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Quantum Chemical Studies on C4H4N2 Isomeric Molecular Species

November 2021
Journal of the Nigerian Society of Physical Sciences 3(4):429-445

DOI:10.46481/jnsps.2021.282

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CC BY 4.0

Authors:

Emmanuel Etim

Federal University Wukari

Onos Godwin

Delta State University

Quantum chemical calculations have been carried out on C4H4N2 isomeric molecular species using the G4 method and compared with experimental values were available, probing parameters like thermochemistry, structural parameters (e.g. Bond length, bond angles), rotational constants, vibrational spectroscopy and dipole moments. Pyrimidine was discovered to be the most stable of all the isomers with \DeltafH0 =37.1 kcal/mol. A critical analysis showed high correlation and consistency between the computed and experimental values of all the parameters under study and therefore providing the needed rationale to validate the values provided for the isomers which do not have available experimental data.

Optimized geometry of pyrimidine

…

Bond Distances/ Angles of Pyrimidine and its Isomers

…

Figures - available via license: Creative Commons Attribution 4.0 International

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Available via license: CC BY 4.0

Content may be subject to copyright.

J. Nig. Soc. Phys. Sci. 3 (2022) 429–445

Journal of the

Nigerian Society

of Physical

Sciences

Quantum Chemical Studies on C4H4N2Isomeric Molecular

Species

E. E. Etima,∗, M. E. Khanb, O. E. Godwina, G. O. Ogofothab

aDepartment of Chemical Science, Federal University Wukari, Nigeria

bDepartment of Chemistry, Federal University Lokoja, Kogi State, Nigeria

Abstract

Quantum chemical calculations have been carried out on C4H4N2isomeric molecular species using the G4 method and compared with experimen-

tal values where available, probing parameters like thermochemistry, structural parameters (e.g. bond length, bond angles), rotational constants,

vibrational spectroscopy and dipole moments. Pyrimidine was found to be the most stable of all the isomers with ∆fH0=37.1 kcal/mol. A critical

analysis showed high correlation and consistency between the computed and experimental values of all the parameters under study and therefore

providing the needed rationale to validate the values provided for the isomers which do not have available experimental data.

DOI:10.46481/jnsps.2021.282

Keywords: Isomers, Pyrimidine, Experimental, Computational

Article History :

Received: 30 June 2021

Received in revised form: 16 August 2021

Accepted for publication: 07 September 2021

Published: 29 November 2021

Communicated by: B. J. Falaye

1. Introduction

Quantum Chemistry is an area of computational chemistry

which could reproduce experimental chemical phenomena math-

ematically, this branch of study avails one the opportunity to

understand the electronic structures and model the nature of in-

teractions molecules undergo not just for stable molecules as

usually provided by experimental procedures but also for the

short-lived intermediates or unstable analogues [1- 4]. It has

been applied in diﬀerent ﬁelds in chemistry where researchers

have been able to make accurate predictions of future reactions

[5, 6], physicochemical properties, docking, rate constants, pro-

tein calculations, calculations of potential energy surfaces, elec-

tronic structures of molecules and their isomers, molecules in

the interstellar medium (ISM) [7].

∗Corresponding author tel. no:

Email address: emmaetim@gmail.com (E. E. Etim )

C4H4N2has many isomeric species of wide spread relevance.

Pyrazines (C4H4N2) also known as 1,4-Diazines are hetero-

cyclic aromatic organic compounds commonly distributed in

nature such as in bacteria, fungi, insects and plants e.g. pota-

toes, coﬀee, nuts. They are responsible for the nutty and roasty

smell which is reminiscent of cocoa and coﬀee. These com-

pounds are used to improve aroma/ﬂavor in food and cosmetic

industries [8 – 11]. Nucleotides (such as cytosine, thymine), vi-

tamin such as thiamine (i.e. vitamin B1), HIV drug Zidovudine

and synthetic compounds like barbitutrates all contain the iso-

mer pyrimidine [12]. The isomer pyridazine ﬁnds applications

as herbicides (such as pyridafol, pyridate, credazine), as drugs

such as minaprine, cadralazine, cefozopran[13].

It has been cumbersome studying certain molecules whose iso-

mers or themselves are unstable molecules such as the present

case. This challenge may be overcome to a certain level by the

application of computational approach which has been shown

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Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 430

Table 1: Standard enthalpy of formation of C4H4N2isomeric species

Molecules ∆fH0(kcal/mol)

1,2-diisocyanoethane 92.4

1,3-butadiene-1,4-diimine 88.0

4-amino-2-butynenitrile 83.0

Iminopyrrole 62.3

2-methylene-2H-imidazole 60.1

Pyridazine 59.0

1,1-dicyanoethane 54.7

Pyrazine 41.0

Pyrimidine 37.1

to be a relative good substitute for experimental approach. Thus,

the present study aims at using computational methods to in-

vestigate the isomers of the C4H4N2group by predicting the

standard enthalpy of formation, bond length and angles, dipole

moment, vibrational frequencies, rotational constants etc., and

comparing their results with the available experimental values

where available.

2. Computational Methods

GAUSSIAN 09 suite of program was employed in perform-

ing all the quantum chemical calculations reported in this study.

The eﬀectiveness of the G4 composite method has been re-

ported in many literatures [14-16] in addition to experience

from our previous studies [17- 23]; as such the molecule un-

der study was optimized using the G4 level of theory.

3. Result and Discussion

The possible isomers of the C4H4N2isomeric group in-

clude; 1,2-diisocyanoethane, 1,3-butadiene-1,4-diimine, 4-amino-

2-butynenitrile, iminopyrrole, 2-methylene-2H-imidazole, pyri-

dazine, 1,1-dicyanoethane, pyrazine, pyrimidine. The results of

the quantum chemical calculations carried out on the C4H4N2

isomeric species using the G4 level of theory are presented and

discussed below under the diﬀerent subheadings:

3.1. Thermochemistry

The focal point of thermochemistry is energy changes such as

enthalpy of formation and many other energy related parame-

ters. Fig 1 shows the optimized geometries of the C4H4N2iso-

meric molecular species while the standard enthalpies of forma-

tion (∆fHO) computed for these isomeric species are presented

in Table 1. Pyrimidine has the least enthalpy of formation of

37.1 Kcal/mol which corresponds to the most stable of all the

isomers, 1,2-diisocyanoethane is shown to be the least stable of

all the isomers of the C4H4N2isomeric group having the value

of 92.4 Kcal/mol as the heat of formation. The experimentally

reported standard heat of formation of pyrimidine ranges from

46.1±0.5 to 47.75±0.4 [24-26], the disparity between the com-

puted and experimental values point towards the possibility of

an error in the experimentally reported value as Weisenburger

and co-workers [27]. According to them, experimental mea-

surement of heat of formation is always inaccurate and imprac-

tical. From previous studies, the G4 method has proven to be

eﬀective in predicting the enthalpy of formation that is in good

accuracy with experimental results [14-23]. Standard enthalpy

of formation is an important parameter that can be applied for

safe and scaling up of chemical processes involving thermal sta-

bility. It helps researchers in predicting the spontaneity of a re-

action, know whether a reaction can be favourable or not and

the reactants and products quantities [27].

3.2. Vibrational Spectroscopy

Table 2 depicts the vibrational frequencies of pyrimidine (the

most stable isomer of the C4H4N2isomeric group) with the cor-

responding spectrum in Figure 2. The vibrational frequencies

and the corresponding spectra for other isomers of the C4H4N2

isomeric group are presented in the appendix (Tables A1-A3

and Figure A respectively). Table 1 contains the calculated and

experimental values of the vibrational frequencies of pyrimi-

dine. The error between the values ranges between 0.3-4 cm−1.

The computed values are in excellent agreement with the re-

ported experimental values. Thus, for the other isomers with

no experimentally measured vibrational frequencies, the val-

ues computed at the G4 level (presented in the appendix) are

believed to be accurate. The G4 composite method has also

been reported to give accurate predictions for vibrational spec-

troscopic parameters for other molecular species with experi-

mentally known values [14-23]. Among other applications, the

vibrational spectroscopy parameters are useful in the chemical

examination of the interstellar medium especially for the astro-

nomical observation of interstellar molecular species with no

dipole moment [17,20].

3.3. Rotational Constants

Rotational spectroscopy remains the most important spectro-

scopic technique employed in the astronomical observation of

molecular species from diﬀerent regions of the interstellar medium.

The experimentally measured rotational constants (from the NIST

Webbook) for pyrimidine and the values obtained at the G4

level are presented in Table 3 below. As shown in the Table,

there is a good agreement between the experimental and the

computed values of the rotational constant of pyrimidine. The

Table also contains the rotational constants calculated for other

isomers of the C4H4N2isomeric group at the G4 level of theory

with no experimentally measured values. Analysis of the dif-

ference showed errors of 0.0261635, 0.0330026 and 0.0156889

GHz for the A, B and C rotational constants of pyrimidine re-

spectively. This level of accuracy suggests a good level of ac-

curacy for the rotational constants obtained for other isomers at

the G4 level with no experimentally measured values.

3.4. Structural Parameters

The bond lengths and bond angles of Pyrimidine are pre-

sented in Table 4 while Fig. 3 depicts the optimized geom-

etry. As shown in the Table, there is an excellent agreement

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Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 431

1,2-diisocyanoethane 1,3-butadiene-1,4-diimine 4-amino-2-butynenitrile

Iminopyrrole 2-methylene-2H-imidazole Pyridazine

1,1-dicyanoethane Pyrazine Pyrimidine

Figure 1: Optimized geometry of C4H4N2isomeric groups

Figure 2: Calculated IR frequencies of pyrimidine

between the experimentally measured values and the computa-

tionally predicted values. For example, both the experimental

(1.087Å) and the computational (1.087Å) values for rCH bond

length. For the other bond lengths reported for pyrimidine, the

diﬀerence between the experimental and the computational val-

ues range 0.36-0.46 Å while for the predicted bond angles, the

diﬀerence between the experimental and the computational val-

ues range from 0.19-1.10 degrees. These ﬁndings suggest that

431

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 432

Table 2: Vibrational frequencies of pyrimidine

Calculated Frequency (cm−1) ExperimentalFrequency (cm−1) Error(cm−1)

353 347 1.69

411 398 2.9

632 621 1.58

693 679 1.45

744 719 3.36

835 804 3.59

988 960 2.74

1009 969 3.96

1011 980 2.97

1030 1033 -0.29

1083 1065 1.01

1095 1155 2.7

1165 1158 0.85

1227 1224 5.6

1260 1356 2.78

1395 1224 2.79

1439 1356 1.95

1496 1411 2.07

1610 1465 2.55

1612 1569 2.48

3154 1572 3.36

3157 3047 3.39

3165 3053 3.51

3207 3082 3.89

Table 3: Rotational Constant of C4H4N2isomers

Molecules Rotation constants (GHz)

A B C

Pyrimidine Calculated 6.3010414 6.0983826 3.0990279

Experimental 6.2748779 6.06538 3.083339

Error 0.0261635 0.0330026 0.0156889

1,2-

diisocyanoethane

Calculated 7.4362588 2.5722569 2.0604923

1,3-

butadiene-

1,4-diimine

Calculated 23.1647044 1.3418215 1.2867453

4-amino-2-

butynenitrile

Calculated 23.0996150 1.3419073 1.2868109

Iminopyrrole Calculated 8.5048965 4.1234186 2.7770331

2-methylene-

2H-imidazole

Calculated 8.7736412 4.2378633 2.8575861

Pyridazine Calculated 6.4337599 5.9503379 3.0913068

Pyrazine Calculated 6.4337599 5.9503379 3.0913068

the bond lengths and bond angles predicted with the G4 method

for the other isomers of the C4H4N2isomeric group presented

in the appendix (Tables A4-A6) with no experimental values

will have a good level of accuracy and can be used when re-

quired.

3.5. Dipole Moments

Dipole moment is useful in determining the polar nature of the

chemical bond. It is also useful in astrophysics and related ar-

eas such as astrochemistry and astrobiology as the dipole of

a molecule plays an important role in the astronomical obser-

vation of such molecule [2]. The dipole moments obtained at

the G4 level for all the isomeric molecular species in this study

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Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 433

Table 4: Bond Distances/Angles of Pyrimidine and its Isomers

Description Calculated

Value (Å)

Exp.

Value (Å)

Error Connectivity

Atom 1 Atom 2 Atom 3

rCH 1.087 1.087 0 4 4 -

rCH 1.079 1.083 0.36 3 3 -

rCH 1.082 1.087 0.46 2 2 -

rCC 1.393 1.389 0.29 3 2 -

rCN 1.328 1.334 0.45 1 1 -

aCCC 117.8 116.5 1.10 4 3 2

aHCC 120.90 121.13 0.19 2 2 3

aCCN 121.20 122.37 0.97 3 4 2

Table 5: Dipole Moment of C4H4N2isomers

Molecule Calculated Dipole

moment (Debye)

Experimental Dipole

moment (Debye)

1,2-diisocyanoethane 5.1506 -

1,3-butadiene-1,4-

diimine

3.6290 -

4-amino-2-butynenitrile 3.7238 -

Iminopyrrole 3.2055 -

2-methylene-2H-

imidazole

1.0758 -

Pyridazine 4.5926 -

1,1-dicyanoethane 4.5904 -

Pyrazine 0.0000 -

Pyrimidine 2.4133 2.33

Figure 3: Optimized geometry of pyrimidine

are presented in Table 5. The experimental dipole moment of

2.33D [29] reported for pyrimidine is in good agreement with

the value (2.41D) calculated at the G4 level. There are no exper-

imentally reported dipole moments values for the other isomers

of the pyrimidine isomeric group. However, the good agree-

ment between the experinmentally measured and the compu-

tationally calculated values for pyrimidine suggest a good ac-

curacy for the dipole moments predicted for those molecular

species with no experimental values.

4. Conclusion

The Gaussian G4 compound model has been applied in com-

puting some quantum chemical properties for the C4H4N2isomeric

molecular species. Spectroscopic parameters (rotational and

vibrational), bond distances, bond angles and dipole moments

have been calculated for all the isomeric molecular species con-

sidered in this study. The results show a good agreement be-

tween the values obtained with the G4 method and the available

experimentally measured values. This good agreement suggests

a good accuracy for those the computationally predicted values

with no experimental values. Thus, the predicted values at the

G4 level of theory could serve as useful data where there are no

experimental values.

Acknowledgments

The authors will like to appreciate the handling editor and

the anonymous reviewers for their advice to make this work a

success.

Appendix

Figure A: IR spectra of C4H4N2isomeric species.

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Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 434

Table A1: IR Frequencies and Intensities of C4H4N2isomers

Pyrazine 1,1-dicyanoethane Pyridazine

Frequency

(cm−1)

IR Intensi-

ties

Frequency

(cm−1)

IR Intensi-

ties

Frequency

(cm−1)

IR Intensities

350.2454 0 142.6498 10.3325 377.4241 8.4376

436.8441 20.8309 212.9721 0.0061 378.1465 0

609.3268 0 217.325 10.417 629.7531 0.1251

718.6392 0 232.5641 0.1562 678.7734 3.7111

784.4478 0 390.8231 0.6653 773.826 26.977

813.6882 16.8768 501.3777 0.5045 784.7741 0

954.5671 0 577.079 2.0394 955.9237 0

995.7849 0 591.9736 0.0401 988.5043 0.0273

1004.4743 0 789.326 0.9436 1015.5701 6.7412

1032.2801 41.3863 924.1966 0.5222 1025.6928 0

1043.5004 0 1024.5549 3.0293 1057.3562 1.8513

1091.2542 11.3623 1077.6373 1.9773 1085.4055 1.9376

1168.3175 3.0353 1137.7852 11.4915 1094.3822 10.9875

1234.2883 3.3451 1293.1894 0.2956 1172.7042 0

1257.5615 0 1325.8192 10.5516 1198.4094 0.0296

1377.4992 0 1412.7563 0.8374 1315.9121 2.7813

1443.5577 32.5811 1489.6743 7.1366 1438.4468 17.1702

1516.3516 1.6121 1495.8979 2.9216 1480.3479 1.0699

1581.3618 0 2369.8219 1.4472 1604.0217 4.1776

1617.6288 0 2375.5886 1.0261 1608.3885 6.5778

3154.1328 0 3040.9897 0.0176 3171.291 11.3104

3154.5805 6.8491 3064.7956 7.0787 3175.4201 0.6737

3170.0288 69.5698 3150.5629 6.2676 3191.228 18.3941

3176.6122 0 3154.8613 4.5128 3205.5438 8.2119

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Table A2: IR Frequencies and Intensities of C4H4N2isomers

2-methylene-2H-

imidazole

Iminopyrrole 4-amino-2-butynenitrile

Frequency

(cm−1)

IR Intensi-

ties

Frequency

(cm−1)

IR Intensi-

ties

Frequency

(cm−1)

IR Intensi-

ties

231.2641 16.2028 222.6459 1.5177 102.9298 3.212

367.2831 5.0478 437.8852 15.624 136.5392 6.7159

545.8568 0 513.7051 0.5416 249.5854 0.2682

729.7105 0.9392 673.5182 13.329 273.9337 21.0114

757.4695 6.9218 709.63 1.5332 384.9431 30.924

778.714 0.0001 821.884 0.5162 500.8402 11.2464

893.0866 0.2762 839.2175 34.5306 575.9942 2.9544

912.9179 8.5062 878.6648 11.3524 582.7078 1.7895

915.8468 10.8072 926.5924 10.2062 699.5133 11.1841

954.3095 42.6853 967.2053 5.8961 889.2243 0.0003

961.4052 0.0001 969.8546 11.5774 895.8998 201.8104

979.8251 16.2158 993.4477 44.2831 1098.3395 26.2627

991.4666 31.7917 1058.7038 51.7342 1148.1344 4.2125

1202.2146 17.8701 1093.3592 5.4566 1183.4347 0.2291

1303.1681 6.2567 1280.4929 34.9662 1356.3555 33.0669

1346.2606 21.0282 1341.6019 75.8567 1383.0345 0.0121

1412.9732 17.8688 1353.3948 11.9765 1459.7535 5.1009

1496.1998 11.0291 1548.0035 19.6616 1669.8384 18.9874

1613.199 2.8089 1646.7243 11.3723 2258.8654 0.001

1714.8692 3.0856 1740.6104 20.5283 2396.7797 101.4735

3180.8768 0.0002 3175.7293 18.3444 3036.9215 13.0137

3196.1465 6.9809 3234.5262 3.2481 3070.8682 4.6604

3211.1464 15.5153 3266.179 1.1482 3496.6081 1.6966

3283.7487 0.0178 3434.2972 4.1245 3574.5662 3.4152

435

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 436

Table A3: IR Frequencies and Intensities of C4H4N2isomers

1,3-butadiene-

1,4-diimine

1,2-diisocyanoethane

Frequency

(cm−1)

IR Intensities Frequency

(cm−1)

IR Intensities

83.6289 4.2328 78.7298 4.2564

127.629 1.9142 168.9156 0.5605

247.6388 0 192.4169 3.7141

413.9178 39.0839 262.623 0.1196

422.8897 0.0001 299.0842 0.3214

553.3442 90.5491 389.5249 0.2258

572.2602 0.0004 551.2205 13.3477

602.0439 17.4793 827.5204 7.2786

678.4837 0 859.6152 9.5185

879.0897 0.0004 1035.2344 3.9097

905.6999 99.6452 1041.9629 7.1071

1033.4248 0.0001 1091.3162 0.7493

1042.7608 612.5875 1268.8807 1.8639

1064.7913 0.0002 1304.1572 0.188

1144.81 40.0234 1384.277 13.328

1186.8856 0 1392.4053 22.9043

1291.0522 42.9681 1485.0234 17.2458

1485.9837 0 1486.765 0.1757

2123.9009 896.411 2224.3091 150.9267

2130.4724 0.1389 2226.309 166.4745

3174.8502 0.0003 3052.5648 3.5487

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Table A4: Bond radius and angles of C4H4N2isomers

Pyrazine 1,1-dicyanoethane Pyridazine

Description Cal.

Value

Description Cal.

Value

Description Cal.

Value

R(1-2) 1.393 R(1-2) 1.154 R(1-2) 1.333

R(1-6) 1.334 R(1-3) 1.470 R(1-6) 1.332

R(1-7) 1.087 R(3-4) 1.470 R(2-3) 1.395

R(2-3) 1.334 R(3-6) 1.549 R(2-8) 1.086

R(2-8) 1.087 R(3-10) 1.098 R(3-4) 1.381

R(3-4) 1.334 R(4-5) 1.154 R(3-7) 1.084

R(4-5) 1.393 R(6-7) 1.092 R(4-5) 1.395

R(4-9) 1.087 R(6-8) 1.091 R(4-9) 1.084

R(5-6) 1.334 R(6-9) 1.092 R(5-6) 1.333

R(5-10) 1.087 A(2-1-3) 178.0 R(5-10) 1.086

A(2-1-6) 122.1 A(1-3-4) 110.7 A(2-1-6) 119.4

A(2-1-7) 120.8 A(1-3-6) 111.3 A(1-2-3) 123.8

A(1-2-3) 122.1 A(1-3-10) 107.3 A(1-2-8) 114.9

A(1-2-8) 120.8 A(4-3-6) 111.3 A(1-6-5) 119.4

A(6-1-7) 117.1 A(4-3-10) 107.3 A(3-2-8) 121.2

A(1-6-5) 115.9 A(3-4-5) 178.0 A(2-3-4) 116.8

A(3-2-8) 117.1 A(6-3-10) 108.9 A(2-3-7) 120.9

A(2-3-4) 115.9 A(3-6-7) 109.5 A(4-3-7) 122.3

A(3-4-5) 122.1 A(3-6-8) 110.5 A(3-4-5) 116.8

A(3-4-9) 117.1 A(3-6-9) 109.5 A(3-4-9) 122.3

A(5-4-9) 120.8 A(7-6-8) 109.0 A(5-4-9) 120.9

A(4-5-6) 122.1 A(7-6-9) 109.3 A(4-5-6) 123.8

A(4-5-10) 120.8 A(8-6-9) 109.0 A(4-5-10) 121.2

A(6-5-10) 117.1 R(1-2) 1.154 A(6-5-10) 114.9

R(1-2) 1.393 R(1-3) 1.470 R(1-2) 1.333

R(1-6) 1.334 R(3-4) 1.470 R(1-6) 1.332

R(1-7) 1.087 R(3-6) 1.549 R(2-3) 1.395

R(2-3) 1.334 R(3-10) 1.098 R(2-8) 1.086

R(2-8) 1.087 R(4-5) 1.154 R(3-4) 1.381

R(3-4) 1.334 R(6-7) 1.092 R(3-7) 1.084

R(4-5) 1.393 R(6-8) 1.091 R(4-5) 1.395

R(4-9) 1.087 R(6-9) 1.092 R(4-9) 1.084

R(5-6) 1.334 A(2-1-3) 178.0 R(5-6) 1.333

R(5-10) 1.087 A(1-3-4) 110.7 R(5-10) 1.086

A(2-1-6) 122.1 A(1-3-6) 111.3 A(2-1-6) 119.4

A(2-1-7) 120.8 A(1-3-10) 107.3 A(1-2-3) 123.8

A(1-2-3) 122.1 A(4-3-6) 111.3 A(1-2-8) 114.9

A(1-2-8) 120.8 A(4-3-10) 107.3 A(1-6-5) 119.4

A(6-1-7) 117.1 A(3-4-5) 178.0 A(3-2-8) 121.2

A(1-6-5) 115.9 A(6-3-10) 108.9 A(2-3-4) 116.8

A(3-2-8) 117.1 A(3-6-7) 109.5 A(2-3-7) 120.9

A(2-3-4) 115.9 A(3-6-8) 110.5 A(4-3-7) 122.3

A(3-4-5) 122.1 A(3-6-9) 109.5 A(3-4-5) 116.8

A(3-4-9) 117.1 A(7-6-8) 109.0 A(3-4-9) 122.3

A(5-4-9) 120.8 A(7-6-9) 109.3 A(5-4-9) 120.9

A(4-5-6) 122.1 A(8-6-9) 109.0 A(4-5-6) 123.8

A(4-5-10) 120.8 R(1-2) 1.154 A(4-5-10) 121.2

A(6-5-10) 117.1 R(1-3) 1.470 A(6-5-10) 114.9

437

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 438

Table A5: Bond radius and angles of C4H4N2isomers

2-methylene-

2H-imidazole

Iminopyrrole 4-amino-2-butynenitrile

Description Cal.

Value

Description Cal.

Value

Description Cal.

Value

R(1-2) 1.413 R(1-2) 1.437 R(1-2) 1.466

R(1-3) 1.295 R(1-3) 1.289 R(1-5) 1.465

R(2-5) 1.414 R(2-8) 1.484 R(1-9) 1.097

R(2-8) 1.339 R(2-9) 1.270 R(1-10) 1.097

R(3-4) 1.473 R(3-4) 1.486 R(2-3) 1.209

R(3-7) 1.084 R(3-7) 1.087 R(3-4) 1.365

R(4-5) 1.295 R(4-6) 1.081 R(4-6) 1.162

R(4-6) 1.084 R(4-8) 1.341 R(5-7) 1.016

R(8-9) 1.082 R(5-8) 1.079 R(5-8) 1.016

R(8-10) 1.083 R(9-10) 1.025 A(2-1-5) 115.2

A(2-1-3) 103.6 A(2-1-3) 104.8 A(2-1-9) 108.9

A(1-2-5) 113.0 A(1-2-8) 109.2 A(2-1-10) 108.9

A(1-2-8) 123.6 A(1-2-9) 125.3 A(1-2-3) 177.1

A(1-3-4) 109.9 A(1-3-4) 114.1 A(5-1-9) 108.7

A(1-3-7) 122.8 A(1-3-7) 121.5 A(5-1-10) 108.7

A(5-2-8) 123.5 A(8-2-9) 125.5 A(1-5-7) 109.7

A(2-5-4) 103.5 A(2-8-4) 106.2 A(1-5-8) 109.7

A(2-8-9) 120.3 A(2-8-5) 124.1 A(9-1-10) 106.0

A(2-8-10) 120.2 A(2-9-10) 108.7 A(2-3-4) 179.7

A(4-3-7) 127.2 A(4-3-7) 124.4 A(3-4-6) 180.0

A(3-4-5) 110.0 A(3-4-6) 125.4 A(7-5-8) 106.2

A(3-4-6) 127.2 A(3-4-8) 105.9 W1(A) 102.9

A(5-4-6) 122.8 A(6-4-8) 128.7 W2(A) 136.5

A(9-8-10) 119.5 A(4-8-5) 129.8 W3(A) 249.6

W1(A) 231.3 W1(A) 222.6 W4(A) 273.9

W2(A) 367.3 W2(A) 437.9 W5(A) 384.9

W3(A) 545.9 W3(A) 513.7 W6(A) 500.8

W4(A) 729.7 W4(A) 673.5 W7(A) 576.0

W5(A) 757.5 W5(A) 709.6 W8(A) 582.7

W6(A) 778.7 W6(A) 821.9 W9(A) 699.5

W7(A) 893.1 W7(A) 839.2 W10(A) 889.2

W8(A) 912.9 W8(A) 878.7 W11(A) 895.9

W9(A) 915.8 W9(A) 926.6 W12(A) 1098.3

W10(A) 954.3 W10(A) 967.2 W13(A) 1148.1

W11(A) 961.4 W11(A) 969.9 W14(A) 1183.4

W12(A) 979.8 W12(A) 993.4 W15(A) 1356.4

W13(A) 991.5 W13(A) 1058.7 W16(A) 1383.0

W14(A) 1202.2 W14(A) 1093.4 W17(A) 1459.8

W15(A) 1303.2 W15(A) 1280.5 W18(A) 1669.8

W16(A) 1346.3 W16(A) 1341.6 W19(A) 2258.9

W17(A) 1413.0 W17(A) 1353.4 W20(A) 2396.8

W18(A) 1496.2 W18(A) 1548.0 W21(A) 3036.9

W19(A) 1613.2 W19(A) 1646.7 W22(A) 3070.9

W20(A) 1714.9 W20(A) 1740.6 W23(A) 3496.6

W21(A) 3180.9 W21(A) 3175.7 W24(A) 3574.6

W22(A) 3196.1 W22(A) 3234.5 R(1-2) 1.466

W23(A) 3211.1 W23(A) 3266.2 R(1-5) 1.465

W24(A) 3283.7 W24(A) 3434.3 R(1-9) 1.097

438

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 439

Table A6: Bond radius and angles of C4H4N2isomers

1,3-butadiene-

1,4-diimine

1,2-diisocyanoethane

Description Cal.

Value

Description Cal.

Value

R(1-2) 1.316 R(1-5) 1.173

R(1-5) 1.226 R(2-3) 1.538

R(2-3) 1.461 R(2-5) 1.416

R(2-9) 1.085 R(2-7) 1.094

R(3-4) 1.316 R(2-8) 1.095

R(3-10) 1.085 R(3-6) 1.416

R(4-6) 1.225 R(3-9) 1.095

R(5-7) 1.023 R(3-10) 1.094

R(6-8) 1.023 R(4-6) 1.173

A(2-1-5) 173.7 A(1-5-2) 179.0

A(1-2-3) 124.3 A(3-2-5) 112.1

A(1-2-9) 116.9 A(3-2-7) 109.7

A(1-5-7) 115.8 A(3-2-8) 108.4

A(3-2-9) 118.8 A(2-3-6) 112.1

A(2-3-4) 124.3 A(2-3-9) 108.4

A(2-3-10) 118.8 A(2-3-10) 109.7

A(4-3-10) 116.9 A(5-2-7) 109.2

A(3-4-6) 173.7 A(5-2-8) 109.2

A(4-6-8) 115.8 A(7-2-8) 108.1

W1(A) 83.6 A(6-3-9) 109.2

W2(A) 127.6 A(6-3-10) 109.2

W3(A) 247.6 A(3-6-4) 179.1

W4(A) 413.9 A(9-3-10) 108.1

W5(A) 422.9 W1(A) 78.7

W6(A) 553.3 W2(A) 168.9

W7(A) 572.3 W3(A) 192.4

W8(A) 602.0 W4(A) 262.6

W9(A) 678.5 W5(A) 299.1

W10(A) 879.1 W6(A) 389.5

W11(A) 905.7 W7(A) 551.2

W12(A) 1033.4 W8(A) 827.5

W13(A) 1042.8 W9(A) 859.6

W14(A) 1064.8 W10(A) 1035.2

W15(A) 1144.8 W11(A) 1042.0

W16(A) 1186.9 W12(A) 1091.3

W17(A) 1291.1 W13(A) 1268.9

W18(A) 1486.0 W14(A) 1304.2

W19(A) 2123.9 W15(A) 1384.3

W20(A) 2130.5 W16(A) 1392.4

W21(A) 3174.9 W17(A) 1485.0

W22(A) 3183.6 W18(A) 1486.8

W23(A) 3422.3 W19(A) 2224.3

W24(A) 3422.6 W20(A) 2226.3

R(1-2) 1.316 W21(A) 3052.6

R(1-5) 1.226 W22(A) 3056.6

R(2-3) 1.461 W23(A) 3096.1

R(2-9) 1.085 W24(A) 3107.6

R(3-4) 1.316 R(1-5) 1.173

439

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 440

Pyrazine

440

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 441

1,1-dicyanoethane

Pyridazine

441

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 442

2-methylene-2H-imidazole

Iminopyrrole

442

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 443

4-amino-2-butynenitrile

1,3-butadiene-1,4-diimine

443

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 444

1,2-diisocyanoethane

444

Etim et al. /J. Nig. Soc. Phys. Sci. 3 (2022) 429–445 445

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Dec 2016
ASTROPHYS SPACE SCI

Linear carbon chain molecular species remain the dominant theme in interstellar chemistry. Their continuous astronomical observation depends on the availability of accurate spectroscopic parameters. Accurate rotational constants are reported for hundreds of molecular species of astrophysical, spectroscopy and chemical interests from the different linear carbon chains;

\mathrm{C}_{{n}}\mathrm{H}

\mathrm{C}_{{n}}\mathrm{H}^{-}

\mathrm{C}_{{n}}\mathrm{N}

\mathrm{C}_{{n}}\mathrm{N}^{-}

\mathrm{C}_{{n}}\mathrm{O}

\mathrm{C}_{{n}}\mathrm{S}

\mathrm{HC}_{{n}}\mathrm{S}

\mathrm{C}_{{n}}\mathrm{Si}

\mathrm{CH}_{3}(\mathrm{CC})_{{n}}\mathrm{H}

\mathrm{HC}_{{n}}\mathrm{N}

\mathrm{DC}_{2{n}+1}\mathrm{N}

\mathrm{HC}_{2{n}}\mathrm{NC}

, and

\mathrm{CH}_{3}(\mathrm{C}\equiv\mathrm{C})_{{n}}\mathrm{CN}

using three to four moments of inertia calculated from the experimental rotational constants coupled with those obtained from the optimized geometries at the Hartree Fock level. The calculated rotational constants are obtained from the corrected moments of inertia at the Hartfree Fock geometries. The calculated rotational constants show accuracy of few kHz below irrespective of the chain length and terminating groups. The obtained accuracy of few kHz places these rotational constants as excellent tools for both astronomical and laboratory detection of these molecular species of astrophysical interest. From the numerous unidentified lines from different astronomical surveys, transitions corresponding to known and new linear carbon chains could be found using these rotational constants. The astrophysical, spectroscopic and chemical implications of these results are discussed.

Thermodynamique de composés azotés: II. — *Étude thermochimique des acides aminobenzoïques, de la pyrimidine, de l’uracile et de la thymine* *

Article

Jan 1977

Thermochemical Data of Organic Compounds

Book

Jan 1986

This reference consists of tables of thermochemical data for many organic compounds. The following topics are covered: standard enthalpies of formation derived from experimental data; prediction of standard enthalpies of formation; group interactions; interpretation of group interactions; prediction of unknown values; and future developments.

Interstellar Protonated Molecular Species

Article

Apr 2017
ADV SPACE RES

Majority of the known interstellar cations are protonated species believed to be the natural precursors for their corresponding neutral analogues formed via the dissociative recombination process. The protonation of a neutral species can occur in more than one position on the molecular structure thus resulting in more than one proton binding energy value and different protonated species for the same neutral species. In the present work, ab initio quantum calculations are employed to calculate accurate proton binding energies for over 100 neutral interstellar molecules of which majority of the neutral molecules are protonated in more than one position. From the results, protonated species resulting from a high proton binding energy prefers to remain protonated rather than transferring a proton and returning to its neutral form as compared to its analogue that gives rise to a lower proton binding energy (PBE) from the same neutral species. For two protonated species resulting from the same neutral molecule, the one that results in a higher PBE is more stable as compared to its counterpart that is responsible for the lower PBE for the same neutral species. Here, the most stable species are highlighted for all the systems considered.

Interstellar isomeric species: Energy, stability and abundance relationship

Article

Dec 2016

Accurate enthalpies of formation are reported for known and potential interstellar isomeric species using high-level ab initio quantum-chemical calculations. A total of 130 molecules comprising of 31 isomeric groups and 24 cyanide/isocyanide pairs with molecules ranging from 3 to 12 atoms have been considered. The results show an interesting relationship between energy, stability and abundance (ESA) existing among these molecules. Among the isomeric species, isomers with lower enthalpies of formation are more easily observed in the interstellar medium compared to their counterparts with higher enthalpies of formation. Available data in the literature confirm the high abundance of the most stable isomer over other isomers in the different groups considered. Potential for interstellar hydrogen bonding accounts for the few exceptions observed. Thus, in general, it suffices to say that the interstellar abundances of related species could be linked to their stabilities if other factors do not dominate. The immediate consequences of this relationship in addressing some of the whys and wherefores among interstellar molecules and in predicting some possible candidates for future astronomical observations are discussed.

A Search for Interstellar Monohydric Thiols

Article

Dec 2016
ASTROPHYS J

It has been pointed out by various astronomers that very interesting relationship exists between interstellar alcohols and the corresponding thiols (sulfur analogue of alcohols) as far as the spectroscopic properties and chemical abundances are concerned. Monohydric alcohols such as methanol and ethanol are widely observed and 1-propanol is recently claimed to have been seen in Orion KL. Among the monohydric thiols, methanethiol (chemical analogue of methanol), has been firmly detected in Orion KL and Sgr B2(N2) and ethanethiol (chemical analogue of ethanol) has been claimed to be observed in Sgr B2(N2) though the confirmation of this detection is yet to come. It is very likely that higher order thiols could be observed in these regions. In this paper, we study the formation of monohydric alcohols and their thiol analogues. Based on our quantum chemical calculation and chemical modeling, we find that `Tg' conformer of 1-propanethiol is a good candidate of astronomical interest. We present various spectroscopically relevant parameters of this molecule to assist its future detection in the Interstellar medium (ISM).

Partition Function and Astronomical Observation of Interstellar Isomers: Is there a link?

Article

Nov 2016
ADV SPACE RES

The unsuccessful astronomical searches for some important astrophysical and astrolobiological molecules have been linked to the large partition function of these molecules. This letter reports an extensive investigation of the relationship between partition function and astronomical observation of interstellar isomers using high level quantum chemical calculations.120 molecules from 30 different isomeric groups have been considered. Partition function and thermodynamic stabilities are determined for each set of isomeric species. From the results, there is no direct correlation between partition function and astronomical observation of the same isomeric species. Though interstellar formations processes are generally controlled by factors like kinetics, thermodynamics, formation and destruction pathways. However, the observation of the isomers seems to correlate well with thermodynamics. For instance, in all the groups considered, the astronomically detected isomers are the thermodynamically most stable molecules in their respective isomeric groups. The implications of these results in accounting for the limited number of known cyclic interstellar molecules, unsuccessful searches for amino acid and the possible molecules for astronomical observations are discussed.

Systematic Theoretical Study on the Interstellar Carbon Chain Molecules

Article

Sep 2016
ASTROPHYS J

In an effort to further our interest in understanding basic chemistry of interstellar molecules, we carry out here an extensive investigation of the stabilities of interstellar carbon chains; Cn, H2Cn, HCnN and CnX (X=N, O, Si, S, H, P, H-, N-). These sets of molecules accounts for about 20% of all the known interstellar and circumstellar molecules, their high abundances therefore demand a serious attention. High level ab initio quantum chemical calculations are employed to accurately estimate enthalpy of formation, chemical reactivity indices; global hardness and softness; and other chemical parameters of these molecules. Chemical modeling of the abundances of these molecular species has also been performed. Of the 89 molecules considered from these groups, 47 have been astronomically observed, these observed molecules are found to be more stable with respect to other members of the group. Of the 47 observed molecules, 60% are odd number carbon chains. Interstellar chemistry is not actually driven by the thermodynamics, it is primarily dependent on various kinetic parameters. However, we found that the detectability of the odd numbered carbon chains could be correlated due to the fact that they are more stable than the corresponding even numbered carbon chains. Based on this aspect, the next possible carbon chain molecule for astronomical observation in each group is proposed. The effect of kinetics in the formation of some of these carbon chain molecules is also discussed.

A computational study on substituted diazabenzenes

Article

Oct 2011
TURK J CHEM

Selcuk Gumus

The results of computational calculations on the aromaticity of the monosubstituted diazabenzenes (pyridazine, pyrimidine, and pyrazine) are reported herein. The aromaticity of the parent heterocycle was enhanced by substitution of strong electron-withdrawing groups. The effects of the position of the substituent on the aromaticity and the stability of the system were also investigated by studying all possible derivatives of the systems.

Quantum Chemical Studies on C4H4N2 Isomeric Molecular Species

Abstract and Figures

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