We used the molecular dynamics method to simulate the behavior of potassium perfluorohexanesulfonate (KPFOS) in water/gas system. The results indicate that PFOS- can spontaneously migrate to the water/gas interface and form a layered structure with hydrophobic tail chains facing the gas phase and hydrophilic sulfonic acid groups immersed in the water phase, while some PFOS- molecules within the solution formed spherical micelles. Both the number density and charge density distributions confirm that PFOS- and K+ are mainly distributed at the water/gas interface, and a small amount of PFOS- and K+ are distributed in the bulk solution. Based on the results of radial distribution function, the probability of K+ appearing near oxygen atoms in PFOS- is very high due to electrostatic attraction. Based on the IGMH analysis, the oxygen atoms in PFOS- can form multiple hydrogen bonds with adjacent water molecules, while there is only weak van der Waals interaction between K+ and water molecules.
Research Article
Molecular dynamics simulation of the distribution of potassium perfluorooctanesulfonate in water
https://doi.org/10.21203/rs.3.rs-3048742/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 14 Aug, 2023
You are reading this latest preprint version
Fluorocarbon surfactant
Molecular dynamics simulation
Weak interaction
Surfactants are widely used in everyday products such as soap and shampoo[1–3]. Surfactants are also used in mineral flotation, textile printing and dyeing, paper manufacturing, and other industrial applications[4–6]. Likewise, in the oil and gas development industry, surfactants have also made a splash. In many cases, oil and gas wells productive are not always satisfactory due to differences in formation pressure. Effective measures must be taken to increase production in wells with low pressure and/or permeability[7]. Hydraulic fracturing is widely regarded as the most effective method of increasing oil and gas well production at the moment[8–10]. During hydraulic fracturing, a high volume of fluid is used to transport a proppant (such as ceramsite and/or quartz sand) into the reservoir, where it is used to create numerous, microscopic cracks in the dense rock. The liquid then flows back, leaving the proppant in the fractures while maintaining the crack patency, which increases oil and gas well production[11–13]. Surfactants are typically added to fracturing fluid to reduce water/gas surface tension and thus reduce liquid flowback resistance[14–16].
There have been extensive studies on fluorocarbon surfactants as they are the most widely used type of surfactant in the oil and gas industry[17–18]. Zhang et al. synthesized some novel oil-soluble fluorinated surfactants[19]. These surfactants showed good effect on reducing the surface tension of organic solutions. The surface tension of nitromethane reduced by about 40% when the concentration of 1e was 0.1 mol/L. The surface tension of toluene was reduced by about 20% when the concentration of 1a was 0.1 mol/L. For real-world use, researchers have focused on perfluorocarbon surfactants that are soluble in water. Chen et al. synthesized fluorinated anionic surfactant sodium p-perfluorononenyloxy benzene sulfonate (SPBS)[20]. This surfactant has excellent surface activity and combined properties; when the concentration of SPBS is 1g/L, the minimum surface tension can reach 18 mN/m. Lee at al. synthesized several novel anionic fluorinated surfactants with two short fluorocarbon chains per molecule[21]. The CMC of the final products were found to be low (0.31–1.15 mmol/L), and their surface tension in 1% aqueous solution was within the range of 15.7–22.8 mN/m.
In the past few decades, both hydrocarbon and fluorocarbon surfactants have been widely reported, with researchers increasingly turning to molecular dynamics (MD) simulation to delve deeply into the mechanism of action of fluorocarbon surfactants at the molecular/atomic level[22–23]. Yuan et al. studied several counterions with dodecyl sulfate (DS−) at the air/water interface using molecular dynamics (MD) simulations[24]. The results show that weak C-H-O hydrogen bonds are formed between the polar head and alkane chains of counterions; the hydrogen bonds play an important role in the formation of mixed adsorption layer. Zhang employed MD simulations to investigate the microscopic properties of nonionic fluorocarbon surfactants at the air/water interface[25]. It was observed that the structure of fluorocarbon surfactants at the air/water interface was more ordered than that of hydrocarbons, which is dominated by the van der Waals interaction between surfactants and water molecules. Dong et al. used a joint experimental and simulation approach to investigate the structure of perfluorooctanoate ammonium (PFOA) micelles in aqueous solutions[26], focusing on the understanding of ethanol addition on PFOA micelle formation and structure. Both experiments and simulations have demonstrated a transition from co-surfactant to co-solvent behavior as ethanol concentration increases, with the latter also providing insight into how to achieve co-solvent conditions with other additives.
In this paper, the MD simulation method was used to simulate the dispersion of a fluorocarbon surfactant in water in order to understand the mechanism of surfactant action from a microscopic perspective. Herein, potassium perflurohexanesulfonate (CAS No: 3871-99-6, abbreviated as KPFOS) was selected as the research object[27]; its CMC is about 0.8 ~ 1 mmol/L in pure water[28–29]. The research method used herein is not limited to KPFOS, and the method can be applied to molecular simulation research on more complex fluorocarbon surfactants.
Firstly, the structure of PFOS− was optimized by using the ORCA software version 5.0.4[30–31] at the B97-3c[32] theoretical level, followed by calculation of single point energy using the B3LYP D3 ma-def2-TZVP[33] theoretical method. GROMACS version 2022.5 software[34–35] was used for MD simulation, GAFF[36] all-atom force field was used to describe PFOS−, and RESP charge[37] was obtained using Multiwfn[38] software. Packmol[39] was used to build the simulation box as shown in Fig. 1A; water is the OPC three-point model[40]. In this work, there are 50 PFOS−, 50 K+, and 16841 water molecules in the simulation box, therefore, the concentration of KPFOS is approximately 40 mmol/L, higher than the CMC of KPFOS. After minimizing the system energy by using the steepest descent algorithm, leapfrog algorithm was used to perform 500 ns MD under the NVT ensemble, parrinello-rahman pressure control algorithm[41] with pressure coupling constant time at 2.5 ps was used. The temperature control algorithm was V-rescale[42] with a temperature of 298.15 K, the temperature coupling constant time was 0.2 ps. The Coulomb interaction calculation method was PME algorithm[43], the cut-off was 1 nm; and the van der Waals interaction algorithm was cut-off with the cut-off distance 1 nm. VMD 1.9.3 software[44] was used for visual observation.
Independent gradient model based on Hirshfeld partition (IGMH) analysis steps: select all atoms/molecules within 3.5 nm of an atom/molecule in VMD and then use ORCA to obtain the wavefunction information; the single point energy calculation level is B3LPY D3 ma-def2-TZVP. After obtaining the wave function information, use Multiwfn for IGMH analysis[45].
3.1. Snapshots before and after simulation
As soon as the simulation begins, we can see the random distributed PFOS− spontaneously migrate to the water/gas interface, and form micelles inside the bulk solution, as shown in the supporting information video. The snapshots before and after the simulation are shown in Figs. 1A and 1B.
Before MD simulation starts, PFOS− and K+ are both randomly distributed in the aqueous solution, as shown in Fig. 1A, and there are few distribution rules. After MD, PFOS− is mainly distributed at the water/gas interface, which is consistent with the theory of surfactants reducing surface tension. At the same time, the spherical aggregate of PFOS− appears in the bulk aqueous solution. That is, at this concentration (40 mmol/L, higher than cmc), PFOS− can not only distribute on the surface of water, but also form spherical micelles in the water. This is also consistent with the theory of forming micelles in water. K+ is randomly distributed in bulk aqueous solution without aggregations.
There are no water molecules or KPFOS in the vacuum layer and all KPFOS are distributed in the solution. As a result, the density of KPFOS (including number density and charge density) within a unit volume in the water phase is of interest.
3.2. Number density distribution
Since PFOS− is mainly distributed at the water/gas interface, and there are also PFOS− micelles in the bulk solution, K+ are distributed inside the solution; as a result, it is worth studying how many PFOS− or K+ are distributed in per unit volume in the simulation box.
With the center of the boxes as the origin, the number density distribution of PFOS− and K+ in Y direction are shown in Fig. 2. Before MD, as depicted in Fig. 2A, the number density of PFOS− and K+ molecules on both sides is 0 and the number density in the bulk solution is irregular, which is consistent with the snapshot of the KFPOS solution shown in Fig. 1A. Interestingly, as the simulation is completed, the number density distribution of PFOS− and K+ in the solution is very regular, the number density graphics are also quite interesting. In Fig. 2B, at a distance of about 4 nm from the center of the box, the number density of PFOS− is the highest, approximately 0.4 per nm− 3; in the center of the box, due to the presence of PFOS− micelles, the highest number density is approximately 0.1 per nm− 3; in the remaining space of the solution, the number density of PFOS− is almost zero. It is evident that compared to PFOS−, K+ is always distributed inside the aqueous solution, and does not appear at the water/gas interface. Within the bulk solution where the PFOS− number density is the highest, the K+ number density is also as high as up to about 0.26 per nm− 3; this means that the probability of K+ appearing near PFOS− is high. Within the solution, the number density of K+ is approximately 0.07 per nm− 3, much lower than that near the water/gas interface.
From Fig. 2B, it can be concluded that the PFOS− layer thickness is about 1.58 nm at the air/water interface. Combining the snapshots in Fig. 1B and Fig. 2B, it can be concluded that at the water/air surface, PFOS− is not a straight molecule but exhibiting a certain degree of curvature, and PFOS− is not uniformly and neatly arranged on the surface of the solution but exhibits multiple layers "lying on the side" on the water surface.
3.3. Charge density distribution
Similarly, charge density distribution is also worth studying. Similar to Fig. 2, taking the center of the boxes as the origin, the charge density distribution of PFOS− and K+ in Y direction are shown in Fig. 3.
In Fig. 3A, the charge density of PFOS− is negative, the charge density of K+ is positive, and charge density distributions are irregular. As shown in Fig. 3B, after the simulation, the distribution of charge density is significantly different from Fig. 3A. Since the negatively charged PFOS− gathers at the water/gas interface, the maximum PFOS− charge density is about 0.02 per nm− 3 at about 3.8 nm from the box center. In addition, the charge density of PFOS− is also negative with very low value in the center of the box, indicating the existence of very small amounts of PFOS− molecules, which is attributed to the spherical micelles in the solution. Comparatively, K+ is distributed within the solution and is mainly located near the location where PFOS− is distributed—due to the attraction with opposite electrical properties, K+ exhibits a layered distribution from 3.5 nm of the center. However, there are still some K+ within the solution, which are free and do not always appear near PFOS−.
3.4. Radial distribution function
From Fig. 4, it is evident that the RDF between the oxygen atom in PFOS− and K+ has the first peak at 0.27 nm, indicating the probability of K+ appearing at a distance of 0.27 nm from the oxygen atom on the sulfonic acid radical is the highest; this is the first coordination layer. A secondary weak peak appears at about 0.47 nm; this is attributed to the second coordination layer. This proves that PFOS− and K+ with opposite electrical properties have a high probability of appearing in pairs, but not every anion can pair with cations.
3.5. Analysis of weak intermolecular interactions
In 2022, Lu et al. proposed an independent gradient model (IGM)[46–47] method based on Hirshfeld partition of molecular density (called IGMH)[45]. IGMH has a rigorous physical basis, it is defined on the actual molecular density rather than the promolecular density, the latter one completely ignores the electron transfer and polarization during formation of the current system from isolated atoms.
As mentioned above, PFOS− is mainly distributed at the water/gas interface and the hydrophilic sulfonic acid mainly faces the water; the weak interaction between water and PFOS− is worth studying. Similarly, the weak interaction between K+ in water and water is also worth studying.
As shown in Fig. 5, there are mainly two kinds of weak interactions in the IGMH analysis graphs. The first one is 5 H-bonds formed by the three oxygen atoms in PFOS− and adjacent water molecules, as shown in the blue isosurface in Fig. 5A. In addition, due to the negative charge of fluorine atoms, and coincidentally, so long as the distance and angle between the fluorine atom and adjacent water molecules conform to the characteristics of H-bond, as shown in the red circle in Fig. 5A, we believe that fluorine atoms can also form H-bonds with water molecules, depending on the distribution of water molecules. This is the difference between our research results and those of Zhang[25].
The second weak interaction, there are several water molecules distributed around the K+, and negative charged oxygen atoms in water molecules are directed towards K+, the weak interaction between water molecules and K+ is van der Waals interaction (green isosurface in Fig. 5B), indicating that the interaction between water molecules and potassium ions is extremely weak. As K+ is a single atom, the direction of van der Waals interactions depends on the distribution of water molecules.
3.6. Quantum chemical calculations
KPFOS is not a new substance, its properties and practical applications have been extensively studied. However, as far as we know, there is no report of KPFOS at the level of quantum chemistry. Since KPFOS is a salt that easily ionizes in water, PFOS− needs to be studied only at the quantum chemistry level.
It is well known that the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) determine the capacity of the molecule to accept electrons and provide electrons[48–49], respectively. From Fig. 6, it is evident that the oxygen atoms in PFOS− mainly determine the capacity of the PFOS− molecule to accept electrons and fluorocarbon chains mainly determine the capacity to provide electrons.
Furthermore, the distribution of electrostatic potential[50] was analyzed by Multiwfn. The overall surface of PFOS− is 294.4 Å2, this is also the total surface area of the negative surface area. The molecular polarity index (MPI) of PFOS− is 0.011 a.u., much higher than the MPI of water (0.003 a.u.), this also proves that PFOS has strong hydrophobicity. The nonpolar surface area of PFOS− is 0 Å2 and the polar surface area is 294.42 Å2, which proves that PFOS− is a total polar molecule and has strong ability to combine with other substances through electrostatic or H-bond interactions. It can be seen from Fig. 7 that the surface electrostatic potential of negatively charged PFOS− is negative, and the electrostatic potential on the fluorocarbon chain is significantly lower than that on the sulfonic acid group (compared in absolute values); that is to say, the net charge is mainly distributed on the sulfonic acid group.
In this paper, we used molecular dynamics method to study the dispersion of a simple surfactant potassium perflurohexanesulfonate (KPFOS) in water. At a concentration higher than the CMC, not only is PFOS− distributed on the surface of water/gas, thereby reducing surface tension, but also forms micelles in aqueous solutions. At the water/gas interface, the hydrophobic fluorocarbon chain of the PFOS− faces toward the gas phase, and the hydrophilic sulfonic acid group is immersed in water, K+ is mainly distributed near the plane layer of sulfonic acid groups and a small proportion is distributed in the bulk solution. Both number density and charge density distribution confirm this point view. The oxygen atom in the sulfonic acid group can inevitably form multiple hydrogen bonds with water, which has a strong attraction effect; fluorine atoms can also form hydrogen bonds with water, resulting in weak attraction, but that's not always the case either as it depends on the distribution distance and angle of water molecules distribution. K+ only have van der Waals interactions with surrounding water molecules, and the oxygen atoms in the water molecules face K+, this is attributed to the mutual attraction of opposite atomic charges.
Competing interests
The authors declare no conflicts of interest.
Ethics approval and consent to participate
Not applicable.
Consent for publication
The authors declare that they have no known competing financial interests or personal relationships that may affect the work reported in this paper.
Availability of data and materials
All the data that support the findings of this study are available on request from the corresponding authors.
Funding
This work was supported by Science and technology project of PetroChina exploration and production company: Technical Improvement and Field Test of Horizontal Shale Gas Wells in SouthWest China (No. 2023ZS0603) and Research on Key Technologies of Tight Gas Engineering in the Central and Western Regions of Sichuan Basin (No. 2022ZD01-03).
- Presley Colby L, Michelle M, Cara B, Ryan L, Melissa L, Heather F, Jesse D, Pulsipher Kayd J, Rundle Chandler W (2021) Dunnick Cory A. The History of surfactants and review of their allergic and irritant properties. Dermatitis 32(5):289–297
- Mondal Subhodip A, Animesh S, Bidyut (2022) Utilization of natural surfactants: An approach towards sustainable universe. Vietnam J Chem 60(1):1–14
- Tripathy Divya B, Anuradha M, James C (2018) Synthesis, chemistry, physicochemical properties and industrial applications of amino acid surfactants: A review. C R Chim 21(2):112–130
- Huang Zhiqiang Z, Shiyong Z, Feng W, Hongling Z, Jianrong Yu, Xinyang L, Rukuan C, Chen (2020) Liu Zuwen, Guo Zhiqun. Evaluation of a novel morpholine-typed Gemini surfactant as the collector for the reverse flotation separation of halite from carnallite ore. J Mol Liq. 313. 113506
- Ambreen R, Sarfraz S, Qamar F, Skinadar S (2021) The use of surface active agents for effective removal of dyes/pigments: A perspective review on solubilization and foam fractionation. J Innovative Sci 7(2):222–228
- Mahmoodabadi Mohammad K, Hamid S, Vahideh (2019) Efficient dye removal from aqueous solutions using rhamnolipid biosurfactants by foam flotation. Iran J Chem Chem Eng 38(4):127–140
- Xinhua MA, Jun XIE (2018) The progress and prospects of shale gas exploration and development in southern Sichuan Basin, SW China. Pet Explor Dev 45(1):172–182
- Barati, Reza (2014) Liang Jenn Tai. A review of fracturing fluid systems used for hydraulic fracturing of oil and gas wells. J Appl Polym Sci. 131(16)
- Fujian ZHOU, Hang SU, Liang Xingyuan, Leifeng MENG, Lishan YUAN, Xiuhui LI, Tianbo LIANG (2019) Integrated hydraulic fracturing techniques to enhance oil recovery from tight rocks. Pet Explor Dev 46(5):1065–1072
- Li L, Jingqiang T, Zhengguang WDavidAZhao, Dirk B, Qiao L, Biao S (2019) Chen Haichao. A review of the current status of induced seismicity monitoring for hydraulic fracturing in unconventional tight oil and gas reservoirs. Fuel 242:195–210
- Zhifeng L, Nanlin Z, Liqiang Z, Yuxin P, Pingli L (2019) Thermoresponsive in situ generated proppant based on liquid–solid transition of a supramolecular self-propping fracturing fluid. Energy Fuels 33(11):10659–10666
- Zou Mingjun Y, Linlin Z, Miao H, Zhiquan Xu, Rongchao D, Zibin Z (2022) Hydraulic fracture to enhance coalbed methane recovery by using coated ceramsite. Greenh Gases Sci Technol 12(6):751–763
- Feng Y-C, Cheng-Yun M, Jin-Gen D (2021) Chu Ming-Ming, Hui Cheng, Luo Yu-Yang. A comprehensive review of ultralow-weight proppant technology. Pet Sci 18:807–826
- Wijaya Nur S, James J (2020) Surfactant selection criteria with flowback efficiency and oil recovery considered. J Petrol Sci Eng 192:107305
- Liang Tianbo, Achour Sofiane H, Longoria Rafael A, DiCarlo David A, Nguyen Quoc P (2017) Flow physics of how surfactants can reduce water blocking caused by hydraulic fracturing in low permeability reservoirs. J Petrol Sci Eng 157:631–642
- SalahEldin HO, Abdalla EK, Abdullah A, Hazlina H, Ahmed B, Lim E (2019) Experimental study on the use of surfactant as a fracking fluid additive for improving shale gas productivity. J Petrol Sci Eng 183:106426
- Fu Lipei L, Kaili G, Jijiang H, Yanfeng G, Wenmin Z, Shifeng (2020) Synergistic Effect of Sodium p-perfluorononenyloxybenzenesulfonate and alkanolamide compounding system used as cleanup additive in hydraulic fracturing. Energy Fuels 34(6):7029–7037
- Li Y, Yanling W, Kun W, Foster G, Gangxiao W, Longhao T, Xufeng R (2018) The effect of N-ethyl-N-hydroxyethyl perfluorooctanoamide on wettability alteration of shale reservoir. Sci Rep 8(1):6941
- Zhang Ding S, Min X, Ping P, Renming L, Xiangyang J (2019) Synthesis of novel oil-soluble fluorinated surfactants via Wittig-Horner reaction. Tetrahedron 75(12):1652–1657
- Chen Lijun S, Hongxin Wu, Hongke X, Juping (2011) Synthesis and combined properties of novel fluorinated anionic surfactant. Colloids Surf A 384(1–3):331–336
- Kang Eun-kyung, Young JG, Hwa JS (2018) Lee Byung Min. Synthesis and surface active properties of novel anionic surfactants with two short fluoroalkyl groups. J Ind Eng Chem 61:216–226
- Van Gunsteren Wilfred F, Berendsen Herman JC (1990) Computer simulation of molecular dynamics: methodology, applications, and perspectives in chemistry. Angewandte Chemie International Edition in English 29(9):992–1023
- Hollingsworth Scott A, Dror Ron O (2018) Molecular dynamics simulation for all. Neuron 99(6):1129–1143
- Liu Guokui L, Ruoxue W, Yaoyao G, Fengfeng W, Honglei Y, Shiling, Liu Chengbu (2016) Molecular dynamics simulations on tetraalkylammonium interactions with dodecyl sulfate micelles at the air/water interface. J Mol Liq 222:1085–1090
- Zhang Li L, Zhipei R, Tao Wu, Pan S, Jia-Wei Z, Wei W (2014) Xinping. Understanding the structure of hydrophobic surfactants at the air/water interface from molecular level. Langmuir. 30(46). 13815–13822
- Dong Dengpan K, Samhitha H, Justin T, Marina B, Dmitry (2021) Alexandridis Paschalis. Controlling the self-assembly of perfluorinated surfactants in aqueous environments. Phys Chem Chem Phys 23(16):10029–10039
- Evans Rachel C, Matti K, Niamh W-F, Mario K, Ann T, Burrows Hugh D (2012) Scherf Ullrich. Cationic polythiophene–surfactant self-assembly complexes: phase transitions, optical response, and sensing. Langmuir 28(33):12348–12356
- Boudreau TM, Sibley PK, Mabury SA, Muir DGC, Solomon KR (2003) Laboratory Evaluation of the Toxicity of Perfluorooctane Sulfonate (PFOS) on Selenastrum capricornutum, Chlorella vulgaris, Lemna gibba, Daphnia magna, and Daphnia pulicaria. Arch Environ Contam Toxicol 44(3):307–313
- Liang Xuanqi GMohammedA, Xiaofeng C, Yamani Zain H, Li Nianwu Lu, Hongling J, Guangbin (2011) Facile preparation of magnetic separable powdered-activated-carbon/Ni adsorbent and its application in removal of perfluorooctane sulfonate (PFOS) from aqueous solution. J Environ Sci Health Part A 46(13):1482–1490
- Neese Frank W, Frank B, Ute R, Christoph (2020) The ORCA quantum chemistry program package. J Chem Phys 152(22):224108
- Neese Frank (2012) The ORCA program system. WIREs Comput Mol Sci 2(1):73–78
- Gerit BJ, Christoph B, Andreas H, Stefan G (2018) B97-3c: A revised low-cost variant of the B97-D density functional method. J Chem Phys 148(6):64104
- Jing Xianwu L, Qin C, Xuefeng W, Qingjiang L, Youquan Fu (2022) Molecular dynamics simulation of CO2 hydrate growth in salt water. J Mol Liq 366:120237
- James AM, Teemu M, Roland S, Szilárd P, Jeremy S, Berk CHess, Erik L (2015) GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX. 1. 19–25
- Van David DS, Erik L, Berk H, Gerrit G, Alan M (2005) Berendsen Herman JC. GROMACS: fast, flexible, and free. J Comput Chem 26(16):1701–1718
- Wang Junmei, Wolf Romain M, Caldwell James W, Kollman Peter A (2004) Case David A. Development and testing of a general amber force field. J Comput Chem 25(9):1157–1174
- Bayly Christopher I, Piotr C, Wendy C, Kollman Peter A (1993) A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model. J Phys Chem 97(40):10269–10280
- Lu, Tian (2012) Chen Feiwu. Multiwfn: A multifunctional wavefunction analyzer. J Comput Chem 33(5):580–592
- Martínez Leandro A, Ricardo, Birgin Ernesto G (2009) Martínez José Mario. PACKMOL: A package for building initial configurations for molecular dynamics simulations. J Comput Chem 30(13):2157–2164
- Izadi Saeed O, Alexey V (2016) Accuracy limit of rigid 3-point water models. J Chem Phys 145(7):74501
- Carretero-González R, Kevrekidis PG, Kevrekidis IG, Maroudas D (2005) Frantzeskakis D. J. A Parrinello–Rahman approach to vortex lattices. Phys Lett A 341(1):128–134
- Bussi Giovanni D, Davide, Parrinello Michele (2007) Canonical sampling through velocity rescaling. J Chem Phys 126(1):14101
- Tom D, Darrin Y, Lee P (1993) Particle mesh Ewald: An N⋅ log (N) method for Ewald sums in large systems. J Chem Phys 98(12):10089–10092
- Humphrey William D, Andrew S, Klaus VMD (1996) Visual molecular dynamics. J Mol Graph 14(1):33–38
- Lu Tian C (2022) Independent gradient model based on Hirshfeld partition: A new method for visual study of interactions in chemical systems. J Comput Chem 43(8):539–555
- Lefebvre Corentin R, Gaëtan K, Hassan (2017) Boisson Jean-Charles, Contreras-García Julia, Hénon Eric. Accurately extracting the signature of intermolecular interactions present in the NCI plot of the reduced density gradient versus electron density. Phys Chem Chem Phys 19(27):17928–17936
- Lefebvre Corentin K, Hassan BJ, Charles (2018) Contreras García Julia, Piquemal Jean Philip, Hénon Eric. The independent gradient model: a new approach for probing strong and weak interactions in molecules from wave function calculations. ChemPhysChem 19(6):724–735
- Saeva FD, Breslin DT, Martic PA (1989) The effect of the nature of the lowest unoccupied molecular orbital (LUMO) of some arylmethylsulfonium salt derivatives on photochemical and redox behavior. J Am Chem Soc 111(4):1328–1330
- Silvarajoo Sharmili, Osman Uwaisulqarni M, Kamarudin Khadijah H (2020) Razali Mohd Hasmizam, Yusoff Hanis Mohd, Bhat Irshad Ul Haq, Rozaini Mohd Zul Helmi, Juahir Yusnita. Dataset of theoretical Molecular Electrostatic Potential (MEP), Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital (HOMO-LUMO) band gap and experimental cole-cole plot of 4-(ortho-, meta- and para-fluorophenyl)thiosemicarbazide isomers. Data in Brief 32:106299
- Zhang Jun Lu, Tian (2021) Efficient evaluation of electrostatic potential with computerized optimized code. Phys Chem Chem Phys 23(36):20323–20328