A study of lone pair description in molecules by the floating spherical gaussian orbital (FSGO) method. Part 2

Journal of Molecular 0166-1280/93/$06.00

Structure (Theochem), 288 (1993) 29-39 0 1993 - Elsevier Science Publishers B.V. All rights reserved

29

A study of lone pair description in molecules by the floating spherical gaussian orbital (FSGO) method. Part 2 A.H. Pakiari*, F. Mohammadi Chemistry Department,

Khalesifard

College of Sciences, Shiraz University, Shiraz, Iran

(Received 3 August 1992; accepted 12 May 1993) Abstract This research is a continuation of a previously published paper with the aim of studying and finding a general description of lone pair orbitals in molecules. The orbital parameters must be known in advance, and the correct geometry of the molecule (bond angles and bond lengths) is dependent upon the appropriate lone pair description, so the floating spherical gaussian orbital (FSGO) method including optimization has been used to obtain the orbital parameters and nuclear coordinates corresponding to minimum energy. The proposed models for lone pair description have been tested by four molecules: CHz (singlet) and the ground states of NHj, H20, and F2. Five models have been used to obtain simultaneously correct bond lengths and bond angles. The linear combination of single p-type and Is-type orbitals for description of a lone pair can predict only correct bond lengths 2.101 Da for CH2; 1.909 Da for NH3; 1.808 Da for H20; 2.68 1 Da for FZ. The linear combination of double p-type and 2s-type orbitals for describing a lone pair can predict rather satisfactory results for both bond lengths and bond angles: 2.120 Da, 102.255” for CH,; 1.893 Da, 106.744” for NHj; 1.723 Da, 104.315” for H20.

Introduction

In this paper, which is the second part of the study of the description of lone pairs in molecules, we extend the investigation to finding correct geometries (inter-bond angles and bond lengths). In the first part [l], attention was paid to obtaining a proper lone pair description in order to obtain correct inter-bond angles. Molecules such as methylene (singlet), and the ground states of ammonia and water have been selected to test the lone pair description proposed in the present paper; the successful description is then applied to the ground state of the fluorine molecule. In this research, all calculations have been performed through the ab initio approach without any * Corresponding

author.

parameterization. As was mentioned in the first part of this work [l], the SCF procedure is not appropriate for this type of investigation, because the orbital description in the SCF method is not known in advance. Therefore, the floating spherical gaussian orbital (FSGO) method is used in the present research. The effect of a lone pair on both inter-bond angles and inter-atomic distances (bond lengths) is a well-known phenomenon in chemistry. An inadequate lone pair description in an FSGO calculation causes an incorrect geometry. Hence, the calculation of a correct geometry in the FSGO method is the result of a correct description of the lone pair orbital. However, because it may be thought possible to obtain correct bond lengths and bond angles by using an entirely SCF procedure with a large

A.H.

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and F. Mohammadi

basis set, it is necessary to give some comparison with SCF calculations for geometry prediction for these molecules (CH2, NH3, H20, and F2). The SCF calculations for these molecules are too many to present, and most of them have been performed without geometry optimization, (this comparison is presented in Table 6.) The FSGO method, which was introduced by Frost in 1967 [2], is quite ab initio and extensively used in the literature [3]. This method is briefly described here. The spherical gaussian, which is the simplest gaussian function and looks like the simplest orbital (1 s), is used as a constructing function for the basis set, i.e. G;(r’- pi) = (2ai/x)3’4 exp [-(?-

gi)20i]

(1)

where the orbital exponent oi and the component of the orbital center vector di are variational parameters. The gaussians, which represent the orbital description, are positioned in the molecule in the same way as in the Lewis concept of valency. The total electronic energy for the single determinantal wavefunction is obtained by

X [2TklTpq - TkqTipl where T = S’, with S the overlap matrix. total energy is obtained by E = Eel + 5

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perpendicular to the principal axis for more than one lone pair on one atom) on either side of the atomic nucleus containing the lone pair - which looks like a p-type orbital - provided a rather good lone pair description, according to the rather accurately calculated inter-bond angles. These results are summarized in Table 1 for methylene (singlet), and the ground states of the ammonia and water molecules. Despite the correct interbond angles obtained by applying a p-type lone pair description, Table 1 shows that the interatomic distances (bond lengths) still have considerable errors. Therefore, the present paper is a further study in order to find a lone pair description that is also adequate for predicting bond lengths. In this paper, the results of some calculations for methylene (singlet), ammonia, water, and fluorine molecules are presented, which have been selected from 116 calculations (the complete report will be given in Ref. 4). Therefore, the conclusions from the results are not accidental; the selection of our results has been made in such a way as to produce a trend in the calculations. For a better understanding of the outline of this research the discussion is classified under five models (Parts A-E); and the most successful models are applied to the fluorine molecule (Part F).

The

ZiZj/Rij

i
and is also optimized with respect to the nuclear coordinates and the orbital parameters in the molecule. In this paper, a linear combination of gaussians has been used for lone pair description. Results and discussion

First, it is necessary to recollect very briefly the conclusions of Part 1 of this work [l] about lone pair description in molecules. It was shown that the positioning of the positive and negative spherical gaussians along the principal axis (or any bther axis

Part A

The results for water (shown in Part 1 [l]) are by using p-type orbitals for the lone pair description. This orbital is constructed by a linear combination of positive and negative lobes (spherical gaussian) with equal exponents and equally off-center in opposite directions. It follows that the sets of p-type orbitals are identical for lone pairs on the X and Z axes. Here, the position of each set of gaussians with equal exponents (which represents the p-type orbital) for different lone pairs are different and are optimized individually. The coefficients of the linear combination of gaussians for constructing a p-type lone pair orbital on the perpendicular axis to the molecular plane (the X axis) are to be fixed at 1.0 and -1.0 respectively; the

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Table 1 Summary of the best previously publisheda results for the description Quantityb

Methylene Single p

(-) Energy (Da) Error (%) Exp. (Da) Bond length (Da) Error (%) Exp. (Da) Bond angle (deg) Error (%) BXP. (deg)

32.874 -15.5 38.891’ 2.054 -2.2 2.1’ 102.053 -0.34 102.4f

31

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of lone pair orbitals and geometry predictions Ammonia

Double p

Single p

33.147 -14.8 38.891’ 2.135 1.7 2.1f 102.256 -0.14 102.4’

“Ref. 1. b Daltons (Da) or atomic units are defined for distances as r/a0

41.495 -15.5 56.21 Id 1.834 -4.1 1.9139 105.270 1.34 106.7g

(a0

= 4q,h2/m,e2)

Water Double p 47.909 -14.8 56.21 Id 1.872 -2.1 1.9139 107.890 1.11 106.7g and for energies as E/E,,,,,,,

Single p 64.295 -15.5 76.060’ 1.665 -7.9 I.8089 104.150 -0.33 104.5s (the hartree

= h2/&n,j. ’ Ref. 14. dRef. 13. ’ Ref. 12. ‘Ref. 6. gRef. 5.

coefficient for the positive lobe on the principal symmetry axis (the 2 axis) is fixed at 1.0 and the negative coefficient is free to be optimized. Therefore, the following three calculations have been performed for the water molecule: (i) a single p-type orbital for lone pair description, with each lone pair off-center by a different amount on the X and Z axes individually, and also to be optimized; (ii) as (i), but with double p-type orbitals for each lone pair; (iii) as (ii), repeated with optimizing of the position of the K-shell gaussian. The optimized orbital and nuclear parameters, total energies, inter-bond angles and bond lengths for water for the above calculations are shown in Table 2. The results of double p-type orbitals (calculations (ii) and (iii)) show considerable improvement in bond lengths compared to single p-type orbital calculations for water (calculation (i) in Table 2 and others in Table 1). Calculation (iii) shows that the freedom of the K-shell position does not significantly improve the results in calculation (ii).

Part B This study is for using the linear combination of single p-type and Is-type orbitals for lone pair description of the geometries of CH2, NHs, and Hz0 molecules. In all calculations, the p-type orbital is constructed by equal exponents of gaussians (positive and negative lobes), equally off-center in opposite directions on the proper coordinate axis. The different arrangements of lone pairs are outlined in the seven types of calculations listed below. (i) The positions of the K shell and 1s orbitals are identical, and the coefficients of the positive and negative lobes are to be fixed at 1.0 and -1.0 respectively. (ii) The positions of the K shell and 1s orbitals are different, but the coefficients of the positive and negative lobes are the same as calculation (i). (iii) The positions of the K shell and 1s orbitals are identical and free to be optimized, but the coefficient of the positive lobe is to be fixed at 1.0; the coefficient of the negative lobe is free to float.

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A.H. Pakiari and F. Mohammadi KhalesifardlJ. Mol. Struct. (Theochem) 288 (1993) 29-39

Table 2 The results of optimized orbital parameters, nuclear coordinates, total energies, bond lengths and bond angles for Hz0 of Part A calculations (i)-(iii)” Quantityb Inner shell orbital parameters ff

i

ii

111

(Da)

Z

Bonding orbital parameters (Da) a Y Z

17.303029 0.000958

17.098006 0.0

17.155111 0.00140

0.593359 ho.596389 0.496388

0.510755 f0.455021 0.419433

0.511630 ho.457485 0.422375

0.627180 f0.154489 fl.O -

0.488617 f0.396293 fl.O 2.895022 f0.074641 zt1.0

0.491662 ho.393881 fl.O 2.895064 f0.074341 zt1.0

0.627180 ~0.152323 1.0 -0.553187 -

0.488614 *0.123938 1.0 2.326896 2.895022 ~0.125226 1.0 - 1.008969

0.491662 f0.119074 1.0 2.338225 2.895064 ~0.125873 1.0 - 1.009363

fl.285075 1.078645

zt1.363228

f1.359758 1.059199

Lone pair orbital parameters on X-axis (Da) q2

Xl ,2 Cl,2 =3,4 x3,4 c3,4

Lone pair orbital parameters on Z axis (Da) ff1,2 z1,2

Cl c2 a3,4 z3,4 c3 c4

Nuclear coordinatesC for H (Da) Y Z

Total Error Bond Error Bond Error

energy (Da) (%) length (Da) (%) angle (deg) (%)

-64.297 -15.5 1.678 -7.19 100.033 -4.27

1.055946 -65.476 -13.9 1.724 -4.65 104.531 0.03

-65.478 -13.9 1.724 -4.65 104.218 -0.27

a See text. b See footnote b to Table 1. ‘The 0 atom is at the origin.

(iv) The positions of the K shell and 1s orbitals are different and to be optimized individually, but the coefficients are the same as calculation (iii). (v) Calculation (iv) is repeated by fixing the centers of both the K shell and the 1s orbitals on the center of the atom (zero coordinates):

(vi) Calculation (iv) is repeated with the position of the K shell optimized and the center of the 1s orbital fixed at the nuclear coordinates (zero). (vii) Calculation (iv) is repeated with the position of the K shell fixed at zero and the center of the Is-type orbital optimized.

A.H. Pakiari and F. Mohammadi Khalesifard/J. Mol. Struct. (Theochem) 288 (1993) 29-39

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Table 3 The results of optimized orbital and nuclear parameters, total energy, bond length and bond angle for calculation for CH2, NH3 and Ha0 molecules

(ii) of Part Ba

Quantityb

Hz0

-

W

Inner shell orbital parameters (Da) a 2 Bonding orbital parameters (Da) a Y Z X

Y

NH3 9.392413 0.000456

12.917930 0.001641

17.180407 0.0

0.368416 f0.914592 0.74828 1 -

0.406950 0.720981 0.479770 f0.624388 -0.360491

0.468090 f0.610173 0.592943 -

Lone pair orbital parameters on X axis (Da) -

q2

XI ,2 Cl c2

(23 X3 C3

0.968492 f0.183654 +1.0 -1.0

-

Lone pair orbital parameters on Z axis (Da) q2

ZI,2 Cl c2 a3 z3 c3

Nuclear coordinatesC for H (Da) Y z X

Y Total Error Bond Error Bond Error

energy (%) length (Da) (%) Angle (deg) (%)

a See text. b See footnote b to Table 1. ‘The C, N, and 0 atoms are at the origin.

0.082251 ~0.245515 1.0 -1.0 0.325720 -0.298735 0.561389

2.124766 ~0.048620 1.0 -1.0 0.359121 -0.000165 1.213717

0.968492 r0.100516 1.0 -1.0 0.482491 0.103092 1.097343

fl.612056 1.348256 -

1.644304 0.970082 f 1.424009 -0.822152

fl.341629 1.212926 -

-33.018 -15.1 2.101 0.05 100.235 -2.1

-47.92 -14.7 1.909 -0.21 96.472 -9.6

-64.401 -15.3 1.808 0.00 95.817 -8.3

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These calculations generally show small percentage errors for bond length prediction and large percentage errors for inter-bond angle prediction. The improvements in the bond lengths are very significant, particularly in calculation (ii) for all three molecules (minimum error). The results of the optimized orbital parameters and nuclear coordinates, total energy, bond length and bond angles for calculation (ii) (for CH2, NH3 and H20) have been collected in Table 3. The results of other types of calculations are quite good: these calculations have maximum percentage errors in bond lengths of -0.67, -0.42, and -0.99, and in bond angles of 0.59, 9.8, and -9.5, for methylene, ammonia and water respectively. Therefore, this type of calculation can help to predict the correct bond length, but not the inter-bond angle. It is interesting to do more calculations for water with the linear combination of single p-type and Is-type orbitals being used for description of both lone pairs (in the previous calculations the above combination was used only for the lone pair on the principal symmetry axis). Two models have been used: (viii) the exponents and the coefficients of the Is-type orbitals are different and optimized for each lone pair separately; (ix) the exponents and the coefficients of the Is-type orbitals are equal and optimized for both lone pairs. The results of these two calculations are: bond lengths, 1.703 and 1.709 Da with -5.8 and -5.5% error respectively; bond angles are 97.879 and 98.215” with -6.3 and -6.0% error respectively. The improvement of the bond angle predicted by calculations (viii) and (ix) suggests that in each case the description of both lone pairs should be identical. Comparison of calculations (viii) and (ix) shows better results in (ix). Therefore, when the linear combination of single p-type and Is-type orbitals are used for both lone pairs, the exponents and positions of both 1s orbitals are chosen to be . identical.

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Part C

Attention is now paid to a study of the lone pair description and the geometry of the molecules using the linear combination of p-type and 2s-type orbitals. There are two reasons behind this type of calculation. First, after the study described in Part B, it may be thought that modification of the Is-type orbital (namely to a 2s-type orbital) would give better results for both bond lengths and bond angles. Secondly, the contribution of the 2s orbital in lone pair description is according to the proposal by Tan and Linnett [7]. The calculations were performed with the same outline as in part B (seven types of calculations). The results show percentage errors for bond length between 2.4 and 3.2 for methylene, 0.73 and -1.52 for ammonia; the corresponding percentage errors for bond angles are between -4.5 and -8.9 for methylene, and - 12.7 and -13.7 for ammonia. The results for water have percentage errors for bond lengths of -10.90 and -10.95 for calculations (i) and (ii) respectively, with the rest being between -5.3 and -5.9; for bond angles the percentage errors are 1.7 and 7.2 for calculations (i) and (ii) respectively, with the rest being between -5.8 and -7.5. These results show an improvement in the bond length compared to the results of the first part of this work [l] (which are summarized in Table 1) but they are not as good as the results obtained in Part B. The predictions of bond angles are still not good. Therefore, by comparison of the results of Parts B and C, the model used in Part B is seen to be the better procedure for obtaining quite accurate bond lengths with negligible error, and requiring lower computational time. Similar calculations as in Part B calculation (ix) have been performed for water in this section. The linear combination of single p-type and 2s-type orbitals has been used for describing both lone pairs (calculations (i)-(vii) above for water with the same combination have been used only for the lone pair on the principal axis). The results of this calculation are a bond length of 1.799 Da with -0.5% error and a bond angle of 100.421” with

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Table 4 The results of optimized orbital and nuclear parameters, total energy, bond length and bond angle for calculations of Part Ea for CHz, NH,, and Hz0 molecules Quantityb Inner (Y

CHz

shell orbital

parameters

orbital

parameters

Y z X

Y Lone pair

orbital

parameters

9.319006 0.002092

12.908864 0.001587

17.144177 0.001505

0.352966 f0.998644 0.803721 -

0.425340 0.891721 0.348597 ho.772253 -0.445860

0.514755 f0.471387 0.430339 -

q2

XI ,2

(and

-

c2 q4 z3,4 x3,4

-

-1.0 0.811443 0.570507 0.002092 0.822046 70.1777765 0.002092

c3 c4 ff5

ZS X5 C5 06 z6 x6

-

-0.019332

c6

coordinatesC

for

Z X

Y energy (Da) (%) length (Da) (%) angle (deg) (%)

on X axis for

HZO)

(Da)

0.390676 ~0.342654 -

1.0 -54.499150 2.410441 ~0.193702 -

11.779490 - 10.798942 3.716304 0.001587 -1.126163 0.382714 0.001587 -

76.166105

0.494706 kO.153021 1.0 2.739689 2.978163 ~0.147192 1.0 -1.011055 2.309424 0.001505 0.023935 4.611612 0.001505 -0.017973

H (Da)

f 1.653273 1.333949 -

Y

Total Error Bond Error Bond Error

on Z axis

-1.0 2.082987 1.539398 fO.176322

Cl

Nuclear

(Da)

0.212882 f0.440953

q2

Hz0

(Da)

Z

Bonding a

NH,

-33.180 -14.7 2.124 1.14 102.255 -0.14

a See text. b See footnote b to Table 1. ‘The C, N, and 0 atoms are at the origin.

1.755072 0.711844 Zt1.519937 -0.877536 -47.948 -14.7 1.893 -1.04 106.744 0.04

f1.360103 1.057626 -

-65.480 -13.9 1.723 -4.7 104.315 -0.18

0.494706 f0.388693 1.0 -1.0 2.978163 kO.071209 1.0 -1.0 2.309424 0.0 0.023935 4.611612 0.0 -0.017973

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CH2, bond length 2.096Da with -0.2% bond angle 106.053” with 3.6% error; for bond length 1.889 Da with - 1.25% error, angle 119.2” with 11.7% error; for Hz0 length 1.701 Da with -5.9% error, bond 114.584” with 10.6% error. It seems that results are not encouraging for improving metry predictions.

-3.9% error. This calculation gives a significant improvement in both bond length and bond angle. Part D

It is interesting to now improve the p-type orbital in the models used in Parts B and C by employing a double p-type orbital in these models. The study using the linear combination of double p-type and Is-type orbitals is presented in this section (Part D) and that employing double p-type and 2s-type orbitals is considered in the next section (Part E). The results of these calculations are: for

29-39

error, NHJ, bond bond angle these geo-

Part E

The calculations formed by using

in Part E have been perthe linear combination of

Table 5 The results of optimized orbital parameters and nuclear coordinates, total energy and bond length for F2 using various model? Quantityb Inner ff

FA

shell

orbital

parameters

for

two F atoms

Bonding a

orbital

parameters

positioned

pair

orbital

parameters

pair

orbital

parameters

(X and Y axes)

on principal

axis

(Z axis)

0.933173 f 1.349405 ho.852314 1.0 -0.048447

QI,2

ZI z2

Cl c2

-

03

-

z3

-

c3

Nuclear

axis

on both

0.933173 ~0.103666 3~0.198977 fl.O

Cl,2

22.238782 f1.339629

22.226753 f1.339632

0.502057

0.502077

of coordinates

of perpendicular

Xl ,2 Y1,2

Lone

at center

0.782069

q2

FB (ii)

(Da)

22.195977 f1.098716

z

Lone

FB (i)

on both

sides

sides

of F2

1.105341 ~0.141364 f0.151690 lkl.0

1.105352 TO.141354 ho.151690 fl.O

1.105341 fl.644733 fl.038875 1.0 -0.013342 0.464857 f1.339629 0.962287

f1.105352 f1.644787 f1.038883 1.0 -0.057731 0.466455 f1.251130 0.985415

of F2

coordinatesC

Z

f 1.099760 -168.380 -15.3 2.199 -17.9

Total Error Bond Error

energy (Da) (%) length (Da)d (%)

a See b See ‘The d The

text. footnote b to Table 1. . molecule lies along the Z axis. SCF energy is -198.768 Da [15]; the experimental

fl.340484 -168.556 -15.2 2.681 0.04

bond length is 2.68 Da [16].

f1.340495 -168.555 -15.2 2.681 0.04

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double p-type and 2s-type orbitals for lone pair description and geometry prediction. Previous experience [4] shows that good prediction of geometry can be obtained by having identical optimized positions of both the K shell and the 2s orbitals. The results of optimized parameters, total energy, bond length and bond

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angle (for CH2, NH3 and H20) are reported in Table 4. For water, both exponents and coefficients of 2s orbitals of both lone pairs are identical. The calculations in this part demonstrate that quite accurate geometries (negligible error in bond angles and small errors in bond lengths) can be obtained by describing the lone

Table 6 Geometry comparison predicted by the results of this paper and other results, by using single determinant minimal basis set Molecule

Bond length

Type of calculation

Ref.

FSGO (single p + 1s) FSGO (double p + 2s) Exp.

This work This work 17 6

2.101 2.124 2.1 2.1

NH3

FSGO (single p + 1s) FSGO (double p + 2s) Min ST0 3-21G 3-21G STO-3G 4-21G 4-31G GTO Exp.

This work This work 18 19 19 19 19 19 26 5

Hz0

FSGO (single p + Is) FSGO (double p + 2s) GTO Min ST0 Min ST0 Min ST0 ST0 ST0 6-21G 3-21G STO-3G 4-21G 4-31G Exp. FSGO (single p + 1s) 6-21G 3-21G STO-3G 4-31G Exp.

CH2

Error (%)

wavefunction

with a

Bond angle (de)

Error (%)

0.05 1.14 0.00 -

100.235 102.255 105 102.4

-2.11 -0.14 2.54 -

1.909 1.893 2.14 1.986 1.896 1.953 1.890 1.873 1.959 1.913

-0.21 -1.04 11.87 3.82 -0.89 2.09 -1.20 -2.09 2.40 -

96.472 106.744 103.7 112.1 112.4 104.2 112.6 112.6 107 106.7

-9.59 0.04 -2.81 5.06 5.34 -2.34 5.53 5.53 0.28

This work This work 20 21 22 23 24 25 26 19 19 19 19 5

1.808 1.723 1.810 1.890 1.810 1.902 1.810 1.824 1.830 1.828 1.871 1.820 1.796 1.808

0.00

-4.70 0.11 4.53 0.11 5.20 0.11 0.88 1.22 1.11 3.48 0.66 -0.66 -

95.817 104.315 104.4 110 100 98 120 104.5 107.5 107.6 100 108.1 111.2 104.5

8.31 -0.18 -0.10 5.26 -4.31 -6.22 14.83 0.00 2.87 2.97 -4.31 3.44 6.41 -

This work 19 19 19 19 16

2.681 2.657 2.650 2.486 2.671 2.68

0.04 -0.86 -1.12 -7.24 -0.34 -

Pa)

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pair with a linear combination and 2s-type orbitals.

of double p-type

Part F

After the experience of the lone pair description used in Parts A-E above, it is appropriate to apply the successful model to the fluorine molecule Fz. This diatomic molecule, with three lone pair orbitals on each side of the molecule, is one of the most difficult tests for any proposed lone pair description from the point of view of geometry prediction. The FSGO calculation (single gaussian) performed for this molecule by Chu and Frost [9] and repeated by Pakiari and Linnett [lo] shows that this molecule will dissociate. Another FSGO calculation [lo] by the open-shell method and with the orbitals positioning according to double quartet theory [l l] shows that the molecule does not dissociate and the predicted bond length is 2.16 Da with 17.9% error (Exp. 2.68 Da). Two models applying the p-type orbitals are used for the F2 molecule (FA and FB). The p-type orbital used for the lone pair on the principal axis (Z axis) for both models has two lobes which are positioned on both sides of the atoms (inner and outer lobes); the coefficients are free to be optimized (inner lobes) and 1.0 (outer lobes). Table 5 shows the other conditions for the other lone pairs (on the X and Y axes). These models are as follows. In FA the single p-type orbital has been used. In FB calculation (i) the linear combination of single p-type and Is-type orbitals is used. In FB calculation (ii) the same conditions as calculation (i) are used, except than the K shell and Is-type orbitals are optimized separately. The results for the optimized orbital parameters and nuclear coordinates, total energy and bond length with both models FA and FB are collected in Table 5. In both models F2 does not dissociate, and comparison of models FA and FB shows that FB can still predict the correct bond length (2.68 Da) with zero percentage error, as before. However, it is interesting to mention that the calculations show

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that it is unimportant whether the coefficients of the lone pair on the principal axis be 1.0 for the inner lobe and free for the outer lobe, or vice versa, or - 1.Oand free respectively, or vice versa. Finally, it would be a good idea to compare our results with those in the literature obtained by the SCF method with a minimal basis set, from the point of view of geometry prediction. This comparison is shown in Table 6. Table 6 clearly demonstrates our success in predicting rather correct bond angles and bond lengths, which suggests that our proposal for lone pair orbital description may perhaps be valid in connection with geometry prediction. Conclusion The purpose of this series of papers is to find a simple method of describing a lone pair in order to generalize and apply it to a chemical system. In this method the centers of the gaussians which form the linear combination used to represent the lone pair are on the coordinate axis (axial). As has been mentioned before, the non-axial lone pair description similar to Linnett’s model for ammonia and methylene [7,8] is difficult to generalize for systems with more than one lone pair orbital, in which an increase of the number of lone pairs on one atom has serious effects on the bond length. The results show the following conclusions. (1) The single p-type lone pair description can improve a rather correct bond angle but not a bond length. (2) The linear combination of single p-type and Is-type orbitals for lone pair description can predict correct bond lengths. (3) The linear combination of double p-type and 2s-type orbitals for lone pair description (2s-type orbitals are used for all lone pairs) can predict satisfactory results for both bond lengths and bond angles. (4) The identical description of Is-type or 2s-type orbitals (combinations of p-type and Is, or p-type and 2s) for molecules having more than one lone pair on one atom is necessary in order to obtain better geometries.

A.H.

Pakiari

and F. Mohammadi

KhalesifardlJ.

Mol.

Struct.

(Theochem)

References 1 F. Mohammadi Khalesifard and A.H. Pakiari, J. Mol. Struct. (Theochem), 236 (1991) 85. 2 A.A. Frost, J. Chem. Phys., 47 (1967) 3707. 3 A.A. Frost, in H.F. Schaefer III (Ed.), Methods of Electronic Structure Theory, Plenum, New York, 1977, p. 29. 4 F. Mohammadi Khalesifard, Ph.D. Thesis, Shiraz University, in preparation. 5 G. Herzberg, Electronic Spectra of Polyatomic Molecules, Van Nostrand, Princeton, NJ, 1966, p. 585, 609. 6 G. Herzberg and J.W.C. John, Proc. R. Sot. London, Ser. A, 295 (1966) 107. 7 L.P. Tan and J.W. Linnett, J. Chem. Sot., Faraday Trans. 2,72 (1976) 2233. 8 L.P. Tan and J.W. Linnett, J. Chem. Sot., Chem. Commun., (1973) 736. 9 S.Y. Chu and A.A. Frost, J. Chem. Phys., 54 (1971) 764. 10 A.H. Pakiari and J.W. Linnett, Int. J. Quantum Chem., 18 (1980) 661. 11 J.W. Linnett, The Electronic Structure of Molecules, Methuen, London, 1966.

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