Ab Initio Study of the Complexes of Aspartic Acid and n Molecules of Water, n = 1 and 2, Formed by Hydrogen Bonds

doi:10.21203/rs.3.rs-2493336/v1

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Ab Initio Study of the Complexes of Aspartic Acid and n Molecules of Water, n = 1 and 2, Formed by Hydrogen Bonds

https://doi.org/10.21203/rs.3.rs-2493336/v1

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published 11 Mar, 2023

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Hydrogen bonds (HB) influence the conformational preferences of biomolecules and their optical and electronic properties. The objective of this work is to study some structures and the S₁← S₀ electronic transitions of aspartic acid (ASP) and complexes formed by HB between ASP-(H₂O)_1,2 in the gas phase. To do this, the DFT and TD-DFT methods were used, using the B3LYP functional with six different basis sets. Interactions between the carboxylic groups of ASP with water molecules, forming cyclic structures with two HB, resulted in more stable and less polar complexes, than other conformers with formed HB between water and the NH₂ group. It was observed that there is a relationship between the deviation in the UV-Vis absorption band of the ASP and the stabilization/destabilization of the S₁ state to the S₀ of the complexes. The electrostatic destabilization of the S₁ state and interactions of water with the HOMO orbital caused a blueshift in the ASP absorption band, while the electrostatic stabilization of the S₁ state and interactions with the LUMO caused a redshift. But in some cases, as it was observed on 1:1 complex ASP-W2, this analysis may not be precise due to the small change in ΔE.

DFT

TD-DFT

Aspartic Acid

Hydrogen bond

Interactions

Complexes

Water

Hydrogen bonds (HB) are usually described as R-X-H···Y, where R is a molecule or group bonded to a proton-donor group, XH, that interacts with another atom or molecular fragment, Y, a proton-acceptor, in which X and Y are atoms with different electronegativities [1]. Although this interaction is not as strong as a covalent bond, HB can provoke charge transfers between the proton-donor and the proton-acceptor, provoking changes in electronic density and dipolar momentum of complex, affecting different processes, from conformational structures and hydration properties to biological and physiological processes of biomolecules [2–5] .

In the last few years, the directional interaction of water molecules, mainly due to HB, has received considerable attention in theoretical studies in the gas phase [6, 7] and experimental studies [8, 9]. The gas phase studies provide a way to understand the intermolecular and hydration interactions between biomolecules, such as between neurotransmitters (NTs), and water molecules [6].

Among the NTs, L-aspartic acid (2-amine-butanedioic acid, C₄H₇NO₄, ASP) is a precursor of biological molecules, such as proteins and nucleic acids [10], and participates in the synthesis of glutamic acid and glycine, the tricarboxylic acid cycle [11], hormone synthesis, RNA synthesis, rises testosterone and growth hormone (GH) levels, and causes resistance to fatigue and depression [12, 13]. ASP is a non-essential amino acid that acts as an excitatory neurotransmitter in the human brain.[14] Excess of ASP may be a reason for Lou Gehrig's disease and is related to early dementia of the Alzheimer's type [11].

ASP has two carboxylic groups, COOH, and a primary amine, NH₂, that ease the interactions with other biomolecules [15–17]. The theoretical study of the interactions between ASP and water molecules has shown fundamental roles in several processes. Water molecules can act as catalysts in deamidation reactions of ASP and glutamic acid (GLN) in proteins and peptides [18, 19]. Also, they participate in the non-enzymatic formation reaction of succinimide from ASP residues [16]. As it presents different functional groups and easily forms inter- and intramolecular HBs, ASP can be considered a prototype for understanding the behavior of NT when interacting by HB with other substances. Interactions with one and two water molecules can be a starting point for understanding these interactions.

Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TD-DFT), using the B3LYP functional, are very efficient for studying these kinds of compounds and HB complexes in the ground and excited states [20, 21]. Several theoretical studies on isolated L-ASP and the formed complexes with water, in both gas and liquid phases, have been done using both DFT and TD-DFT formalisms [15, 22–24]. He, Fan, and Tang (2010) studied the energetic contributions and structural changes caused by intramolecular HB between the atoms of the functional groups of ASP and found 122 stable geometries.[25] Chen and Lin (2007) reported 139 canonical conformers of isolated ASP in the gas phase, at B3LYP/6-311 + + G(d) level of theory, and zwitterionic conformers in an aqueous solution.[15] They also studied the complexes of ASP with one and two molecules of water at MP2/6-311 + + G(d,p) level of theory [15]. However, these authors did not perform calculations with other basis sets and hybrid functionals and did not study electronic transitions involving ASP and water complexes.

The objective of this work is to study the structural and energetical characteristics of ASP and the complexes ASP-(H₂O)_n, for n = 1 and 2, as well as the electronic transitions S₁← S₀, using DFT and TD-DFT formalisms with the B3LYP functional and six different sets of bases. The article is organized as follows. Section 2 presents the methodology. Sections 3 and 4 are devoted to the results, discussion and the conclusions.

In order to find the different conformers of isolated L-ASP and the L-ASP-(H₂O)_n complexes (n = 1 and 2), the landscapes of the ground state surface were explored, using the DFT formalism, with the B3LYP functional, and the 6–31 + + G(d,p)[26], and 6-311 + + G(d,p)[26], D95++(d,p) and D95V++(d,p) basis sets [27]. The optimized geometries were obtained with the cc-pVDZ and cc-pVTZ basis sets [28–30], considering the polarization effects and electronic correlation, without symmetry constraints. The calculations were performed with the Gaussian 09 software package [31]. The visualization of the molecular geometries and figures were made with the Visual Molecular Dynamics (VMD) software [32].

The energies of the optimized geometries on the S₀ state were calculated with the cc-pVTZ basis set and corrected with the Zero Point Energy (ZPE), which can be approximated to

$$ZPE=\frac{1}{2}{\sum }_{i}{h\nu }_{i},$$

where ${\nu }_{i}$ are the frequencies of the normal modes of the complex, and h is the Planck constant [33]. Also, to get an approximation to the true $ZPE$, a scale factor of 0.9889 [34] was used in the correction of the energy of the isolated ASP and the complexes with the cc-pVTZ base set:

$${E}_{ZPE}= E + 0.9889 ZPE.$$

The binding energy between ASP and water molecules was calculated as

$${\Delta }{E}_{BE}={E}_{ZPE}\left(complex\right)-[{E}_{ZPE}\left(ASP\right) \times$$

$$n{E}_{ZPE}\left({H}_{2}O\right)]$$

where ${E}_{ZPE}\left(complex\right)$, ${E}_{ZPE}\left(ASP\right)$ and ${E}_{ZPE}\left({H}_{2}O\right)$ are the corrected energies, and n = 1, 2 [35, 36].

The binding energies defined in this way are affected by the basis set superposition error (BSSE) [36–38], which can be estimated using the counterpoise procedure (CP) available on Gaussian 09 package [36, 38–40]. The CP correction is an approximate but satisfactory method for correcting basis set deficiencies in the calculations of the monomers [39, 41]. This method was extensively discussed in the literature [36, 38–40], having arguments in favor and against these corrections. A discussion of these different approaches is beyond the scope of this article. The corrected binding energy is

$${\Delta }{E}_{BE}^{C}={E}_{ZPE}\left(complex\right)-{[E}_{ZPE}\left(ASP\right)+$$

$$n{E}_{ZPE}\left({H}_{2}O\right)]+BSSE$$

The electronic transitions, S₁←S₀, and their properties were calculated using the TD-DFT formalism at B3LYP/cc-pVTZ level, using the optimized geometries for S₀ with the same basis set [42] for the isolated ASP and the ASP-(H₂O)_n complexes. In order to analyze the vertical transitions of isolated ASP and the ASP-(H₂O)_n complexes, the electrostatic energy was calculated as

$$\left|{\Delta }{E}_{Coulomb}\right|=\sum _{i}^{{H}_{2}O}\sum _{j}^{ASP}\frac{{q}_{i}{q}_{j}}{{r}_{ij}}$$

where q_i are the net atomic charges of H₂O molecules and q_j are the net charges of the atoms of ASP molecule, r_ij is the distance between the atoms. The values of $\left|{\Delta }{E}_{Coulomb}\right|$ are expressed in eV [36, 43]. To provide a simple interpretation of the results, the charge distribution per atom and basis function were obtained from the Mulliken population analysis [44]. There are several models to predict individual atomic charges and charge transfers in complexes formed by HB. However, the Mulliken population analysis is probably the best-known model and still one of the most used, especially for its simplicity [45, 46]. Differences in $\left|{\Delta }{E}_{Coulomb}\right|$ of the S₀ and S₁ states obtained from the Mulliken analysis proved to be similar to those obtained with the Natural Populational Analysis (NPA) [47]. However, the comparison between the different analyses is beyond the objectives of this work.

The obtained structure of isolated ASP at B3LYP/cc-pVTZ calculations is shown in Fig. 1. In this structure, there is an intramolecular HB between N1–H11···O4 ($105.79$°, $r(\text{H}11···\text{O}4) = 2.29 Å$, $r(\text{N}1-\text{H}11) = \text{1,01}$ Å) and N1–H10···O7 ($\text{108,46}^\circ$, $r(\text{H}10···\text{O}7) = \text{2,55}$ Å, $r(\text{N}1-\text{H}10) = \text{1,01}$Å). This structure corresponds to the most stable conformer of ASP reported by Chen and Lin in 2007, and for He, Fang, and Tang in 2010 [15, 25].

1:1 Complexes

We have explored the geometry of the ASP-(H₂O)_n conformers for n = 1 and 2 molecules of water. Trying several initial configurations, five 1:1 complexes, named ASP-W1, ASP-W2, ASP-W3, ASP-W4 and ASP-W5 were found, whose structures are shown in Fig. 2, are shown, the red dot-line represents the HB. In ASP-W1, water interacted with the O4 and H16 atoms of the $\alpha$-carboxyl group. In ASP-W2, water interacted with the O7 and H15 atoms of the $\beta$ -carboxyl group. In ASP-W3, water interacted only with N1 atom of NH₂ group. In ASP-W4 water interacted with H10 atom of NH₂ group, and with O7 of $\beta$-carboxyl group. In ASP-W5 water interacted between H11 atom of NH₂ group and O4 atom of $\alpha$-carboxyl group.

The calculated minimum energies, $E$, $ZPE$, ${E}_{ZPE}$, and $\varDelta {E}_{BE}^{C}$ (with cc-pTVZ), as well as the dipolar moment and rotational constants for isolated ASP and the different 1:1 complexes are shown in Table 1. The energies of the complexes are in Hartree, and to facilitate the analysis, $\varDelta {E}_{BE}^{C}$ they are in kJ mol^− 1. In Table S1, the bond distances, bond angles, and dihedral angles are also shown for isolated ASP and 1:1 complexes, calculated at B3LYP/cc-pVTZ level.

The most stable 1:1 complex is ASP-W1, which has ${E}_{ZPE}=-588.8624$ Hartree (Table 1). ASP-W1 has a cyclic structure with two HB, one involving the atoms O9–H16···O17 (158.77°, $r(\text{H}···\text{O}) = 1.76$Å) and the other, the atoms O17–H19···O4 ($136.96^\circ ,$ $r(\text{H}···\text{O}) = 2.00$ Å). This structure is similar to that obtained for the most stable conformer of glycine-H₂O by Aiken and Gordon in 2006 [48]. Chen and Lin (2007) [15] also observed that in the lower energy structures of the ASP-H₂O complexes, the water molecules interact near the $\alpha$-carboxyl group (Fig. 2).

In the case of ASP-W2, the ${E}_{ZPE}$ obtained was from $-588.8619$ Hartree (Table 1). In this conformer, a cyclic structure is formed with one HB between O8–H15···O17 ($138.05^\circ ,$ $r(\text{H}···\text{O}) = 1.99$Å) and other HB between O17–H19···O7 atoms ($158.43^\circ ,$ $r(\text{H}···\text{O}) = 1.77$ Å) (Fig. 2).

In ASP-W3 there is a single HB between O17-H19···N1 atoms (161.12°, r(H···N) = 1.97 Å), with ${E}_{ZPE}=-588.8499$ Hartree. In this structure, there is not a possibility to form a cyclic structure (Fig. 2). In ASP-W4, a cyclic structure is formed with an HB between O17–H19···O7 atoms ($163.97$°, $r\left(\text{H}···\text{O}\right)= 1.93$ Å) on other HB between N1–H10···O17 = ($143.25$°, $r\left(\text{H}···\text{O}\right)= 2.20 Å$) atoms. The energy for this complex is ${E}_{ZPE}= -588.8483$Hartree (Table 1).

Table 1

Results of minimum energies ($E$), zero-point energy ($ZPE$), and energy corrected by the ZPE (${E}_{ZPE}$, in Hartree), the Basis Set Superposition Error (BSSE^CP, in Hartree), the Hydrogen bond energy corrected by ZPE and BSSE (${\Delta }{E}_{BE}^{C}$, in kJ/mol^− 1, rotational constants (in GHz), and dipole moment (in Debyes) of ASP and ASP–(H₂O)₁ 1:1 complexes, at B3LYP/cc-pVTZ level of theory. For the calculation of ${\Delta }{E}_{BE}^{C}$, the H₂O E_ZPE was considered, in the S₀ state, equal to -76.4388 Hartree, at the B3LYP/cc-pVTZ level.
Bases	Parameters	ASP	ASP-W1	ASP-W2	ASP-W3	ASP-W4	ASP-W5
6–31 + + G(d,p)	E	-512.3565	-588.8083	-588.8076	-588.8041	-588.8019	-588.7997
6-311 + + G(d,p)	E	-512.4871	-588.9626	-588.9620	-588.9583	-588.9567	-588.9544
D95++(d,p)	E	-512.4522	-588.9224	-588.9218	-588.9182	-588.9160	-588.9138
D95V++(d,p)	E	-512.4509	-588.9211	-588.9204	-588.9168	-588.9146	-588.9124
cc-pVDZ	E	-512.3582	-588.8058	-588.8052	-588.7925	-588.7892	-588.7883
cc-pVTZ	E	-512.5294	-589.0090	-589.0085	-588.9963	-588.9943	-588.9926
	ZPE	0.123102	0.1482	0.1482	0.14815	0.1477	0.1475
	E_ZPE	-512.4077	-588.8624	-588.8619	-588.8499	-588.8483	-588.8470
	BSSE^CP	—	0.003466	0.003483	0.004434	0.003086	0.003323
	${\Delta }{{E}}_{{B}{E}}^{{C}}$ (kJmol^− 1)	—	-32.65	-31.29	+ 2.71	+ 3.38	+ 7.41
	A(GHz)	3.3806	2.9394	3.2437	1.6353	1.4795	1.9116
	B (GHz)	0.9010	0.5447	0.5270	0.7722	0.8105	0.6487
	C (GHz)	0.7734	0.4839	0.4810	0.6825	0.6153	0.5135
	\|$\mu$\| (D)	3.36	2.41	2.89	0.82	1.78	2.07

In ASP-W5, one HB is formed between O17–H19···O4 atoms ($158.05^\circ$, $r(\text{H}···\text{O}) = 1.97$ Å) and other between N1–H11···O17 atoms ($160.27$°, $r(\text{H}···\text{O}) = 2.20$ Å). Even one molecule of water is interacting with the $\alpha$-carboxyl, ${E}_{ZPE}=-588.8470$Hartree, which is the least stable 1:1 complex. In comparison, the formation of a hydrogen bond with one H₂O and $\text{N}{\text{H}}_{3}^{+}$ and $\text{C}\text{O}{\text{O}}^{-}$ from zwitterionic ASP is the most stable conformer obtained by SCRF methods, at MP2/6-311 + + level, performed by Chen and Lin (2007) [15]. The distance N1–H11···O17 observed in ASP-W5 is similar to that obtained for N1–H10···O17 in ASP-W4, but the distance O17–H19···O(H₂O) is longer in ASP-W5 than that obtained in ASP-W4.

The decreasing order of stability for the 1:1 complexes is: ASP-W1 > ASP-W2 > ASP-W3 > ASP-W4 > ASP-W5 (Fig. 3). The HB interaction energies also follow this trend, ASP-W1 has ${\Delta }{E}_{BE}^{C}=-32.62$ kJ mol^− 1, and ASP-W2 has ${\Delta }{E}_{BE}^{C}=-31.29$ kJ mol^− 1. The other three more energetic conformers, ASP-W3, ASP-W4 and ASP-W5, have the weaker HB with positive values of ${\Delta }{E}_{BE}^{C}$, $2.71$, $3.38$, and $7.41$ kJ mol^− 1, respectively. The participation of the N-H group as the acceptor of H in ASP-W4 and ASP-W5 provokes a more unstable interaction, in comparison when the N atom acts as a proton donator as in ASP-W3.

The formed cyclic structures between H₂O and $\alpha$-carboxyl in ASP-W1 and ASP-W2 keep a planar structure, with dihedral angles of $- 4.90$^° and $0.17^\circ$, respectively. This also results in greater stability for these complexes. But when H₂O interact with the NH₂ group and with the O atom from $\alpha$- or $\beta$ -carboxyl group, the O–H bond in water is out-of-plane, forming non-planar structures with dihedral angles of $-116.32^\circ$ and $119.78$° for ASP-W3, $-32.50$^°, and $4.08^\circ$ for ASP-W4, $56.36^\circ$ and $-3.81^\circ$ for ASP-W5 (Table S1).

The lack of planarity observed in ASP-W4 and ASP-W5 conformers and the formation of barely one HB in ASP-W3 could contribute to the instability of the HB systems. This instability has been observed in performed calculations by Kagra et al. (2020) [49]. The calculations of HB energies in 1:1 complexes of amino acids with water (such as leucine and glycine), indicates that a planar cyclic structure between the COOH group and water is the most stable geometry in all levels of theory [50, 51].

There are no relevant changes in distances and angles of the other bonds on the ASP molecule, but dihedral angles (Table S1) varied significantly due to the influence of HB that causes the rotation of the NH₂ group, on the carbon atoms of the chain of ASP and carbonyl groups. This behavior has also been observed in other molecules [16, 52]. In general, the most altered dihedral angles were between the atoms that water interacted with in each complex. The 1:1 complexes that showed the greatest changes in the dihedral angles on the ASP region were ASP-W3 and ASP-W4 complexes. Minor changes were observed in ASP-W2 and ASP-W1 complexes.

1:2 Complexes

The calculated minima energies, $E$, $ZPE$, ${E}_{ZPE}$, and ${\Delta }{E}_{BE}^{C}$, as well as the dipolar moment and rotational constants for isolated ASP and the different 1:2 complexes, are shown in Table 2. In Table S2, the bond distances, bond angles, and dihedral angles are also shown for isolated ASP and ASP −(H₂O)₂ complexes, calculated at B3LYP/cc-pVTZ.

Trying several initial configurations, three lower energy 1:2 complexes were found. In the three 1:2 complexes, there are cyclic structures formed between each H₂O molecule and ASP (Fig. 4). As shown in Fig. 3, the most stable 1:2 conformer is ASP-2Wa, with ${E}_{ZPE}= -665.3078$ Hartree (Table 2). In this conformer, H₂O interacts with the $\alpha$-carboxyl group, forming a cyclic structure with two HB, between the atoms O9–H16···O17 ($158.74$°, $r(\text{H}···\text{O}) = 1.75$ Å) and the atoms O17–H19···O4 ($137.70^\circ$, $r(\text{H}···\text{O}) = 1.99$ Å). The other H₂O molecule also forms a cyclic structure with the $\beta$-carboxyl group, forming two HB between the atoms O8–H15···O20 ($158.30^\circ$, $r(\text{H}···\text{O})= 1.77$ Å) and the atoms O20–H22···O7 ($139.05^\circ$, $r(\text{H}···\text{O})=1.97$ Å).

The ASP-2Wb conformer is more unstable than ASP-2Wa, with ${E}_{ZPE}=-665.3020$ Hartree (Table 2). One H₂O interacts with $\alpha$-carboxyl group, forming two HB, O9–H16···O17 ($158.71$°, $r(\text{H}···\text{O}) = 1.75$ Å) and O17–H19···O4 ($137.40^\circ$, $r(\text{H}···\text{O}) = 1.99$ Å). The second H₂O interacts with NH₂ group and $\beta$-carboxyl group, doing other two HB, N1–H10···O20 ($146,64^\circ$, $r(\text{H}···\text{O}) = 2.18$ Å) and O20–H22···O7 ($164.21^\circ$, $r(\text{H}···\text{O}) = 1.92$ Å). The water molecule shows a preference to form HB with the O atom of COOH, in comparison with the N atom of the imidazole group in histidine [51].

The most unstable 1:2 conformer is ASP-2Wc, with ${E}_{ZPE}=-665.3001$ Hartree (Table 2, Fig. 3). One H₂O interacts with O4 and NH₂ group, forming two HB similar to ASP-W5 conformer, O17–H19···O4 ($158.52^\circ$, $r(\text{H}···\text{O}) = 1.97$ Å) and N1–H11···O17 ($159.92$^°, $r(\text{H}···\text{O}) = 2.20$ Å). The other H₂O interacts with $\beta$-carboxyl, similar to ASP-W2, O8–H15···O20 (158.7°, r(H···O) = 1.76 Å) and O20–H21···O7 (158.52°, r(H···O) = 1.99 Å). This structure is similar to that obtained by Chen and Lin (2007) for zwitterionic ASP and two water molecules at MP2/6-31G + + level [15]. Even forming four HB with two cyclic structures, as in the case of ASP-2Wa, the HB involving the NH₂ group presented a high instability.

The N–H···O bonds, presented in ASP-W4, ASPW5, ASP-2Wb, and ASP-2Wc complexes, are similar to those found in lateral chains of ASP and arginine (ARG) in proteins that bind to DNA [53], and those interactions between ASP and the primary amine groups of guanidine from ARG, which have HB distances around 2.00 and 2.10 Å, and bond angles between $149.00^\circ$ and $153.00^\circ$[54].

Table 2

Results of minimum energies ($E$), zero-point energy ($ZPE$), and energy corrected by the ZPE (${E}_{ZPE}$, in Hartree), the Basis Set Superposition Error (BSSE^CP, in Hartree), the Hydrogen bond energy corrected by ZPE and BSSE (${\Delta }{E}_{BE}^{C}$, in kJ/mol^− 1, rotational constants (in GHz), and dipole moment (in Debyes) of ASP and ASP–(H₂O)₂ 1:2 complexes, at B3LYP/cc-pVTZ level of theory. For the calculation of ${\Delta }{E}_{BE}^{C}$, the H₂O E_ZPE was considered, in the S₀ state, equal to -76.4388 Hartree, at the B3LYP/cc-pVTZ level.
Bases	Parameters	ASP	ASP-2Wa	ASP-2Wb	ASP-2Wc
6–31 + + G(d,p)	E	-512.3566	-665.2593	-665.2533	-665.2509
6-311 + + G(d,p)	E	-512.4871	-665.4374	-665.4318	-665.4294
D95++(d,p)	E	-512.4522	-665.3920	-665.3859	-665.3835
D95V++(d,p)	E	-512.4509	-665.3905	-665.3845	-665.3820
cc-pVDZ	E	-512.3582	-665.2440	-665.2356	-665.2344
cc-pVTZ	E	-512.5294	-665.4792	-665.4727	-665.4709
	ZPE	0.1231	0.1734	0.1727	0.1727
	E_ZPE	-512.4077	-665.3078	-665.3020	-665.3001
	BSSE^CP	—	0.007061	0.006603	0.006842
	${\Delta }{{E}}_{{B}{E}}^{{C}}$ (kJmol^− 1)	—	-40.53	-28.51	-20.89
	A(GHz)	3.3806	2.8692	1.4284	1.7004
	B (GHz)	0.9010	0.3535	0.4827	0.4152
	C (GHz)	0.7734	0.3277	0.4023	0.3491
	\|$\mu$\| (D)	3.36	1.27	2.70	2.06

The interaction energy for the ASP-2Wa, ASP-2Wb and ASP 2Wc conformers is ${\Delta }{E}_{BE}^{C}= -40.53 \text{k}\text{J} {\text{m}\text{o}\text{l}}^{-1}$, $-28.51 \text{k}\text{J} \text{m}\text{o}{\text{l}}^{-1}$ and $-20.89 \text{k}\text{J} \text{m}\text{o}{\text{l}}^{-1}$, respectively. Therefore, ASP-2Wa is the 1:2 most stable conformer, followed by ASP-2Wb and ASP-2Wc (Table 2, Fig. 3). The interaction of one water molecule with NH₂ group and O7 (in ASP-2Wb), and NH₂ group and O4 (in ASP-2Wc) provoked an energetic destabilization.

In the 1:2 conformers, there are more planar structures between H₂O molecules and COOH groups, resulting in dihedral angles between $-4.33^\circ$ and $9.26^\circ$ (Table S2). Even with the influence of the water molecule interacting with the other COOH group, the interactions with the NH₂ group, and the O atoms from COOH groups in ASP-2Wb e ASP-2Wc, there are non-planar structures with O-H bond from a water molecule. The changes in the dihedral angles on $\alpha$ or $\beta$-carboxyl groups, and the C and NH₂ atoms are higher in ASP-2Wb than those in ASP-2Wa and ASP-2Wc.

The HB formed by two water molecules interacting simultaneously with the $\alpha$ and $\beta$-carboxyl groups in ASP-2Wa provoke minors changes in the dihedral angles on ASP than those observed in ASP-W1, ASP-W2, and ASP-2Wb. The differences in the dihedral angles next to the $\beta$ -carboxyl group in ASP-2Wb are higher than those observed in ASP-W1, but the changes on the dihedral angles next to NH₂ and $\beta$-carboxyl are lower in ASP-2Wb in comparison to ASP-W4 and ASP-W5.

Electronic Properties

Tables 1 and 2 show the absolute value of the dipole moment of the isolated ASP and of the 1:1 and 1:2 complexes, respectively. The absolute value of the dipole moment, $\left|\mu \right|,$ of isolated ASP is 2.07 D (Tables 1 and 2). The decrescent order of polarity on the 1:1 and 1:2 complexes is ASP-W5 ($3.36$ D), ASP-2Wb ($2.70$ D), ASP-W3 ($2.89$ D), ASP-W4 ($\text{2,41}$ D), ASP-2Wc ($2.06$ D), ASP-W1 ($1.78$ D), ASP-2Wa ($1.27$ D), and ASP-W2 ($0.82$ D). In all the cases, where one of H₂O molecules interacts with NH₂ group, or between NH₂ and O4 or O7 atoms, are more polar than isolated ASP. The conformers where there are interactions between H₂O molecule(s) and COOH group are less polar than isolated ASP and the other complexes. The 1:1 complex where H₂O interacts with the $\beta$-carboxyl is less polar than isolated ASP, and on 1:2 complex, where H₂O molecules interact with each COOH group is also less polar. Even with the interaction of one water molecule with $\alpha$-carboxyl group in ASP-2Wb, the interaction of H₂O with NH₂ group results in a more polar 1:2 complex.

The Mulliken charges in the isolated ASP and 1:1 and 1:2 complexes, obtained at B3LYP/cc-pVTZ level, are shown in Table S3 and S4, in the S₀ state, and in Table S5 and S6 in the S₁ state (electronic transition). Some changes are observed, especially in the regions where water interacts. The presence of H₂O molecules provokes an increase on the negative charge of the N1 atom in the complexes compared to isolated ASP (Fig. S1). In ASP-W1 and ASP-W2, the lower increase is observed in Table S3, indicating that the interaction of the water molecule with the $\beta$-carboxyl group increases the negative charge on N1.

Electronic Transitions

When a molecule absorbs energy, in the UV and Visible region of the spectra, one electron is promoted from one orbital of low energy to another orbital of high energy [55]. The energy of absorbed electromagnetic radiation is equal to the difference of energies between the involved orbitals, $\varDelta E$ which is the minimum energy to excite the molecule [56]. In general, the electronic transition S₁←S₀ most likely to occur is from the Highest Occupied Molecular Orbital, HOMO, to the Lowest Unoccupied Molecular Orbital, LUMO, which are denoted frontier orbitals [55]. In this situation, there is an increase of the electronic density of the atoms involved in the LUMO orbital and decrease in the electronic density on the atoms that participate of the HOMO orbital [56]. The HOMO and LUMO orbitals of isolated ASP and 1:1 and 1:2 complexes, obtained at TD-DFT/cc-pVTZ level of calculations are shown in Fig. S2 and S3.

On Table 3 the values of $\varDelta E$, wavelength, λ, and the oscillator strength, f, for the isolated ASP and the respectively 1:1 and 1:2 complexes obtained at TD-DFT/cc-pVTZ are shown. In Fig. 5, the shifts on $\varDelta E$ for the 1:1 and 1:2 complexes are also shown. For isolated ASP, $\varDelta E = 5.4101 \text{e}\text{V}$ ($229.17$ nm), in good agreement with the obtained experimental ($5.6698$ eV) and theoretical ($5.3979$eV) results by Alam and Ahmad (2012) [22]. This $\varDelta E$ value for isolated ASP is higher than it was experimentally obtained on anhydrous crystal of L-aspartic acid by Silva et al. [57], which it is was $5.020$ eV.

As a result of electrostatic interactions and the rearrangement of electron densities and charge transfers between the monomers, when two molecules approach each other in the complex formed by HB, there is a change in the energy levels of the HOMO and LUMO orbitals and, consequently, in the $\varDelta E$ of the biomolecule [58]. Because of this, there may be an increase in $\varDelta E$ and decrease in wavelength (blue shift), or a decrease in ∆E and increase in wavelength of the UV-Vis absorption band of the biomolecule (red shift). If HB is strengthened in an S₁ state, the energy level of this excited state of the complex will be less energetic than that of the monomer, resulting in a decrease in $\varDelta E$ relative to the isolated monomer (red shift) [59, 60]. In contrast, if HB is weakened in the S1 state, the energy level of this excitation state of the complex will be higher than that of the monomer, resulting in an increase in $\varDelta E$ relative to the isolated monomer [59, 60].

The 1:1 conformers, ASP-W1, ASP-W4 and ASP-W5, showed a red-shift of the values of $\varDelta E$, compared to isolated ASP, of $0.02720$, $0.2320$, and $0.2552$eV respectively (Fig. 5). ASP-W2 and ASP-W3 conformers show a blue-shift of $0.0028$ and $0.4004$ eV respectively, compared to that transition on isolated ASP. The three 1:2 conformers show red-shifts, compared to $\varDelta E$ of isolated ASP, of $0.0072$ eV (ASP-2Wa), $0.2620$ eV (ASP-2Wb) and $0.2294$ eV (ASP-2Wc).

The electronic density and, consequently, the electrostatic interactions determine the nature of the observed shifts on complexes formed by HB [61–63]. In calculations on the complexes of formic acid and water molecules, the observed red-shift is due to the increase of the electrostatic interactions in the S₁ state, and the blue-shifts are due to the increase of the repulsive forces on S₁ state compared to the S₀ state [47].

In order to analyze the changes of the electrostatic interactions on S₀ and S₁ states of the complexes, the coulombic interaction energy is calculated, $\left|{\Delta }{E}_{Coulomb}\right|$ (Table 3). In Fig. 5 the values of $\left|{\Delta }{E}_{Coulomb}\right|$ of S₀ and S₁ for 1:1 and 1:2, at TD-DFT/cc-pVTZ level are shown. In the conformers ASP-W1, ASP-W4, ASP-W5, ASP-2Wa, ASP2Wb e ASP-2Wc, it is observed a red-shift in the $\varDelta E$, which corresponds to the increase of the $\left|{\Delta }{E}_{Coulomb}\right|$ of $0.06620$eV, $0.1709$ eV, $0.1059$ eV$, 0.01570$ eV, $0.1722$ eV, and $0.08370$ eV, respectively, with the Mulliken charges (Fig. 5, Table 3). The excited states of these conformers are more stable compared to the excited state of isolated ASP. This stabilization of S₁ state on HB complexes is also observed in other systems [64]. It has already been demonstrated for other systems that the differences in the $\left|{\Delta }{E}_{Coulomb}\right|$ of the S₀ and S₁ states obtained with the Natural Populational Analysis (NPA) present the same trends as those obtained with the Mulliken analysis [47].

In the conformers ASP-W2 e ASP-2Wa, minor differences have been obtained on the values of S₁, corresponding to the values of $\left|{\Delta }{E}_{Coulomb}\right|$. In the most unstable 1:1 conformers on S₀ state, ASPW4 and ASP-W5, the greatest decrease in the values of $\varDelta E$, compared to $\varDelta E$ of ASP, were obtained, corresponding to the greatest increase in the values of $\left|{\Delta }{E}_{Coulomb}\right|$ (Fig. 5). In ASP-W3, which shows the greatest increase on $\varDelta E$, there was an electronic destabilization of $0.05061$ eV on S₁ state, respect to S₀ state. In ASP-W3 the water molecule just interacts with the atoms on HOMO, but does not interact with LUMO atoms, that leads to the electrostatic destabilization of S₁ state (Fig. S3).

In summary, if there is a rise on the value of $\varDelta E$ of the complex, compared to that of isolated ASP, there will be an electrostatic destabilization on S₁ state of the complex, as shown on ASP-W3. When the values of $\varDelta E$ are small, the values of $\left|{\Delta }{E}_{Coulomb}\right|$ are also small, and it would be hard to predict the stabilization or destabilization, of S₁ state only regarding the analysis of the coulombic energy.

Table 3

Electronic transitions S₁←S₀ data of isolated ASP and 1:1 and 1:2 complexes, at B3LYP/cc-pVTZ level of calculation. ΔE(in eV) is the energy difference between the HOMO-LUMO energy, λ is the transition wavelength, f, is the force of the oscillator, and $\left|\varDelta {E}_{Coulomb}\right|$ ( in eV) is the modulus of energy variation of Coulomb interactions for the S₀ and S₁ states of the complexes.
Parameter	ASP	ASP-W1	ASP-W2	ASP-W3	ASP-W4	ASP-W5	ASP-2Wa	ASP-2Wb	ASP-2Wc
${\Delta }\text{E}$	5.4101	5.3829	5.4129	5.8105	5.1779	5.1549	5.4029	5.1481	5.1807
${\lambda }$ (nm)	229.17	230.33	229.05	213.38	239.45	240.52	229.48	240.83	239.32
$f$	0.0044	0.0066	0.0059	0.0017	0.0035	0.0057	0.0068	0.0047	0.0059
$\left\|\varDelta {E}_{Coulomb}\right\|$	—	0.158 (S₀) 0.224 (S₁)	0.161 (S₀) 0.186 (S₁)	0.104 (S₀) 0.0537(S₁)	0.156 (S₀) 0.327(S₁)	0.125 (S₀) 0.231 (S₁)	0.405 (S₀) 0.421 (S₁)	0.353 (S₀) 0.525 (S₁)	0.328 (S₀) 0.412 (S₁)

The results show that the change of electrostatic energy on the states S₁ and S₀ of the ASP-(H₂O)_1,2 complexes could be useful to predict or justify the deviations of the UV-Visible band absorption compared to that of isolated ASP, but in some cases, as in the case of ASP-W2, this analysis could be incomplete, being necessary to analyze additional factors that are also present in these systems [47]. The frontier orbitals showed to be useful for the analysis of the motives of electrostatic stabilization (or destabilization) of the excited state of the complexes.

The presented results show that the HB are preferably formed by the water molecule and the $\alpha$-carboxyl group of ASP, and in the case of 1:2 complexes, the interactions are between the carboxyl groups of ASP and water molecules. In the interactions with the NH₂ group or O7 and O4 atoms of COOH groups, the HB are more unstable and the complexes are more polar and energetic.

Due to the electrostatic stabilization of S₁ state, there is a decrease of $\varDelta E$ (compared to that of isolated ASP) leading to an increase of the absorption wavelength in the UV-Visible region. The higher deviation on $\varDelta E$, and subsequently, the rise in the coulombic interaction energy on S₁ state is observed for the more unstable complexes. If there is an increase in the attractive interactions between the atoms, leading to a red-shift on the values of $\varDelta E$.

In ASP-W3 there is an increase of the value of $\varDelta E$, a blue-shift, compared to $\varDelta E$ of isolated ASP. The repulsive interactions rise provoking the destabilization of the S₁ state. In the case of ASP-W2, there is an electrostatic stabilization of S₁ state, but there is a blue-shift on the value of $\varDelta E$. In this conformer, water molecule interacts with the atoms of the complex on LUMO, to provoke an increase of the electronic density in those atoms (state S₁).

The comparison of the electrostatic interaction energy between the S₀ and S₁ states are useful to analyze the shifts on the UV-Visible absorption spectra of the complexes formed by HB, but in some cases, this analysis could be non-conclusive.

In future works, the optimized structures of ASP and the ASP(H₂O)_1,2 complexes on the S₁ state will be done, in order to examine the structural and energy changes due to the influence of formed HB.

Acknowledgments

We gratefully acknowledge the Laboratório de Modelagem Molecular, GTI-CES and UFCG-CES for the help and support in this work. The authors thank Secretaria de Estado do Distrito Federal (SEEDF) and Fundação de Apoio e Pesquisa do Distrito Federal (FAPDF).

Funding

This work was supported by the Molecular Modeling Laboratory, GTI-CES and Centro de Educação e Saúde of Universidade Federal de Campina Grande, CES-UFCG.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Author Contributions

AM Lima and GF Velardez performed the computer simulations and analysis of the results. AM Lima produced the figures under the supervision of NF Frazão and GF Velardez. AM Lima wrote the first draft of the manuscript. All authors corrected, commented, and approved this version of the manuscript.

Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Ab Initio Study of the Complexes of Aspartic Acid and n Molecules of Water, n = 1 and 2, Formed by Hydrogen Bonds

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1:1 Complexes

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Parameter	ASP	ASP-W1	ASP-W2	ASP-W3	ASP-W4	ASP-W5	ASP-2Wa	ASP-2Wb	ASP-2Wc
\({\Delta }\text{E}\)	5.4101	5.3829	5.4129	5.8105	5.1779	5.1549	5.4029	5.1481	5.1807
\({\lambda }\) (nm)	229.17	230.33	229.05	213.38	239.45	240.52	229.48	240.83	239.32
\(f\)	0.0044	0.0066	0.0059	0.0017	0.0035	0.0057	0.0068	0.0047	0.0059
\(\left\|\varDelta {E}_{Coulomb}\right\|\)	—	0.158 (S₀) 0.224 (S₁)	0.161 (S₀) 0.186 (S₁)	0.104 (S₀) 0.0537(S₁)	0.156 (S₀) 0.327(S₁)	0.125 (S₀) 0.231 (S₁)	0.405 (S₀) 0.421 (S₁)	0.353 (S₀) 0.525 (S₁)	0.328 (S₀) 0.412 (S₁)