Ab initio Molecular Dynamics Simulation Study of Dissociation Electron Attachment to Lactic Acid and Isomer

Dissociation processes of lactic acid and its isomer formed by low-energy dissociation electron attachment (DEA) in the gas phase are investigated by using ab initio molecular dynamics (MD) simulations. The ab initio MD simulations using an atom-centered density matrix propagation (ADMP) method are carried out to investigate the DEA dissociation process of lactic acid and its isomer. The analysis of the simulated dissociation trajectories of lactic acid and its isomer indicates that the C-C, C-H, and C-O bonds are cleaved within femtoseconds of the simulation time scale in the DEA dissociation process, and the difference in dissociation trajectory depends on the size of the three basis sets. The simulation results enable us to gain insights into the DEA dissociation process of lactic acid and its isomer. In this work, we present a comparative study of the 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets of the DEA dissociation simulation of lactic acid and its isomer. The comparative study results indicate that the 6-311++G(2d,2p) is an excellent basis set for the ADMP trajectory simulation of lactic acid and its isomer in the DEA dissociation process. The natural bond orbital (NBO) analysis is carried out to characterize variation in the charge population and charge transfer accompanied by the C-C, C-H, and C-O bond dissociation processes for lactic acid and its isomer in the ADMP trajectory simulation. ADMP simulation and NBO analysis of the dissociation trajectory is considered an important initial and decisive step in DEA dissociation dynamics for lactic acid and its isomer.

To account for the underlying dynamics in radiation damage with biological systems, a large number of secondary particles, such as low-energy electrons (less than 20 eV), should be considered; the generation of these particles leads to irreversible damage to cellular, DNA nucleobases, organic acids, and amino acids [1][2][3][4][5][6] . Although low-energy electrons are resonant attachments to biological systems, they may cause dissociation, including processes termed as dissociation electron attachment (DEA), to form neutral molecular fragmentation of biological systems [7][8][9] . In DEA, which is a commonly known two-step process, low-energy electrons attach to molecules, forming the short-lived transient negative ions (TNIs) via a Franck-Condon transition. The TNIs dissociate from the final products of fragments of neutral molecules (A) and negative ions (B − ). In general, a fragmentation reaction in the DEA process can be written as follows (for example, the target is diatomic molecules): The intensive DEA research on biological systems (e.g., DNA, proteins, and amino acids) focuses on electron attachment mechanism and molecule dissociation dynamics [10][11][12][13][14][15][16] ; limited studies report the lactic acid dissociation dynamics in the DEA process. Most importantly, lactic acid and its isomer, which are essential products of metabolism, coexist in organisms. The DEA process can produce fragments that affect the process of metabolism, leading to abnormal vital signs. It is therefore not surprising that lactic acid and isomer which low-energy electrons are attached to lactic acid and isomer forming is the target of theoretical work on DEA dissociation process. Consequently, the dissociation dynamics of lactic acid and its isomer on the DEA process in the gas phase must be researched to understand the radiation damage in biological systems. 1

computational Methods
All calculations presented in this work are performed using the Gaussian 09 software package, and the results are visualized through GaussView5 29 . The ground state geometry of lactic acid and isomer are optimized by employing the Becke3-parameter Lee-Yang-Parr (B3LYP) functional of the density functional theory 30 coupled with the 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets. This level of theory, which is highly efficient and has become one of the most preferred theoretical methods of geometry optimization and DEA dissociation process in complicated biomolecules systems, successfully predicts the experimentally observed dissociation process 21 . Vibrational frequency calculations are performed to verify that the optimized lactic acid and its isomer correspond to a local minimum at the B3LYP theory level. The vibrational frequencies are calculated at the levels of the B3LYP theory and 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets using the optimized geometries. No symmetry restrictions are applied for geometry optimization and vibrational frequency calculations.
The ADMP method of ab initio MD simulation is used for the classical dissociation trajectory calculation of lactic acid and its isomer; the method is performed by employing the B3LYP functional of density functional theory and 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets. The structural propagation of ADMP simulation is initiated at the Franck-Condon region of the DEA process, with vertical electron attachment to the neutral target of optimized lactic acid and its isomer. The ADMP simulation is carried out to 500 femtoseconds (fs) with a time interval 0.1 fs and is sampled with the initial internal energy 1.0 eV. A total simulation of 5000 steps is run for each trajectory. In our ADMP calculations, no restriction is applied for the dissociation trajectory calculations, so all the dissociations cannot be presented in a finite number of trajectories. The Gibbs free energy for lactic acid and its isomer dissociation processes are calculated at the levels of the B3LYP theory and 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets in the gas phase. Natural bond orbital (NBO) analyses, which provide insights into the DEA dissociation process, are run using the optimized lactic acid and its isomer in this work and at the B3LYP level of density functional theory in conjunction with the 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets.

Results and Discussion
Optimization geometries of lactic acid and its isomer. Geometry optimization of lactic acid and isomer is a crucial step in the theoretical research of the ADMP dynamics trajectory simulation. The ground state of geometries lactic acid and its isomer are optimized using the B3LYP theory with the 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets. Figure 1 presents the optimized geometries, and Table 1 lists our optimized geometrical parameter results, including bond lengths, angles, and dipole moments, for the ground state lactic acid and its isomer. Analyzing the results of the C-C bond length of the lactic acid and its isomer, the values of the 6-31 + G(d,p) basis set are 1.529 Å and 1.528 Å, respectively. These numbers differ from the bond length observed for the 6-311++G(2d,2p) and Aug-cc-pVDZ basis sets, in which the C-C bond length are 1.527 Å and 1.526 Å; and 1.524 Å and 1.525 Å, respectively. The optimized C-H bond length of lactic acid and its isomer are 1.093 Å and 1.095 Å for the 6-311++(2d,2p) basis set and 1.094 Å and 1.093 Å for the Aug-cc-pVDZ basis set, respectively, and they are slightly shorter than the results obtained for the 6-31 + (d,p) basis set. Notably, the cases of the optimized C-O and O-H bonds with the three basis sets for lactic acid and isomer are same as that for the other optimized bonds. Similar observations can be obtained concerning the optimized bond angle. The6-31 + G(d,p) basis set yields the highest optimized bond angle results among the three basis sets. The 6-31 + G(d,p) basis set, which yield the least values in the three basis sets, elongats bond lengths in geometry optimization for lactic acid and its isomer due to the inclusion of diffuse and polarization functions. Lastly, the Aug-cc-pVDZ basis set results from geometry optimizations are remarkably similar to those obtained for the 6-311++G(2d,2p) basis set. The dipole moment µ in Table 1 displays that the values are larger than 2.8 D with the three different basis sets. According to previous research 21, 31 , a large dipole moment indicates the formation of valence-bound anion and the existence of strong electrostatic dipole fields, benefitting the capture of low-energy electron in the DEA process. However, these dipole moments perform poorly in the dissociation trajectory simulation. The 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets are employed to eliminate interferences in dipole-bound interaction for the ADMP dynamics trajectory simulation.
The harmonic vibrational frequencies of lactic acid and its isomer, as reported in Tables 2 and 3, are calculated at the B3LYP level for the 6-31 + G (d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets. Lactic acid and its isomer exhbit minima corresponding to their potential energy surfaces, where magnitudes of all the predicted vibrational frequencies are real positive values. No imaginary frequencies are detected for lactic acid and its isomer. As shown in Tables 2 and 3, the C-C bond stretching vibrational frequencies of lactic acid and its isomer with the 6-311++G(2d,2p) and Aug-cc-pVDZ basis sets are 787.69, 787.75, 811.66, and 811.54 cm −1 , respectively. Similar results show that the C-H bond stretching vibrational frequencies of lactic acid and its isomer with the 6-311++G(2d,2p) and Aug-cc-pVDZ basis sets are also predicted to be of low values at 1822.21 and 1821.77; and    23 and 326.72 km mol −1 , respectively, which are the highest and may serve as experimental fingerprints for identifying lactic acid and its isomer. Compared with the given harmonic vibrational frequencies results of lactic acid and its isomer with the three basis sets, the results by the 6-31 + G(d,p) basis set exhibit distinct differences from the findings obtained by the 6-311++G(2d,2p) and Aug-cc-pVDZ basis set. Consequently, the distinct discrepancy obtained using the three basis sets at the B3LYP theory level indicates that the DEA dissociation trajectories of lactic acid and its isomer should be different. The C-O bond vibrational mode of lactic acid is in stretching vibrational mode, whereas that of the isomer is in wagging vibration mode. This finding implies that the DEA dissociation processes of lactic acid and isomer should also differ. , and Aug-cc-pVDZ basis sets, several interesting points rapidly emerge. First, the C-C bond stretches rapidly after additional cycles of vibration, and the C-C distance elongates linearly with the evolution of time, indicating the direct cleavage of the C-C bond; there is not backed into a bonded state in ADMP trajectory simulation process. Second, the 6-31 + G(d,p) basis set result shows significant differences in dissociation time and trajectory simulation. The present simulation results reveal that the C-C bond of lactic acid and isomer dissociation time and dissociation processes are similar with the 6-311++G(2d,2p) and Aug-cc-pVDZ basis sets. Figures 4(b) and 5(b) illustrate the simulated time evolution of the C-H bond with the ADMP trajectories corresponding to those of lactic acid and isomer. For lactic acid and its isomer, the C-H bond distance stretches rapidly around 170 fs, and as time proceeds, the C-H bond starts to cleavage. The distant H atom is ~4 Å away from the C atom. Then, the H atom gradually approaches the C atom until the former reaches a bonded state. Given the difference in size of the three basis sets, the C-H bond between the dissociation time and simulated trajectories shows significant differences. However, the C-H bond dissociation trajectories of lactic acid and its  Table 3. Frequencies (cm −1 ) and IR intensities (km mol −1 ) of the C-C and C-H bond stretching vibration modes and the C-O and O-H wagging vibrational modes for the isomer.   www.nature.com/scientificreports www.nature.com/scientificreports/ ADMP simulation process, as shown in Fig. 5(c). The trajectory simulation results indicate that the oscillated curve is more complex, similar to the O-H bond, and that vibration mode of the C-O bond produces an effect on its dissociation in the trajectory simulation process. The result with 6-311++G(2d,2p) basis set is highly similar with that of the Aug-cc-pVDZ basis set.

ADMp simulation of lactic acid and isomer dissociation process. The typical snapshots in
The simulated trajectories of lactic acid of the O-H bond as a function of time evolution are shown by the black, red, and blue lines in Fig. 4(d). Our simulation results for the three basis sets show that the O-H bond is not cleaved in the ADMP simulation for the DEA dissociation process. The simulated trajectories of the O-H bond rapidly present an oscillated curve. Here, the present results suggest that the wagging vibration mode of the O-H bond may affect its dissociation in the DEA dissociation process. R. Janečková et al. 33 have proposed a similar mechanism to explain how the O-H bond vibration mode influences the DEA dissociation process of small biomolecules. The vibrational mode is observed in the DEA of small biomolecules 34 ; this mode also plays an important role in the dissociation process. Furthermore, a similar trend is observed when the O-H bond results from the isomer simulated with the three basis sets as presented in Fig. 5(d). For the isomer, the O-H bond is not cleaved in the ADMP simulation for DEA dissociation process. The 6-31 + G(d,p) basis set shows a large discrepancy between the 6-311++G(2d,2p) and Aug-cc-pVDZ basis sets for the O-H bond result of the lactic acid and its isomer.
According to the simulation results, the three basis sets show evident distinction in simulating the dissociation trajectory for lactic acid and its isomer. Especially, the result of the 6-31 + G(d,p) basis set is the most different with the other basis sets. Recently, an assessment theoretical research had shown that the 6-31G + (d,p) basis set had obtained results that agreed with experimental and theoretical investigations on ADMP simulation 22 . However, the 6-31G + (d,p) basis set without polarization functions is unsuited for lactic acid and isomer during ADMP simulation. The Aug-cc-pVDZ basis set is a correlation-consistent basis set, which improves the accuracy but increases computational time. For this reason, the 6-311G++(2d,2p) basis set is the most appropriate and used for ADMP dynamics trajectory simulation of the DEA dissociation process. Our ADMP dynamical simulation results indicate that the C-C, C-H, and C-O bond dissociations of lactic acid and its isomer are the most probable DEA dissociation processes, whose animated dissociation trajectory is used as reference for the lactic acid DEA experimental research. The ADMP dynamical simulation yields accurate and highly efficient computational method of researching molecular dissociation process of DEA.
The Gibbs free-energy calculation is widely used to confirm ADMP dissociation processes of lactic acid and isomer. The Gibbs free-energy along dissociation processes is calculated by the 6-31 + G(d,p), 6-311++G(2d,2p) and Aug-cc-pVDZ basis set, as shown in Figs. 6 and 7, respectively. According to these two figures, the Gibbs free-energy diagrams predict that the C-H bond is the most active in dissociation processes, clearly highlighting the C-H bond is easily broken in dissociation processes from a thermodynamic perspective. For lactic acid, the nBo analysis of the dissociation process of lactic acid and its isomer. The calculation of the NBO method is the most prevalent method of charge population and charge transfer analysis, which are the foremost applications of quantum chemistry calculation in biomolecule systems. Figures 8 and 9 show the charge population data calculated with NBO analysis during the ADMP simulations of lactic acid and isomer dissociation. Notably, the results of charge population are distinct for the three basis sets for lactic acid and its isomer, suggesting that the variations in charge population are accompanied by the C-C, C-H, and C-O bond dissociation processes.
At the beginning of simulation for Fig. 8(a), the charge populations of the C-C bond reach 49.13%, 51.17%, and 50.8% localization toward the C atom from the 6-31G + (d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets, respectively. Around 370 fs, the dissociation process is short-lived, the C-C bond is cleaved, and the charge population is changed, whereas the values of charge population of the C-C bond localization toward the C atom are the lowest. The trend of charge population rises again, until the charge population of the C-C bond approaches 47.22%, 47.31%, and 47.35% localization toward the C atom, which are little equivalent to the prime simulation with the 6-31G + (d,p), 6-311++G(2d,2p), and Aug-CC-pVDZ basis sets, respectively. Similar results can be found for the C-H bond localization toward the C atom in Fig. 8(b). Around 170 fs, the C-H bond cleaved, and the charge population changes, whereas the values of the C-H bond localization toward the C atom total 63.44%, 61.32%, and 62.43% with the 6-31G + (d,p), 6-311++G(2d,2p), and Aug-CC-pVDZ basis sets, respectively. At 500 fs, the values of the C-H bond localization toward the C atom reach 62.75%, 61.12%, and 61.91%, which are less than the prime simulation with the 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-CC-pVDZ basis sets, respectively. Figure 8(c) depicts the C-O bond charge population localization toward the C atom with the three basis sets for lactic acid. As shown in Fig. 8(c), the charge population evidently decreases to the simulation time of 150 fs, and the values of the C-O bond localization toward the C atom amount to 35.2%, 34.72%, and 34.62% with the 6-31G + (d,p), 6-311++G(2d,2p), and Aug-CC-pVDZ basis sets, respectively. Remarkably, the difference in charge population of the three basis sets is accompanied by the C-O bond dissociation process. A similar research on biomolecules has previously been demonstrated 14 .
For the isomer in Fig. 9(a), the C-C bond charge population localization toward the C atom values reach 52.15%, 52.23%, and 52.28% with the 6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ basis sets, Figure 6. Gibbs Free-energy diagram (kcal mol −1 ) along to dissociation processes of lactic acid obtained with the 6-31 + G(d,p), 6-311++G(2d,2p) and Aug-cc-pVDZ basis set. www.nature.com/scientificreports www.nature.com/scientificreports/ respectively, for the initial ADMP simulations. The most important variation is observed for the C-C bond cleavage, whose charge population localization toward the C atom reaches 47.02%, 47.05%, and 47.04% with the 6-31 + G(d,p), 6-311++G(2D,2P), and Aug-cc-pVDZ basis sets, respectively. These results indicate that any variations in charge population are affected by the chemical bond changes between lactic acid and its isomer. Figure 9(b) illustrates the C-H bond charge population localization toward the C atom of isomer; the variations trend is similar with that of lactic acid.
Comparing the results of NBO analysis charge population for lactic acid and its isomer, differences in the three studied basis sets, including the influence of charge population along with ADMP dissociation processes, are notable, especially when using the 6-311++G(2d,2p) and Aug-cc-pVDZ basis sets. Our calculations indicate that the use of NBO analysis charge population is reasonable with large basis sets, such as 6-311++G(2d,2p) and Aug-cc-pVDZ. From the results of previous research, the charge population of NBO analysis may be a better  www.nature.com/scientificreports www.nature.com/scientificreports/ candidate for larger basis sets with more diffuse functions 13 . Considering the size of this research system and computational time, the 6-311++G(2d, 2p) basis set is the best choice for charge population of NBO analysis.

conclusions
In the present paper, the dissociation dynamics of lactic acid and its isomer in gas phase for the DEA process is investigated by using ab initio MD simulations combined ADMP method. The ADMP simulations coupled with the B3LYP theory of the 6-31G + (d,p), 6-311++G(2d,2p), and Aug-cc-pDVZ basis sets are employed to optimize the ground state geometries and obtain dipole moments and harmonic vibrational frequencies of lactic acid and its isomer. The ADMP dynamics trajectory simulation results indicate that the C-C, C-O, and C-H bond result from the cleavage of lactic acid and its isomer within femtoseconds of the simulation time scale in the DEA dissociation process, and the difference in dissociation trajectories depends on the size of the three basis sets and vibration mode of the chemical bond. ADMP simulation is a qualitative analysis of the dynamic dissociation trajectory in the DEA process for lactic acid and its isomer, and it can be helpful in performing experimental research. The analysis of NBO calculation results of charge population and second-order perturbation theory for lactic acid and its isomer indicate the charge transfer between the C-C, C-O, and C-H bonds, and this result confirms dissociation in the DEA process from a different perspective. Comparison between the ADMP and NBO analysis results reveal that the 6-311++G(2d,2p) is an excellent basis set for lactic acid and isomer theoretical calculations of the dissociation dynamics of DEA processes.
On-going works from our group aim at the DEA experiments of lactic acid, in light of the conclusions drawn from this study. Finally, we believe that the research on lactic acid and its isomer and dissociation dynamics of DEA can be useful for understanding the radiation damage with biological systems, in particular, to guide scientists in conducting lactic acid DEA experiments in the future. Table 6. NBOs with second-order perturbation stabilization energy E(2) (kcal mol −1 ) analysis of the C-O bond for lactic acid. Results are obtained at the B3LYP/6-31 + G(d,p), 6-311++G(2d,2p), and Aug-cc-pVDZ levels.