Theoretical Researches On Binding Modes and Stability of Hydrogen Bonds Between Uracil and Formic Acid


 The hydrogen bond formation with formic acid would affect the complementary pair of bases between uracil and adenine, but the binding modes and spectral properties of hydrogen bonds are still obscure. Density functional theory and time-dependent density functional theory were applied to investigate the intermolecular hydrogen bonds between uracil and formic acid. The reduced density gradient (RDG), bond lengths and vibration absorption frequencies revealed that the most probable uracil-formic acid (U-FA) interaction mode formed in the position c of FA and the site 1 of U, that is, the mode 1c. The theoretical parameters in excited state complexes manifested that the variety of hydrogen bond configurations led to different degrees of strengthening or weakening of molecular interaction. In the implicit solvent (water), the formations of O-H∙∙∙O in the uracil-formic acid complexes were promoted obviously. These theoretical studies would positively affect the researches of life science and medicinal chemistry.


Introduction
Hydrogen bonds play an important role in living organisms, participating in various life processes, such as gene and protein structure formation [1][2][3], enzyme reactions [4] and biomolecular interaction [5]. Hydrogen bond (X-H•••Y), a non-covalent interaction, can be regarded as a kind of donor-acceptor orbital interaction from a certain perspective [6,7]. In biological systems, hydrogen bonds are an important factor in stabilizing biologically active molecules (such as DNA and proteins). In the dynamic system, the intermolecular hydrogen bonds with the low bond energy are easily promoted to break and form continuously [8][9][10]. Therefore, the researches on the interaction of hydrogen bonds between molecules have received extensive attention.
Uracil, a unique nucleic acid base in RNA, can form hydrogen bond with adenine to participate in transcription and translation, and then maintain inheritance, immune and other life activities. Various studies have reported that uracil can bind to water, ketones and other small molecules through hydrogen bonds [11][12][13][14][15][16][17], affecting the structure and properties of uracil. Formic acid, with the least steric hindrance in fatty acids, exists in the muscles, blood and excreta of the human body. The high probability of hydrogen bond formation of formic acid would affect the complementary pair of bases between uracil and adenine, thus blocking RNA replication and destroying the reproduction of viruses, which is of great signi cance to life science and pharmaceutical chemistry [18][19][20][21]. However, the effect of hydrogen bonds on the binding modes, stability and spectral properties between uracil and formic acid in different states seems still ambiguous.
To solve these issues, density functional theory (DFT) and time-dependent density functional theory (TD-DFT) are used to systematically investigate the hydrogen bond binding modes between uracil and formic acid. The behaviors of hydrogen bond formation between two molecules are theoretically revealed with the mode features, electronic spectra and vibrational absorption spectra. In addition, since uracil is a strong absorber of ultraviolet rays [22], the effect of excited uracil-formic acid complexes on intermolecular hydrogen bonding is also discussed. changes of intermolecular hydrogen bonds in different states.
The reduced density gradient (RDG) function combined with sign(λ2)ρ(r) was applied to distinguish hydrogen bond interactions from other weak interactions [26,27]. The calculation formula of RDG could be expressed as: Where ▽, ρ and |▽ρ(r)| are the gradient operator, the electron density and the modulus of the electron density gradient, respectively.
The calculation method of hydrogen-bond binding energy, proposed by Lu et al. [28], was based on the le containing the wave function generated after the optimization of the hydrogen bond complexes, and then using Multiwfn 3.7 [29] to obtain the electron density at the bond critical point (BCP) of the hydrogen bond to be investigated, and nally substituting it into the following formula: 2 Where x, y are the electron density at the bond critical point (BCP) and the hydrogen-bond binding energy, respectively.
Atoms in Molecules (AIM) analysis was performed using Multiwfn 3.7 [29] combined with VMD 1.9.4 software [30] to study the nature of the interaction between molecules.
The in uence of water as implicit solvent on the intermolecular hydrogen bonds formed by the U-FA complexes was considered by using the DFT method with the same functional and basis sets in the integral equation formalism polarizable continuum model (IEFPCM).

Results And Discussion
For the convenience of description, the different binding sites of U as 1, 2, 3, and of FA as a, b, c (Fig S1), were marked to nine U-FA complexes. Our calculated bond length results of isolated U and FA were basically consistent with those reported by Epifanovsky et al. [31] and Buemi [32], respectively. The optimized structures of nine U-FA complexes in the S 0 state were represented in Fig. 1. The dihedral angle data (Table S1) proved that the S 0 state structure of nine U-FA complexes were plane.
In order to visually understand the non-covalent bond interactions, Fig. 2 [33].
The hydrogen-bond binding energy of nine U-FA complexes in the S 0 state arranged by energy intensity (Fig. 3)   For a better understanding of the properties of the U-FA complexes, the electron density topological analysis of the optimized modes in the S 0 state were carried out by Multiwfn 3.7 [29] and VMD 1.9.4 [30]. The topological analysis diagrams of the U-FA complexes were listed in Fig. 5. Table 1 summarized the values of the electron density (ρ), the Laplacian of electron density (▽ρ 2 ) and the energy density (H) at the BCP. The values of ρ at the BCP of all U-FA complexes were positive, revealing that they were all closed-shell interactions [39]. The large the value of ρ at the BCP revealed the short bond distance and the strong bonding ability [40].  Electronic spectra and frontier molecular orbitals The electron excitation energy, oscillator strength of isolated uracil and U-FA complexes were represented in Table 2 (the major orbital contributions were listed in Table S2). The calculated electronic absorption spectra result of isolated uracil and formic acid were basically in line with those reported by Improta et al. [44] and Li et al. [45], respectively. The maximum oscillator strength of isolated uracil and U-FA complexes were both at S 2 state, indicating that U-FA complexes were more likely to be in the S 2 state. In S 2 state, the absorption of complexes formed by site 2 with formic acid blue shifted, while formed by site 3 with formic acid had red shifts. The modes 1a and 1b red shifted and mode 1c blue shifted in the S 2 state.
The S 2 state of the U-FA complexes were mainly contributed to HOMO->LUMO (about 90%) (Table S2). Figure 6 showed the frontier molecular orbital diagram of the mode 1c (other modes were presented in Fig. S3). In S 2 state of the U-FA complexes, the main transition process from HOMO to LUMO was π→π*. In addition, the electrons of the HOMO and LUMO orbitals of the U-FA complexes were mainly distributed in the uracil, which symbolized the U-FA complexes were locally excited [34]. The frontier molecular orbital diagram (Figure 6 and Fig. S3) illustrated that the charge distribution variation during the transition from HOMO orbital to LUMO orbital would affect the polar atoms of the uracil. So, we realized that the intermolecular hydrogen bond would change in the S 2 state [34], which would be discussed in the next section. Based on the previous analysis, we had discovered that relatively stable U-FA complexes were formed by the position c of FA with uracil and the intermolecular hydrogen bonds would be varied in the S 2 state. Therefore, TD-B3LYP-D3(BJ)/6-31+G(d,p) was performed to optimize the structure in the S 2 state of the three complexes including modes 1c, 2c, and 3c.
The basic geometric structure of three U-FA complexes in the S 2 state was presented in Fig. 7. The dihedral angle data (Table   S3) showed that the modes 1c and 2c were basically plane, while the mode 3c was distorted. From the RDG isosurface maps and RDG scatter plots (Fig. 7), it was intuitively observed that only the 3c con guration changed. In the S 0 state, the mode 3c In order to visually observe the variations of the intermolecular hydrogen bonds of the U-FA complexes after being excited, the histogram of the hydrogen-bond binding energy in the S 2 and S 0 states was presented in Fig. S4. The increased hydrogenbond binding energy absolute value of 2c', 3c and 2c revealed that the intermolecular hydrogen bond of them strengthened. The strength of hydrogen bond of 1c and 1c' reduced. These results were completely consistent with the bond length analysis.
The electronic spectrum revealed that the local excitation of the U-FA complexes occurred on uracil rather than formic acid. So, the vibration mode of the formic acid was more easily in uenced by the hydrogen bond rather than the electronic excitation [34], which meant that the frequency changes of the C=O and O-H groups of formic acid in the S 0 state and the S 2 state can be compared to determine the changes in hydrogen bonds.
The vibrational absorption spectra of U-FA complexes in different electronic states were showed in Fig. 8.

Solvent effect
The in uence of water as implicit solvent on the intermolecular hydrogen bond of U-FA complexes was considered. The basic geometries in the water were not signi cantly different from that in the gas phase (Fig. S5). The dihedral angle data denoted that the nine geometries were basically plane (Table S4). Some phenomena were found by comparing the bond lengths in the gas phase and in the water (Fig. S5). The water could promote the formation of intermolecular hydrogen bonds with red-shifted wavelengths, while water could disturb the formation with the blue-shifted wavelengths (Fig. S6). In mode 1c, due to the in uence of water, the formation of Data Availability All relevant data are given in the supporting information le.
Competing Interests The authors have no relevant nancial or non-nancial interests to disclose. The frontier molecular orbital diagram of the mode 1c (Top) The basic geometric structure and partial bond length (Middle) RDG isosurface map (isosurface: 0.5) and (Bottom) RDG scatter plot of modes 1c, 2c and 3c in S 2 state at TD-B3LYP-D3(BJ)/6-31+G(d,p) levels