 47.67 7.43

48 1-Chloropropane 10.65 46.60 43.27 3.33

49 1,3-Difluoropropane 10.50 41.60 40.88 0.72

50 1,3-Dichloro-1,1,2,2,3,3-hexafluoropropane 10.23 35.70 36.43 K0.73



53 1-Chloro-1,1-difluoropropane 10.03 25.40 33.24 K7.84

54 1,1,1,2,3-Pentafluoropropane 9.22 20.00 20.05 K0.05

55 1,1-Difluoropropane 8.66 7.50 10.85 K3.35

56 2-Chloro-1,1,1,2,3,3,3-heptafluoropropane 7.93 K2.00 K0.97 K1.03

57 2-Fluoropropane 7.96 K9.70 K0.48 K9.22

58 1,1,1-Trifluoropropane 7.74 K12.50 K4.07 K8.43

59 Hexafluoroethane 3.95 K78.20 K65.91 K12.29

60 1-Chloro-1,1,2,2,2-pentafluoroethane 6.24 K38.00 K28.60 K9.40

61 1,1-Dichloro-1,2,2-trifluoroethane 10.20 30.20 35.99 K5.79



Table 6 (continued)


62 1,1,2-Trichloro-1-fluoroethane 13.17 88.50 84.36 4.14

63 1,1,1-Trichloro-2,2-difluoroethane 12.53 73.00 74.07 K1.07

64 1,1,2-Trichloro-1,2,2-trifluoroethane 10.99 47.60 48.90 K1.30

65 1,1,2,2-Tetrachloroethane 15.88 146.30 128.65 17.65

66 1,1,2,2,3-Pentachloropropane 20.33 196.00 201.13 K5.13




70 1,1,1,2,3,3-Hexachloro-3-fluoropropane 20.53 207.00 204.50 2.50

71 1,1,1,3,3,3-Hexachloro-2,2-difluoropropane 19.83 194.20 192.95 1.25


73 1,1,1,2,3,3,3-Heptachloropropane 22.87 249.00 242.58 6.42

74 1,2-Dichloro-1,1,2,3,3-pentafluoropropane 11.36 56.30 54.99 1.31

75 1,1,2-Trichloropropane 15.78 133.00 126.99 6.01


77 1,1,2-Trichloro-1,2-difluoropropane 14.03 97.70 98.46 K0.76


79 2-Chloro-1,1,1,3,3,3-hexafluoropropane 8.69 15.50 11.44 4.06

80 1,3-Dichloropropane 14.46 120.80 105.46 15.34

81 1,2-Dichloro-1-fluoropropane 13.57 93.00 90.89 2.11

82 1,1-Dichloro-1,2,2-trifluoropropane 11.75 60.20 61.23 K1.03



85 1,1,1-Trichloro-3,3,3-trifluoropropane 13.75 95.10 93.81 1.29


87 1,1,2,2-Tetrachloro-1-fluoropropane 16.31 135.00 135.68 K0.68

88 1,1,1,2-Tetrachloro-3,3,3-trifluoropropane 15.78 125.10 127.01 K1.91

89 1,1,2,3-Tetrachloro-1,2,3,3-tetrafluoropropane 14.97 112.50 113.84 K1.34

90 1-Fluoropropane 8.67 K2.30 10.98 K13.28

91 Octafluoropropane 5.65 K38.00 K38.20 0.20

92 1,1,1,3,3,3-Hexafluoropropane 6.66 0.80 K21.76 22.56

93 3-Chloro-1,1,1-trifluoropropane 10.89 45.10 47.28 K2.18

94 2-Chloro-1,1,1-trifluoropropane 10.16 30.00 35.40 K5.40

95 1-Fluorobutane 10.05 32.20 33.58 K1.38

96 2-Fluorobutane 9.35 24.70 22.12 2.58

97 1,1,1,2,2,3,3,4,4-Nonafluorobutane 8.49 14.00 8.17 5.83

98 Decafluorobutane 7.35 K2.00 K10.47 8.47

99 2-Chlorobutane 11.30 68.50 53.99 14.51

100 1-Chloro-1,1-difluorobutane 12.16 55.50 67.91 K12.41

101 1-Chloro-1,1,3,3-tetrafluorobutane 11.76 70.50 61.47 9.03

102 4-Chloro-1,1,1,2,2,3,3,4,4-nonafluorobutane 9.64 30.00 26.84 3.16

103 1,2-Dichlorobutane 15.39 123.50 120.62 2.88

104 1,3-Dichlorobutane 15.39 133.00 120.62 12.38

105 1,3-Dichloro-1,1,3-trifluorobutane 14.05 129.00 98.70 30.30

106 3,4-Dichloro-1,1,1,2,2,3-hexafluorobutane 13.46 72.00 89.17 K17.17

107 2,3-Dichloro-1,1,1,4,4,4-hexafluorobutane 13.44 78.00 88.78 K10.78

108 4,4-Dichloro-1,1,1,2,2,3,3-heptafluorobutane 13.00 76.50 81.62 K5.12

109 4,4-Dichloro-1,1,1,2,2,3,3,4-octofluorobutane 12.10 62.80 67.02 K4.22

110 1,4-Dichloro-1,1,2,2,3,3,4,4-octofluorobutane 11.93 64.00 64.15 K0.15

111 2,2-Dichloro-1,1,1,3,3,4,4,4-octofluorobutane 11.92 64.00 63.97 0.03

112 1,1,1-Trichlorobutane 16.96 133.50 146.16 K12.66


114 4,4,4-Trichloro-1,1,1,2,2,3,3-heptafluorobutane 14.44 96.50 105.10 K8.60

115 1,1,4,4,-Tetrachlorobutane 20.68 200.00 206.94 K6.94

116 1,2,3,4-Tetrachloro-1,1,2,3,4,4-hexafluorobutane 16.49 134.00 138.61 K4.61

117 1-Chloroisobutane 12.02 68.30 65.69 2.61

118 1,1-Chloroisobutane 14.81 105.00 111.16 K6.16

119 1,1-Chloro-1-fluoroisobutane 14.61 107.00 107.91 K0.91

120 1,1,2,3-Tetrachloroisobutane 19.71 191.00 191.15 K0.15

121 1,1,2,3-Tetrachloro-2-chloromethylpropane 22.86 227.00 242.51 K15.51

122 1-Fluoroisobutane 10.04 16.00 33.40 K17.40

123 2-Fluoroisobutane 8.81 12.00 13.37 K1.37

124 1,1,1,3,3,3-Hexafluoroisobutane 9.28 21.50 21.05 0.45



Table 6 (continued)


125 1,1,1,3,3,3-Hexafluoro-2-difluoromethylpropane 9.08 33.00 17.76 15.24

126 1,1,1,3,3,3-Hexafluoro-2-trifluoromethylpropane 7.94 12.00 K0.89 12.89

127 Decafluoroisobutane 7.85 K0.30 K2.37 2.07

128 2,3-Dichloro-1,1,1-trifluoroisobutane 14.10 93.50 99.56 K6.06

129 1,1,2-Trichloroisobutane 16.37 163.00 136.58 26.42

130 2,3,3-Trichloro-1,1,1-trifluoroisobutane 15.79 123.70 127.21 K3.51

131 1,1,1,3,3,3-Hexafluoro-2-trichloromethylpropane 15.03 107.00 114.68 K7.68

132 1,1,1,2-Tetrachloro-3,3,3-trifluoroisobutane 16.95 148.50 146.09 2.41

133 1,1,1,2,3-Pentachloroisobutane 21.19 211.00 215.13 K4.13

134 1-Chloro-1,1,2,2-tetrafluoropropane 9.28 19.90 21.05 K1.15



137 2,2-Difluorobutane 9.23 30.90 20.15 10.75

138 1,2-Difluoroethane 8.37 26.00 6.21 19.79

Here DCW is denoting of the DCW(AOk,GAONNCk,

GAOHBI).

Table 7

Experimental from Ref [25] and calculated by Eq. (9) values of the haloalkanes normal boiling points on the Test Set


1 1,1,1,2,2-Pentachloro-2-fluoroethane 15.79 137.90 127.16 10.74

2 1,1,1,2-Tetrachloro-2-fluoroethane 14.83 117.00 111.42 5.58

3 1,1,2-Trichloroethane 14.19 113.70 101.00 12.70

4 1,1,2-Trichloro-2-fluoroethane 13.67 102.40 92.55 9.85

5 1,1,2,2-Tetrachloro-1,2-difluoroethane 13.46 92.70 89.08 3.62

6 1,1,1-Trichloroethane 12.51 74.00 73.63 0.37

7 1,1,2-Trichloro-1,2-difluoroethane 12.49 72.50 73.35 K0.85

8 1,2-Dichloro-1,2-difluoroethane 11.45 58.50 56.45 2.05

9 1,1-Dichloroethane 11.04 57.20 49.64 7.56

10 1,1,1-Trichloro-2,2,2-trifluoroethane 11.04 45.80 49.66 K3.86


12 2-Chloro-1,1-difluoroethane 9.68 35.10 27.54 7.56


14 1-Chloro-1-fluoroethane 8.82 16.10 13.54 2.56

15 Chloroethane 8.99 12.30 16.23 K3.93

16 1-Chloro-1,1,2-trifluoroethane 8.72 12.00 11.88 0.12

17 1,1,2-Trifluoroethane 7.70 5.00 K4.75 9.75

18 1,2-Dichloro-1,1,2,2-tetrafluoroethane 8.53 3.60 8.72 K5.12

19 1-Chloro-1,1,2,2-tetrafluoroethane 7.74 K12.00 K4.19 K7.81

20 1,1-Difluoroethane 6.53 K25.80 K23.82 K1.98

21 1,1,1,2-Tetrafluoroethane 6.43 K26.10 K25.43 K0.67

22 1,1,1-Trifluoroethane 5.42 K47.30 K41.95 K5.35







29 1,1,2,2-Tetrachloropropane 17.33 153.00 152.32 0.68

30 1,1,1,3-Tetrachloro-2,2-diflouropropane 16.92 151.20 145.56 5.64



33 1,2,3-Trichloro-2-fluoropropane 16.35 130.80 136.26 K5.46








41 1,3,3-Trichloro-1,1,2,2-tetrafluoropropane 13.59 91.80 91.22 0.58



Table 7 (continued)



43 2,3-Dichloro-1,1,2,3-tetrafluoropropane 12.86 89.80 79.44 10.36

44 1,2,3-Trichloro-1,1,2,3,3-pentafluoropropane 12.51 73.70 73.66 0.04


46 1,2-Dichloro-1,1-difluoropropane 12.45 70.00 72.71 K2.71


48 1,1-Dichloro-1-fluoropropane 12.49 66.60 73.42 K6.82

49 1-Chloro-1,2-difluoropropane 11.61 52.90 59.02 K6.12


51 3,3-Dichloro-1,1,1,2,2-pentafluoropropane 11.30 45.50 53.91 K8.41

52 2-Chloropropane 9.92 35.70 31.38 4.32

53 3-Chloro-1,1,1,2,2-pentafluoropropane 9.83 27.60 29.99 K2.39


55 1,1,2,2,3,3-Hexafluoropropane 8.29 10.50 4.86 5.64

56 1,1,1,2,3,3-Hexafluorepropane 8.24 5.00 3.97 1.03

57 1,1,1,2,2,3-Hexafluorepropane 7.85 1.20 K2.31 3.51

58 1,1,1,2,3,3,3-Heptafluoropropane 6.74 K19.00 K20.43 1.43

59 1-Chloro-2-fluoroethane 10.35 53.00 38.51 14.49

60 1-Chloro-1,1-difluoroethane 7.71 K9.80 K4.63 K5.17

61 1,2-Dichloroethane 12.33 83.50 70.80 12.70



64 1,1,2-Trichloro-2,2-difluoroethane 12.24 71.20 69.26 1.94

65 1,1,1,2-Tetrachloroethane 15.50 130.50 122.44 8.06

66 1,1,1,2-Tetrachloro-2,2-difluoroethane 13.33 91.60 86.98 4.62

67 1,1,1,2,2-Pentachloroethane 17.04 161.90 147.52 14.38

68 1,1,2,3,3-Pentachloropropane 20.63 199.00 205.99 K6.99



71 1,1,1,3,3-Pentachloro-2,2,3-trifluoropropane 17.49 153.00 154.87 K1.87






77 1,1,1-Trichloro-2,2-difluoropropane 14.08 102.00 99.31 2.69


79 3-Chloro-1,1,1,3,3-pentafluoropropane 8.95 28.40 15.55 12.85

80 3-Chloro-1,1,1,2,2,3,3-heptafluoropropane 7.94 K2.50 K0.88 K1.62




84 1,2-Dichloro-2-fluoropropane 13.20 88.60 84.90 3.70

85 1,1-Dichloro-2,2-difluoropropane 12.77 79.00 77.87 1.13

86 1,3-Dichlo-1,1-difluoropropane 13.18 80.80 84.60 K3.80



89 1,3-Dichloro-1,1,2,2-tetrafluoropropane 12.12 68.20 67.30 0.90



92 1,1,2-Trichloro-3,3,3-trifluoropropane 14.70 106.80 109.30 K2.50



95 1,1,2,3-Tetrachloropropane 18.93 180.00 178.34 1.66

96 1,1,1,2-Tetrachloro-2-fluoropropane 16.37 139.60 136.54 3.06

97 1,1,1,3-Tetrachloro-3,3-difluoropropane 16.03 132.00 131.12 0.88



100 2,2-Difluoropropane 7.57 -0.50 K6.89 6.39

101 1,1,1,3-Tetrafluoropropane 8.91 29.40 14.99 14.41

102 1,1,1,2,2,3,3-Heptafluoropropane 6.79 -17.00 K19.55 2.55

103 1-Chloro-1-fluoropropane 10.95 48.00 48.20 K0.20

104 2-Chloro-1,1-difluoropropane 11.27 52.00 53.53 K1.53(continued on next page)


Table 7 (continued)


105 1,1,1,2,2,4,4,4-Octafluorobutane 8.00 18.00 0.20 17.80

106 1,1,2,2,3,3,4,4-Octafluorobutane 9.64 43.00 26.81 16.19

107 1-Chlorobutane 12.03 78.50 65.87 12.63

108 1-Chloro-4-fluorobutane 14.14 115.00 100.21 14.79

109 3-Chloro-1,1,1-trifluorobutane 12.49 66.00 73.27 K7.27

110 2-Chloro-1,1,1,4,4,4-hexafluorobutane 11.40 51.00 55.58 K4.58

111 4-Chloro-1,1,1,2,2,3,3-heptafluorobutane 11.18 54.00 51.94 2.06

112 1,1-Dichlorobutane 14.82 115.00 111.34 3.66

113 1,4-Dichlorobutane 16.12 155.00 132.50 22.50

114 1,4-Dichloro-1,1,3-trifluorobutane 15.97 118.50 130.08 K11.58




118 1,1,4-Trichlorobutane 18.63 183.80 173.54 10.26

119 2,2,3-Trichloro-1,1,1,4,4,4-hexafluorobutane 14.96 104.00 113.59 K9.59



122 1,2,4,4-Tetrachloro-1,1,2,3,3,4-hexafluorobutane 16.67 134.00 141.56 K7.56

123 1,1,2,3,4,4-Hexachloro-1,2,3,4-tetrafluorobutane 21.42 208.00 218.98 K10.98

124 2-Chloroisobutane 9.77 50.70 28.91 21.79

125 1-Chloro-1-fluoroisobutane 12.60 82.50 75.06 7.44

126 1,2-Dichloroisobutane 13.85 106.50 95.55 10.95

127 1,3-Dichloroisobutane 16.11 136.00 132.33 3.67

128 1,2,3-Trichloroisobutane 17.67 163.00 157.74 5.26

129 1,2,3-Trichloro-2-chloromethylpropane 21.01 211.00 212.31 K1.31

130 1,1,1,3,3,3-Hexafluoro-2-fluoromethylpropane 10.14 40.00 35.00 5.00

131 3-Chloro-1,1,1,3,3-pentafluoroisobutane 11.57 59.00 58.36 0.64

132 1,1,1,3,3,3-Hexafluoro-2-chloromethylpropane 12.12 58.00 67.29 K9.29

133 2,3-Dichloro-1,1,1,3,3-pentafluoroisobutane 12.15 75.30 67.83 7.47

134 2,3-Dichloro-1,1,1,3,3-pentafluoro-2-trifluoro-

methylpropane

11.09 65.00 50.49 14.51

135 1,2,3-Trichloro-1,1-difluoroisobutan 16.39 132.00 136.88 K4.88

136 2,3-Dichlorobutane 14.66 116.00 108.73 7.27


138 1,4-Difluorobutane 12.16 77.80 67.91 9.89

Here DCW is denoting of the DCW(AOk,GAONNCk,

GAOHBI).


where CW(HBI) is correlation weight of the HBI.

Calculating of the HBI for a LHFG is defined as

HBI Z 5000 CNh K ðNCl CNFÞ (7)

where Nh, NCl, and NF are numbers of hydrogen, chlorine,

and fluorine atoms in given compounds, respectively. 5000

is chosen with the purpose to exclude numerical concur-

rence HBI to values of other local invariants under

consideration. Analogically, calculating the HBI for a

GAO is defined as

GAOHBI Z 5000 CNð1s1ÞK ½Nð3p5ÞCNð2p5Þ� (8)

It is to be noted both invariant types calculated with

Eqs. (7) and (8) are global ones. In other words they are

characteristics of molecular graph in total, whereas

invariant types calculated with Eqs. (2)–(4) are character-

istics of some fragments of the molecular graphs.

3. Results and discussion

Comparison of OCWLI probes based on different

versions of Eqs. (1) and (6) is shown by Tables 4 and 5.

From these results one can see that best model of normal

boiling points of haloalkanes under consideration has been

obtained with the OCWLI based on GAO with taking into

account correlation weights of the GAOHBI (Table 5).

The model is the result of third probe of the GAO

OCWLI with using as local invariant the GAONNC of

Eq. (4). The NBP model calculated as

NBP ZK130:32 C16:306DCWðAOk;GAO NNCk;

GAO HBIÞ

n Z 138; r2 Z 0:9897; s Z 7:87ð8CÞ;

F Z 13094 ðTraining SetÞ n Z 138; r2 Z 0:9871;

s Z 6:94ð8CÞ;F Z 10374 ðTest SetÞ n Z 276; r2 Z 0:9886;

s Z 7:41ð8CÞ;F Z 23863 ðall compoundsÞ ð9Þ

Calculation of the haloalkanes normal boiling points by

means of Eq. (9) is demonstrated in Table 6 (Training Set)

Table 8

Correlation weights obtained in third OCWLI probe with the DCW(AOk,GAONNCk,

GAOHBI)

GAO invariant Correlation weights

Atomic Orbitals, AOk

1s1 0.036

1s2 K0.371

2s2 K0.152

2p2 2.164

2p5 K0.235

2p6 K0.057

3s2 0.689

3p5 0.076GAONNCk

0310 0.460

0603 K0.566

0613 K0.275

0802 K0.028

0803 K0.092

0812 0.116

0822 K0.146

1001 K0.597

1002 0.220

1011 K0.107

1012 0.155

1021 0.010

1031 K0.021

1200 K1.436

1201 K0.379

1202 0.600

1210 K0.477

1211 0.035

1220 K0.341

1221 0.041

1230 K0.039

1400 K1.115

1401 0.019

1410 K0.335

1411 0.153

1420 K0.201

1430 K0.342

1600 K0.703

1601 0.462

1610 K0.134

1620 K0.061

1800 K0.200

1810 0.023

2000 0.284GAOHBI

4990 K0.521

4992 K0.360

4994 K0.199

4996 0.315

4998 0.758

5000 1.044

5002 1.173

5004 1.106

5006 0.571

5008 K0.237

Tab

le9

Cal

cula

tio

no

fth

eD

CW

(AO

k,G

AO

NN

Ck,

GA

OH

BI)

on

GA

Oo

ffl

uoro

eth

ane:

GA

OH

BIZ

50

04,

CW

(50

04

)Z1

.106

,D

CW

(AO

k,G

AO

NN

Ck,

GA

OH

BI)

Z7

.01

12

34

56

78

91

01

11

21

31

4

1s2

1O

OO

11

11

11

OO

OO

O

2s2

2O

OO

11

11

11

OO

OO

O

2p

23

OO

O1

11

11

1O

OO

OO

1s1

41

11

OO

OO

OO

OO

OO

O

1s1

51

11

OO

OO

OO

OO

OO

O

1s1

61

11

OO

OO

OO

OO

OO

O

1s2

71

11

OO

OO

OO

11

11

1

2s2

81

11

OO

OO

OO

11

11

1

2p

29

11

1O

OO

OO

O1

11

11

1s2

10

OO

OO

OO

11

1O

OO

OO

2s2

11

OO

OO

OO

11

1O

OO

OO

2p

51

2O

OO

OO

O1

11

OO

OO

O

1s1

13

OO

OO

OO

11

1O

OO

OO

1s1

14

OO

OO

OO

11

1O

OO

OO

NN

Ck

61

36

13

61

33

10

31

03

10

81

28

12

81

23

10

31

03

10

31

03

10

CW

(AO

k)

K0

.371

K0

.152

2.1

64

0.0

36

0.0

36

0.0

36

K0

.371

K0

.152

2.1

64

K0

.37

1K

0.1

52

K0

.235

0.0

36

0.0

36

CW

(NN

Ck)

K0

.275

K0

.275

K0

.27

50

.460

0.4

60

0.4

60

0.1

16

0.1

16

0.1

16

0.4

60

0.4

60

0.4

60

0.4

60

0.4

60

CW

(AO

k)C

CW

(NN

Ck)

K0

.646

K0

.427

1.8

89

0.4

95

0.4

95

0.4

95

K0

.256

K0

.036

2.2

80

0.0

89

0.3

08

0.2

25

0.4

95

0.4

95


and Table 7 (Test Set). Numerical values of the CWs for

calculation of the DCW(AOk,GAONNCk,

GAOHBI) are listed

in Table 8. Calculation the DCW(AOk,GAONNCk,

GAOHBI)

on fluoroethane is shown in Table 9.


4. Conclusions

Comparison of results from Tables 4 and 5 allows

concluding that by taking into account correlation weights

of the HBI the OCWLI prediction has been improved. Also

one can see, that OCWLI prediction based on the GAO is

better than that prediction based on the LHFG. Finally, one

can see, that using of the NNC gives better OCWLI model

than using of the Morgan extended connectivity.

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