A two level approach to predict minimum energy structures of higher hydrated clusters of oxalic acid
Graphical abstract
Most stable structure of hydrated oxalic acid, (COOH)2·12H2O.
Atom centered Density Matrix Propagation (ADMP) molecular dynamic simulation is applied to find suitable input for geometry optimization following first principle based DFT procedure.
Introduction
Studies of molecular clusters have gained popularity as it helps in bridging the gap between a single molecule and the bulk material [1], [2]. Growth of systems from molecule to bulk is expected to be reflected in many properties of the molecular clusters. The shaping of molecular clusters is influenced by intermolecular interactions such as hydrogen bonding, π-π interactions, van der Waals interactions etc. With the advent of high resolution spectroscopy, experimental measurements of molecular clusters are now possible. The study of molecular interactions, structure and properties of clusters has wide range of implications in physical, chemical and biological areas [3], [4], [5]. Complementing experimental measurements with ab initio calculations are useful in exploring structure-property correlations and energetics of molecular clusters. However, application of post Hartree-Fock methods, incorporating electron correlation, like Møller–Plesset second order (MP2) theory and coupled cluster singles and doubles with perturbative triples (CCSD(T)), for the calculation of large molecular clusters are often beyond the scope due huge computational cost. The CPU time to study water cluster with eight water molecules at CCSD(T)/aug-cc-pVDZ level of theory has been reported to be 1820 min [6]. Moreover, non-covalent interactions give much flexibility to the systems, making ab initio geometry optimization of molecular clusters very challenging [7]. The most common algorithm for finding the equilibrium geometry of a molecular system applying electronic structure theory is Newton-Raphson method. The problem with this procedure is that the geometry converges to the nearest local minimum. Hence, the choice of initial guess structures is very important. The number of possible initial input geometries increases with the size of the system. The huge computational cost limits the number of initial guess structures that can be tried for large clusters. However, there is a possibility of missing important input structures.
Different approaches have been reported to study theoretically the structure and properties of large size molecular clusters. They include semi-empirical methods, reduced scaling methods and fragmentation methods. Of these, the fragmentation based methods are quite popular [8]. Molecular tailoring approach (MTA), a fragmentation based method has been proposed for estimating molecular electrostatic potential (MESP) of zeolites [9]. The large system is fragmented to smaller systems in MTA. The properties of the original system are obtained by combining the corresponding properties of all the smaller systems. This can affect the accuracy of the energy obtained for the system, though efforts have been made to overcome these errors [6]. However, there is a chance to miss an important structure as this one has also initial value problem.
Recently, significant efforts are also put in stochastic search techniques and these can be separated into two broad categories. One deals with a single solution and during evolution the solution is subjected to be updated according to certain criteria as wanted eg. Simulated Annealing (SA) technique. The other types of stochastic search techniques deal with multiple solutions and these solutions need to be handled in parallel. Genetic Algorithm (GA), Parallel Tempering techniques etc. belong to this category. However, accuracy of these techniques depends on interaction potentials and often these potentials are either empirical or not available in the literature [10]. Thus, these methods are not so popular in calculation of molecular clusters.
Herein, we present a simple method to ensure a thorough scan of the potential energy surface. We take an example of large hydrated clusters of oxalic acid. The geometries of hydrated clusters of oxalic acid, (COOH)2·nH2O, n = 9–12, clusters are studied, first applying cost effective MD simulations at lower level of theory. The low energy equilibrium conformers obtained from the MD simulations are fine tuned applying more accurate level of theory following DFT based electronic structure theory. Low molecular weight dicarboxylic acids are present in the atmosphere, produced from automobile exhausts, pyrolysis of organic compounds etc. These have been reported to aid cloud formation [11]. There have been previous studies on oxalic acid-water clusters [12], [13], [14], [15]. But to the best of our knowledge, higher hydrates of oxalic acid ((COOH)2·nH2O, n = 9–12) have not been yet reported. The geometries of most stable conformers of (COOH)2·nH2O, n = 9–12, clusters are presented here.
Section snippets
Theoretical methods
Initial input guess geometries are generated applying Atom centered Density Matrix Propagation (ADMP) MD model, at B3LYP/6-31G(d) level of theory [16]. ADMP based molecular dynamics is an extended Lagrangian approach that makes use of Gaussian basis functions and propagates the density matrix. Under this framework, fictitious masses for the electronic degrees of freedom are set to be small enough that thermostats are not required for good energy conservation in the simulations. This also allows
Results and discussion
Of all the structures obtained from the present ADMP-MD simulations considering micro-canonical ensemble, a set of structures are selected based on total energy of the hydrated cluster calculated at B3LYP/6-31G(d) level of theory. The set of geometries consists of the most stable one and those are within 0.008 a.u. (5.0 kcal/mol) of energy of the most stable structure. This set of structures is further optimized applying a more accurate level of theory, namely, ωB97XD/aug-cc-pVDZ. Hessian
Conclusion
We present an alternative simple route to study the geometries of large-sized molecular clusters ensuring that the global minimum is not missed out. Equilibrium structures of hydrated oxalic acid clusters, (COOH)2·nH2O, n = 9–12 are reported. Calculations of minimum energy structures are carried out first applying ADMP MD simulations for initial screening. All the equilibrium structures having relative energy greater than the minimum energy structure by 5.0 kcal/mol thus obtained are further
CRediT authorship contribution statement
Parvathi Krishnakumar: Conceptualization, Investigation, Writing - original draft. Dilip Kumar Maity: Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
Authors wish to thank computer centre for generous computer time. P. K. thanks Homi Bhabha National Institute for research fellowship
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2022, ChemosphereCitation Excerpt :Varying from the oxalic acid system, no suppression of TC degradation was observed as the concentration of l-tartaric acid increased. It is because that the acidity of l-tartaric acid is weaker (pKa1 = 2.98) (Oh et al., 2016) than that of oxalic acid (pKa1 = 1.23) (Krishnakumar and Maity, 2020), the reaction to reduce MnO2 to Mn2+ could not be easily carried out in the MnO2/l-tartaric acid system under the experimental conditions. And therefore, no inhibiting effect but promoting effect on TC degradation was observed as the concentration of l-tartaric acid increased.