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Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

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American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
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American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
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American Journal of Cancer Prevention
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American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
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Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
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Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

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Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

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Computational Prediction of pKaH of Conjugate Acids Pentazinium (CH₂N₅₊) and Hexazinium (HN₆₊) of the Two Hypothetical Molecules Pentazine and Hexazine

K.B. Shanti Sudha, Sanjeev Rachuru*, Jagannadham Vandanapu*, Adam A Skelton

Department of Chemistry, St. Ann's College for Women, Mehdipatnam, Hyderabad 500 028, Telangana, IndiaDepartment of Chemistry, Osmania University, Hyderabad-500007, India

Abstract: In our earlier article we had determined the pKaH of the two conjugate acids Pentazinium (CH₂N₅₊) and Hexazinium (HN₆₊) of the two hypothetical molecules Pentazine (CHN₅) and Hexazine (N₆) respectively; this we had done by exploiting Katritzky graphical method. In this article we have reinforced our determination of pKaH of the two conjugate acids Pentazinium (CH₂N₅₊) and Hexazinium (HN₆₊) by DFT calculations. These DFT calculations can easily be carried out by Graduate students. This would be a good exercise/project-based learning activity for Graduate students to run the SMDsSAS model calculations

Keywords: pKaH, Pentazinium, Hexazinium, DFT & SMDsSAS

Received May 07, 2026; Revised June 09, 2026; Accepted June 16, 2026

Citation: K.B. Shanti Sudha, Sanjeev Rachuru, Jagannadham Vandanapu, Adam A Skelton, Computational Prediction of pKaH of Conjugate Acids Pentazinium (CH₂N₅₊) and Hexazinium (HN₆₊) of the Two Hypothetical Molecules Pentazine and Hexazine. World Journal of Chemical Education, 14 (2). 36-39. January 2026. doi:10.12691/wjce-14-2-2

1. Introduction

In our earlier article [1], we had taken the 8 aromatic azines (Table 1) out of which the last two are hypothetical molecules Pentazine and Hexazine and have not been synthesized. The pKaH of the first six protonated species were available in the literature [2,3,4]. For the last two members of azine series that is Pentazinium (Equation 1) and Hexazinium (Equation 2) the pKaH was determined using two Graphical plots. Out of the two graphical plots, the first one (Plot1) was that of pKaH, versus number of Nitrogen atoms of aromatic azines, that is, Katritzky graphical method [5].

The plot 1 was extrapolated to 5th (Pentazinium) and 6th (Hexazinium) Nitrogen atoms; thus, yielding pKaH, of Pentazinium and Hexazinium. In this article, as already mentioned in the abstract we have reinforced the determination of pKaH of Pentazinium and Hexazinium by DFT calculations. These simple computational calculations can easily be carried out by Graduate students. It can be given as project-based learning activity. After carrying out the these DFT calculations, the Graduate students, will be able to run the SMDssas (SOLVENT MODEL DENSITYscaled solvent-accessible surface) model calculations.

2. Methods

Gaussian 09 [6] software was used to carry out all the theoretical calculations. The pKaH values were determined using SMDsSAS (scaled solvent-accessible surface) model. The geometries were optimized at the M06-2X/6-31+(d,p) level. The optimization and frequency calculations were performed simultaneously. The method for the determination of pKaH is the same as that described in Lian et al. [7]. The nonspecific form of Equation 1 and Equation 2 is given by Equation 3 [7]:

AH⁺(aq) AH(aq) + H⁺(aq) (3)

where AH⁺(aq) is either Pentazinium cation or Hexazinium cation. AH(aq) is either Pentazine or Hexazine. The free energies of AH⁺(aq) and AH(aq) are obtained from the optimized (opt + freq) structures using M06-2X functional and 6-31+(d,p) basis set.

The pKaH of cation AH⁺ is calculated according to Eqn 4:

pKaH = ΔG*aq/2.303RT (4)

The free energy in the 1 M standard state, ΔG*aq,, was calculated directly from the aqueous Gibbs free energies of the acid and conjugate base using Eqn 5:

ΔG*aq = G*aq(AH) + G*aq(H⁺) – G*aq(AH⁺) (5)

The gas-phase standard phase correction term, Go→* for both acid and conjugate base, cancel in this equation. The standard state aqueous free energy of proton, G*aq(H⁺), was calculated using Eqn 6:

G*aq(H⁺) = Gog(H⁺) + ΔG*aq,solv(H⁺) + ΔGo→* (6)

In the above equation Gog(H⁺) = –6.29 kcal mol⁻¹ and the experimentally measured hydration free energy ΔG*aq,solv(H⁺) = –265.9 kcal mol⁻¹ was taken from the literature [8,9,10,11,12]. ΔGo→* is the gas-phase standard correction and is used to convert from 1 atm ideal gas standard state to 1 M standard state, where superscripts o and * indicate 1 atm and 1 M standard states, respectively: ΔGo→* = RT ln 24.26 = 1.89 kcal mol–1 at 298 K [13]. Therefore, substituting in equation 6,

G*aq(H⁺) = (-6.29) + (-265.9) + (1.89)

= -270.3 kcal mol⁻¹

This G*aq(H⁺) = -270.3 kcal mol⁻¹ is substituted in equation 5, along with G*aq(AH) and G*aq(AH⁺).

The synopsis of the above method is to find the free energy of G*aq(AH⁺) i.e. say Pentazinium ion, G*aq(AH) say Pentazine and taking the G*aq(H⁺) as -270.3 kcal mol⁻¹ we get ΔG*aq. This ΔG*aq is substituted in equation 4 to get the pKaH.

3. Discussion

Lian et al [7] mentioned that in the continuum model, the cavity formed by the solute-solvent boundary is one of the most important factors for accuracy of the model. He conveyed that the essence of SMDsSAS (scaled solvent-accessible surface) approach is to improve the accuracy of the SMD (solvent model density) continuum model by optimizing the solute-solvent boundary. In the SMDsSAS model a scaling factor α is introduced to tune the size of the cavity, thereby improving the solute-solvent interaction. Thus, the factor α is extremely crucial in SMDsSAS model. One can refer to reference [7] for further details regarding the merits of SMDsSAS model. In his article Lina et al [7] proved that SMDsSAS method gave the most accurate pKa values of carboxylic acids, amines and thiols. Liean et al had taken the α value of 0.485 (for elements H, C and N). In the present article we have used SMDsSAS model for the accurate determination of pKaH of aromatic azines (Table 1). Since our compounds contained H, C & N atoms we took a cue from Lian et al [7] article (he reported the α value of 0.485 for H, C and N atoms) to choose the crucial α value. The crucial α value was further tuned to get the accurate value of pKaH values (Table 1). To make it lucid and comprehensible to Graduate students, the following input file of Pentazinium ion is depicted (the bottom of the input file has the crucial alpha value, which has been tuned to 0.447 for Pentazinium ion).

%chk=mol.chk

%lindaworkers=cnode1362.cm.cluster

# opt freq m062x/6-31+g(d,p) scrf=(solvent=water, read) pop=nbo geom=connectivity

Pentazinium ion

1 1

N

N 1 B1

C 1 1.28750605 2 119.32188762

N 2 B2 1 A1 3 D1

N 3 B3 1 A2 2 0.00000000

H 3 B4 1 120.59325302 2 180.00000000

N 5 B5 3 A3 1 D2

H 1 B6 3 A4 5 D3

B1 1.40002009

B2 1.23803184

B3 1.46404372

B4 1.07000000

B5 1.23231199

B6 1.00000000

A1 120.66752010

A2 118.81349395

A3 119.14599004

A4 120.33905619

D1 -0.00000000

D2 -0.00000000

D3 -180.00000000

1 2 1.0 3 2.0 8 1.0

2 4 2.0

3 5 1.0 6 1.0

4 7 1.0

5 7 2.0

6

7

8

surface=sas

alpha=0.447

The crucial SMDsSAS α (alpha) value = 0.447 is for Pentazinium ion. SMDsSAS α (alpha) values of all the compound are given in Table 1. The pKaH values of the first six members (Table 1) are available in the literature and we got almost the same pKaH values. The pKaH of protonated hypothetical molecules Hexazine and Pentazine were not reported in the literature. We reported pKaH of protonated Hexazine and Pentazine (Plot1) by Katritzky graphical method [1]. In the present study by SMDsSAS method we got almost the same (Table 1) for protonated Pentazine -9.56 (~0.74% error) and Hexazine -13.06 (~0.4% error). Thus, we can conclude that pKaH of protonated Hexazine and Pentazine are reasonably correct. Further, we can also infer that SMDsSAS is a reasonably good method to determine the pKaH values for this azine series.

LEARNING OUTCOMES

1).Students would be able to find the pKaH values by Katrizky graphical method (to be more correct, this method was reported in our earlier article [1])

2).Students would have mastered the prediction of pKaH values by SMDsSAS solvent model.

3).We want the graduate students to figure out the correct method to find the crucial alpha value and understand the significance of alpha from reference [7].

Plot 1. pKaH versus Number of N atoms of Azines

Table 1. Aromatic azines with their corresponding data

4. Conclusion

The pKaH of the two cations (eqn. 1 and 2) Pentazinium and Hexazinium () of the two hypothetical molecules Pentazine (CHN₅) and Hexazine (N₆) were determined by our group with the help of Katritzky plot [1]; they turned out to be -9.49 and -13.1 respectively. In this article we determined the same by DFT calculations; we got -9.56 for Pentazinium and -13.06 for Hexazinium, bolstering our pKaH determinations. The fact that we are getting the same pKaH values by both the methods, that is Katritzky graphical method and SMDsSAS method, we can infer that our values are reasonably correct. Further, we can also infer that SMDsSAS is a reasonably good method to determine the pKaH values for this azine series. After successfully finding the pKaH of all the compounds (Table1), the Graduate students would have mastered the SMDsSAS model calculations. Thus, it is a good exercise/project-based learning activity to master the SMDsSAS model calculations.

Funding

The research did not receive any specific funding.

Conflict of Interest Statement

The authors declare no conflicts of interest

Availability of Data and Material

All the electronic data related to this article is provided in the supplementary material.

Author Contributions

Equal contribution from all the four authors.

ACKNOWLEDGMENT

The authors are grateful to the Centre for High Performance Computing (CHPC), Cape Town, South Africa, for their generous allocation of super computer time.

References

[1]  
R.Sanjeev, R.Ravi, D.A.Padmavathi, V.Jagannadham, “pKa of the two conjugate acids (CH₂N₅⁺) and HN₆⁺ of the two hypothetical molecules the Pentazine (CHN₅) and the Hexazine (N₆) of Azabenzene series: A chemical education perspective, ” World Journal of Chemical Education, 10(3), 105-109, August, 2022.

[2]   | J. M. Essery & K. Schofield, “The influence of steric factor on the properties of 4-amino pyridine derivatives, “ J. chem. Soc, 3939-3953, 1961.
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