Quantitative assessment of intramolecular hydrogen bonds in neutral histidine

Abstract

Experimentalists recently characterized the difficulty in isolating gaseous histidine in its neutral form. To understand the factors which stabilize neutral histidine, the intrinsic nature of the intramolecular hydrogen bonding networks in the four most stable histidine conformers was investigated via density functional theory combined with the local vibrational mode analysis originally introduced by Konkoli and Cremer, quantum theory of atoms in molecules, non-covalent interaction analysis, and natural bond orbital population analysis. Our results show a positive correlation between intramolecular hydrogen bond strength and structural stability, where the presence of the $\hbox {O}{-}\hbox {H}\cdots \hbox {N}_{\alpha }$ bond type is a major factor.

1 Introduction

Histidine (HIS) is one of the twenty essential amino acids relevant to biological organisms [1] and involves innate processes such as tissue growth and muscle repair [2, 3]. HIS consists of an imidazole (Im) ring and a side chain with branched amine ($\hbox {NH}_{2}$) and carboxyl ($\hbox {CO}_{2}\hbox {H}$) groups, which can switch from neutral ($\hbox {R}{-}\hbox {NH}_{2}$ and $\hbox {R}{-}\hbox {CO}_{2}\hbox {H}$) to zwitterionic forms ($\hbox {R}{-}\hbox {NH}_{3}^+$ and $\hbox {R}{-}\hbox {CO}_{2}^-$), depending on physiological conditions such as pH and temperature [4]. Hence, HIS acts as both proton acceptor and donor in biochemical reactions [5]. Additionally, Im-N ($\hbox {N}_{\delta }$) can be de-protonated ($\varepsilon$ tautomer) or protonated ($\delta$ tautomer), allowing for inter- and intramolecular hydrogen bonds (HBs). Functionality in HIS relates to its three-dimension conformation [6], which in turn depends on non-covalent interactions (NCIs) [7]. Experimental and theoretical studies suggest that the conformational preference of HIS is primarily influenced by the stabilizing presence of intramolecular hydrogen bonds (IMHBs) [8, 9], but to our best knowledge this has not been quantified.

HIS exists predominantly as a zwitterion, where it gains extra stabilization energy through interactions with polar environments [10]. The zwitterion exists over a wide pH range in liquid and solid phases [11]. Due to its high melting point, low vapor pressure, and thermal instability, neutral HIS has proven difficult to isolate and experimentally characterize. $\varepsilon \hbox {I} \hbox {I}_{a}$ (Fig. 1) is the most stable/common in nature [12, 13] and was recently isolated and characterized in the gas phase for the first time using laser ablation techniques [14], which has opened the door for research aimed at better understanding the factors involved in stabilizing this neutral form.

In this work, we present for the first time a quantitative analysis of IMHB strength in the four most stable HIS conformers ($\varepsilon \hbox {I} \hbox {I}_{a}$, $\varepsilon \hbox {I} \hbox {I}_ b$, $\delta \hbox {I} \hbox {I}_{a}$, and $\delta \hbox {I}_{a}$) with the aim of answering the following questions:

• (i) Which theoretical (DFT) method gives the best description of IMHBs?

• (ii) Which types of IMHBs are possible in neutral HIS?

• (iii) How strong are the IMHBs in neutral HIS?

• (iv) What factors stabilize neutral HIS?

• (v) Why is $\varepsilon \hbox {I} \hbox {I}_{a}$ more stable than $\delta \hbox {I} \hbox {I}_{a}$? What factors stabilize $\varepsilon \hbox {I} \hbox {I}_{a}$?

2 Computational methods

The major reason why IMHBs in HIS have not been quantified so far has been the lack of a reliable intrinsic bond strength measure. Detailed information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes are generally delocalized in polyatomic molecules because of electronic and mass coupling. [15,16,17,18] Therefore, the corresponding normal mode frequencies and force constants are not suitable bond strength descriptors [19]. Konkoli, Cremer, and co-workers provided a solution to this problem utilizing a mass-decoupled analogue of Wilson’s equation of vibrational spectroscopy leading to local vibrational modes (LVMs) that are free from any mode–mode coupling [20,21,22,23,24]. Each local mode is associated with an internal coordinate $q_n$ (e.g., bond length r) which drives the local vibration and a corresponding local mode frequency $\omega ^a$ and local mode force constant $k^a$. Zou and co-workers demonstrated that there is a one-to-one relationship between the local and normal vibrational modes, that can be verified by an adiabatic connection scheme (ACS), providing the physical fundament for the LMVs.[25] Zou and Cremer further proved that the local stretching force constant $k^a$ is directly related to the intrinsic strength of a bond, which qualifies $k^a$ as unique quantitative bond strength measure based on vibrational spectroscopy.[26] So far, the local mode analysis has been successfully applied to characterize covalent bonds [26,27,28,29,30,31,32] and weak chemical interactions such as halogen [33,34,35,36], chalcogen  [37,38,39], pnicogen  [40,41,42], and tetrel interactions [43] as well as intra- and intermolecular hydrogen bonding in various forms and systems.[44,45,46,47,48,49,50]

To simplify the comparison of local stretching force constants $k^a$, we generally convert $k^a$ values into bond strength orders (BSO n) most chemists are more acquainted with [28, 29, 44, 51] via a generalized Badger rule [27, 52] which states that the strength of a bond correlates with the local force constant in the form of a power relationship:

$$\begin{aligned} {\hbox {BSO}~n = a(k^a)^b}. \end{aligned}$$

(1)

The constants a and b can be determined from 2 reference molecules with defined BSO n and known $k^a$ values and the assumption that $k^a$ = 0 corresponds to n = 0. In this work, we used as references $\hbox {HF}$ (BSO $n = 1$ and $k^a = 9.350$ mdyn/Å) and $\hbox {HF}_{2}^-$ (BSO $n = 0.5$ and $k^a = 0.852$ mdyn/Å). This led to $a=0.524$ and $b=0.289$. We determined the covalent character of the IMHBs via the Cremer–Kraka criterion [53, 54] for covalent bonding which is based on the local energy density $H(\mathbf {r})$

$$\begin{aligned} H(\mathbf {r}) = G(\mathbf {r}) + V(\mathbf {r}), \end{aligned}$$

(2)

where $G(\mathbf {r})$ is the kinetic energy density (positive, destabilizing) and $V(\mathbf {r})$ is the potential energy density (negative, stabilizing). Taken at the bond critical point $\mathbf {r}_b$ of the electron density $\rho (\mathbf {r}$) [55, 56] between two bonded atoms, $H(\mathbf {r}_b) < 0$ points to a covalent interaction, while $H(\mathbf {r}_b) > 0$ indicates an electrostatic interaction.

To find a practical and reliable computational method for describing weak IMHBs, the influence of dispersion corrections was evaluated using (i) the semiclassical $\hbox {C}_6$-based schemes of Grimme’s D2 [57], D3 [58], and D3(BJ) [59] dispersion corrections in combination with B3LYP [60] and (ii) the range-separated, dispersion-corrected $\omega$B97X-D [61] functional. We also compared Pople’s 6-311$++$G(d,p) [62] triple-$\zeta$ augmented basis set with polarization and diffuse functions with Dunning’s aug-cc-pVTZ [63] correlation-consistent triple-$\zeta$ basis set of the same quality and features [64]. B3LYP-D3(BJ)/aug-cc-pVTZ turned out to be the most accurate level of theory for this work. The aug-cc-pVTZ basis set contains higher-quality polarization and diffuse functions compared to 6-311$++$G(d,p), and the B3LYP-D3(BJ) functional/dispersion correction combination provided a more accurate description of IMHBs compared to $\omega$B97X-D (See Supporting Information).

A dual-level strategy was utilized, where geometry optimizations and frequencies were calculated at the B3LYP-D3(BJ)/aug-cc-pVTZ level of theory. Single-point energies were then calculated via the domain local pair natural orbital coupled cluster theory with singles, doubles, and perturbative triples (DLPNO-CCSD(T)) method [65, 66] and aug-cc-pVTZ basis set.

DFT calculations were performed using Gaussian09 version D.01 [67]. Geometry optimizations and vibrational frequencies were calculated with an ultra-fine integration grid and tight convergence criteria for forces and displacement. DLPNO-CCSD(T) single-point energies were calculated using ORCA [68]. Charge distribution and local charges were calculated using NBO6 [69, 70]. LVM frequencies ($\omega ^a$) and $k^a$ were calculated using COLOGNE2017 [71]. Electron density ($\rho (\mathbf {r}_b)$) [72] and $H(\mathbf {r}_b)$, where $\mathbf {r}_b$ is a bond critical point, were calculated using AIMAll [73]. Structural models were made with UCSF Chimera [74]. NCI plots were made with ‘isosurface NCIPLOT’ in Jmol [75, 76]. Standard gradient cutoff of $s = 0.5$ a.u. (s: the reduced density gradient) with color scale $-0.04< \rho < 0.04$ au was utilized [75]. LVM, AIMALL, and NCI plots all support the IMHBs discussed in the following section. To provide further support for this work, the density-dependent density overlap regions indicator (DORI) analysis was utilized (see Supporting Information) [77].

3 Results and discussion

Table 1 Relative electronic plus zero-point energies ($\varDelta E$), electronic plus thermal enthalpies ($\varDelta H$), electronic plus thermal free energies ($\varDelta G$), CCSD(T) $\varDelta E$ corrections ($\varDelta E_\mathrm{corr}$), IMHB distances (r), local stretching force constants ($k^a$), local mode frequencies ($\omega ^a$), bond strength order (BSO n), electron density ($\rho (\mathbf {r}_b)$), local energy density ($H(\mathbf {r}_b)$), and bond degree ($\hbox {BD} = H(\mathbf {r}_b)/\rho (\mathbf {r}_b)$)

Fig. 1

(top) Structures of $\varepsilon \hbox {I} \hbox {I}_{a}$, $\varepsilon \hbox {I} \hbox {I}_ b , \delta \hbox {I} \hbox {I}_{a}$, and $\delta \hbox {I}_{a}$ showing selected NBO charges and IMHBs as green dashed bonds. H, N, O, and C charges are shown in black, blue, red, and gold, respectively. (bottom) NCI plots showing isosurfaces and local vibrational force constants ($k^a$) for each IMHB. Blue surfaces represent strongly attractive, green/yellow surfaces are weakly attractive, and orange/red surfaces are repulsive

Fig. 2

Local stretching force constant ($k^a$) plotted with respect to IMHB length

Fig. 3

Power relationship between bond strength order (BSO n) and local stretching force constants ($k^a$) of IMHBs in $\varepsilon \hbox {I} \hbox {I}_{a}, \varepsilon \hbox {I} \hbox {I}_ b , \delta \hbox {I} \hbox {I}_{a}$, and $\delta \hbox {I}_{a}$

Fig. 4

Bond strength order (BSO n) plotted with respect to local energy density at the bond critical point ($H(\mathbf {r}_b)$)

Fig. 5

Bond strength order (BSO n) plotted with respect to electron density at the bond critical point ($\rho (\mathbf {r}_b)$)

Fig. 6

Sum of local stretching force constants ($k^a$) plotted with respect to relative (with respect to $\varepsilon \hbox {I} \hbox {I}_{a}$) CCSD(T) correction to DFT electronic plus zero-point energy ($\varDelta E_\mathrm{corr}$)

Table 1 summarizes relative (with respect to $\varepsilon \hbox {I} \hbox {I}_{a}$) electronic plus zero-point energies ($\varDelta E$), electronic plus thermal enthalpies ($\varDelta H$), electronic plus thermal free energies ($\varDelta G$), CCSD(T) $\varDelta E$ corrections ($\varDelta E_\mathrm{corr}$), IMHB distances (r), local mode force constants ($k^a$), local mode frequencies ($\omega ^a$), bond strength order (BSO n), electron density ($\rho (\mathbf {r}_b)$), local energy density ($H(\mathbf {r}_b)$), and bond degree (BD: $H(\mathbf {r}_b)/\rho (\mathbf {r}_b)$) [78]. Calculated molecular geometries, selected NBO atomic charges, IMHBs (green dashed bonds), bond distances (r) reported in Å, and NCI isosurfaces (bottom row) are shown in Fig. 1. For the NCI plots, blue isosurfaces represent strongly attractive interactions, green/yellow surfaces indicate weakly attractive interactions, and orange/red surfaces point to repulsive interactions.

In Fig. 2, local stretching force constants $k^a$ of IMHBs are plotted with respect to IMHB distance r. Figure 3 shows a power relationship between BSO n and $k^a$ of the 12 IMHBs in this work. In Fig. 4, BSO n is plotted with respect to local energy density at the BCP ($H(\mathbf {r}_b)$), where the vertical dashed line at $H(\mathbf {r}_b) = 0$ separates the covalent ($H(\mathbf {r}_b) < 0$) and electrostatic ($H(\mathbf {r}_b) \ge 0$) regions according to the Cremer–Kraka criterion. Figure 5 reveals a correlation between BSO n and $\rho (\mathbf {r}_b)$, where increased electronic density correlates with increased IMHB strength. Figure 6 shows the sum of IMHB $k^a$ values for each HIS conformer plotted with respect to $\varDelta E_\mathrm{corr}$.

3.1 Intrinsic strength of IMHBs

Each conformer has a unique network of IMHBS, together comprising eight different IMHB types:

• 1. $\hbox {N}_{\alpha }{-}\hbox {H}{\cdots }\hbox {N}_{\delta }$ ($\varepsilon \hbox {I} \hbox {I}_{a}, \varepsilon \hbox {I} \hbox {I}_ b$), donor/acceptor $= \hbox {NH}_{2}$/Im-N, [purple circles]

• 2. $\hbox {N}_{\delta }{-}\hbox {H}{\cdots }\hbox {N}_{\alpha }$ ($\delta \hbox {I}_{a}$), donor/acceptor $=$ Im-NH/ $\hbox {NH}_{2}$, [orange diamond]

• 3. $\hbox {N}_{\alpha }{-}\hbox {H}{\cdots }\hbox {O}$ ($\delta \hbox {I}_{a}$), donor/acceptor $= \hbox {NH}_{2}$/carbonyl-O, [brown hexagon]

• 4. $\hbox {C}_{\beta }{-}\hbox {H}{\cdots }\hbox {O=C}$ ($\varepsilon \hbox {I} \hbox {I}_{a}, \delta \hbox {I} \hbox {I}_{a}$), donor/acceptor $= \hbox {CH}_{2}$/carbonyl-O, [red squares]

• 5. $\hbox {C}_{\beta }{-}\hbox {H}{\cdots }\hbox {OH}$ ($\delta \hbox {I}_{a}$), donor/acceptor $= \hbox {CH}_{2}$/OH, [red squares]

• 6. $\hbox {O}{-}\hbox {H}{\cdots }\hbox {N}_{\alpha }$ ($\varepsilon \hbox {I} \hbox {I}_{a}, \varepsilon \hbox {I} \hbox {I}_ b , \delta \hbox {I} \hbox {I}_{a}$), donor/acceptor = OH/$\hbox {NH}_{2}$, [blue triangles]

• 7. $\hbox {N}_{\delta }{-}\hbox {H}{\cdots }\hbox {O}$ ($\delta \hbox {I} \hbox {I}_{a}$), donor/acceptor $=$ Im-NH/carbonyl-O, [blue pentagon]

• 8. $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {C}_{\delta }$ ($\delta \hbox {I} \hbox {I}_{a}$), donor/acceptor $= \hbox {NH}_{2}$/Im-C, [green triangle]

Note: donor/acceptor refers to HB donor/HB acceptor, [color shape] indicates plot points in Figs. 2, 3, 5 and 6, $\hbox {N}_{\alpha } = \hbox {amino-N}, \hbox {N}_{\delta }= \hbox {Im-N}, \hbox {C}_{\delta } = \hbox {Im}{-}\hbox {C}$, and $\hbox {C}_{\beta } = \hbox {aliphatic-C}$.

Despite different physical location and pairs, IMHB type 1, type 2, and type 3 have comparable bond distances and strengths. The nature of IMHB type 1, type 2, and type 3 is electrostatic. IMHB type 1 is found in $\varepsilon \hbox {I} \hbox {I}_{a}$ and $\varepsilon \hbox {I} \hbox {I}_ b$, where $\hbox {N}_{\alpha }{-}\hbox {H}{\cdots }\hbox {N}_{\delta }$ found in $\varepsilon \hbox {I} \hbox {I}_{a}$ is longer and weaker than the one found in $\varepsilon \hbox {I} \hbox {I}_ b$. Type 2 and type 3 are uniquely found in $\delta \hbox {I}_{a}$.

Type 4 and type 5 are electrostatic in nature. Type 4 having a carbonyl-O as a HB acceptor is found in $\varepsilon \hbox {I} \hbox {I}_{a}$ and $\delta \hbox {I} \hbox {I}_{a}$, whereas type 5 having a hydroxyl-O as a HB acceptor is uniquely found in $\delta \hbox {I}_{a}$. The $\hbox {C}_{\beta }{-}\hbox {H}$ acts as a HB donor on the both types. Both types are longer than types 1–3 yet slightly stronger by ca. 0.024 mdyn/Å. IMHB type 5 are found to be ‘intermediates’ in terms of bond strength as illustrated in Fig. 3 ($0.260< \hbox {BSO} n < 0.330$).

IMHB type 6 is found in $\varepsilon \hbox {I} \hbox {I}_{a}, \varepsilon \hbox {I} \hbox {I}_ b$, and $\delta \hbox {I} \hbox {I}_{a}$. Type 6 is the shortest and strongest HB studied in this work. The local stretching force constant $k^a$ values of type 6 are 79.35% larger than other IMHB types. The IMHB type 6 is covalent in nature as shown in Fig. 4. The IMHB type 6 links $\hbox {CO}_{2}\hbox {H}$ group to $\hbox {NH}_{2}$ group.

As a result of poor HB acceptor and poor HB donor, these types are the longest and weakest IMHB studied in this work. Types 7–8 are on average 63.16% weaker than other types. IMHB type 7 and type 8 are found uniquely in $\delta \hbox {I} \hbox {I}_{a}$. Though it is rarely discussed, the existence of IMHB type 8 has been verified experimentally using X-ray crystallography, and in computational reports [79].

3.2 IMHB networks in each conformer

$\varepsilon \hbox {I} \hbox {I}_{a}$ contains a three-IMHB network: $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {N}_{\delta }$ (type 1), $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {O}=\hbox {C}$ (type 4), and $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ (type 6). None of these interactions are unique to $\varepsilon \hbox {I} \hbox {I}_{a}$, but the combination is unique. This network links $\hbox {NH}_{2}$ to $\hbox {CO}_{2}\hbox {H}$, $\hbox {NH}_{2}$ to Im, and $\hbox {CO}_{2}\hbox {H}$ to the C-backbone. $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ ($k^a = 0.277$ mdyn/Å, BSO $n = 0.362$) is the strongest IMHB of $\varepsilon \hbox {I} \hbox {I}_{a}$ (also of the four conformers), followed by $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {O}=\hbox {C}$ ($k^a = 0.142$ mdyn/Å, BSO $n = 0.298$), then $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {N}_{\delta }$ ($k^a = 0.116$ mdyn/Å, BSO $n = 0.281$). Force constants of the three IMHBs sum to $k^a_{\varepsilon \hbox {I} \hbox {I}_{a}} = 0.535$ mdyn/Å, the largest value compared to $\varepsilon \hbox {I} \hbox {I}_ b$ (0.382 mdyn/Å), $\delta \hbox {I} \hbox {I}_{a}$ (0.512 mdyn/Å), and $\delta \hbox {I}_{a}$ (0.344 mdyn/Å). $\hbox {H}{\cdots }\hbox {N}_{\delta }$ is 2.176 Å in length with $\varDelta q$ of 0.910 e. $\hbox {H}{\cdots }\hbox {N}_{\alpha }$ is significantly shorter ($r = 1.861$ Å) and more polar ($\varDelta q = 1.379$ e) due to the close proximity of $\hbox {NH}_{2}$ and $\hbox {CO}_{2}\hbox {H}$ and the quality of the donor (OH). The third IMHB of $\varepsilon \hbox {I} \hbox {I}_{a}$ ($\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {O}=\hbox {C}$) is the longest and least polar of the three interactions ($r = 2.621$ Å, $\varDelta q = 0.833$ e). This IMHB type, though often neglected in the HB conversation [80], is well characterized [81] and plays an important role in the structures of proteins, amino acids, and crystals [82,83,84].

$\varepsilon \hbox {I} \hbox {I}_ b$, the R-enantiomer of $\varepsilon \hbox {I} \hbox {I}_{a}$, has two IMHBS: $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {N}_{\delta }$ (type 1) and $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ (type 6) with $r = 2.163, 1.892$ Å and $\varDelta q = 0.913, 1.378$ e, respectively. Once again, neither type is unique to $\varepsilon \hbox {I} \hbox {I}_ b$, but the combination is unique. Analogous to $\varepsilon \hbox {I} \hbox {I}_{a}$, NCI plots show $\hbox {H}{\cdots }\hbox {N}_{\delta }$ being weakly attractive and $\hbox {H}{\cdots }\hbox {N}_{\alpha }$ being strongly attractive. A tiny isosurface is seen between O and the $\hbox {H}-\hbox {C}_{\beta }$, but $\hbox {C}_{\beta }\hbox {H}{\cdots }\hbox {O}$ is 0.104 Å longer than that of $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {O}=\hbox {C}$ in $\varepsilon \hbox {I} \hbox {I}_{a}$ and LVM/AIMALL calculations do not support a bond. In terms of $k^a$, $\hbox {H}{\cdots }\hbox {N}_{\delta }$ is stronger ($+0.016$ mdyn/Å) and $\hbox {H}{\cdots }\hbox {N}_{\alpha }$ is weaker ($-0.027$ mdyn/Å) than respective counterparts in $\varepsilon \hbox {I} \hbox {I}_{a}$ (Fig. 2). BSO n values for $\hbox {H}{\cdots }\hbox {N}_{\delta }$ and $\hbox {H}{\cdots }\hbox {N}_{\alpha }$ are 0.292 and 0.351, respectively. $\hbox {H}{\cdots }\hbox {N}_{\alpha }$ is characterized as a covalent IMHB, with $\rho (\mathbf {r}_b) = 0.257$ e/Å$^3$ and $H (\mathbf {r}_b) = -\,0.022$ Hartree/Å$^3$, whereas $\hbox {H}{\cdots }\hbox {N}_{\delta }$ is electrostatic in nature ($\rho (\mathbf {r}_b) = 0.129$ e/Å$^3$, $H (\mathbf {r}_b) = 0.012$ Hartree/Å$^3$).

$\delta \hbox {I} \hbox {I}_{a}$ is an N-tautomer of $\varepsilon \hbox {I} \hbox {I}_{a}$ with its Im ring flipped 179.14$^{\circ }$ and is the only conformer with four IMHBS: $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {O=C}$ (type 4), $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ (type 6), $\hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {O}$ (type 7), and $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {C}_{\delta }$ (type 8) with $r = 2.635, 1.906, 2.281, 2.861$ Å and $\varDelta q = 0.847, 1.366, 1.045, 0.465$ e, respectively. The NCI plot confirms that $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ is a strongly attractive interaction, while the other three IMHBs are all weakly attractive. $\hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {O}$ and $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {C}_{\delta }$ are unique to $\delta \hbox {I} \hbox {I}_{a}$ as the only IMHBs with donor/acceptor combinations being $\hbox {H}-\hbox {N}_{\delta }$/carbonyl-O and $\hbox {H}-\hbox {N}_{\alpha }/\hbox {C}_{\delta }$, respectively. These two IMHBs are the only interactions with $k^a < 0.100$ mdyn/Å and BSO $n < 0.250$. $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ is the only strong and covalent ($H (\mathbf {r}_b) = -\,0.016$ Hartree/Å$^3$) IMHB out of the four. $\varepsilon \hbox {I} \hbox {I}_{a}$ is more stable than $\delta \hbox {I} \hbox {I}_{a}$ because: (i) $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ and $\hbox {O}{\cdots }\hbox {H}-\hbox {C}_{\beta }\hbox {H}$ are stronger in $\varepsilon \hbox {I} \hbox {I}_{a}$, and (ii) the intermediately strong $\hbox {N}_{\delta }{\cdots }\hbox {H}-\hbox {N}_{\alpha }\hbox {H}$ in $\varepsilon \hbox {I} \hbox {I}_{a}$ is replaced by the weak $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {C}_{\delta }$ in $\delta \hbox {I} \hbox {I}_{a}$.

$\delta \hbox {I}_{a}$ is another tautomer of $\varepsilon \hbox {I} \hbox {I}_{a}$, with $\hbox {CO}_{2}\hbox {H}$ and $\hbox {NH}_{2}$ rotated $\approx 180^{\circ }$ about their $\hbox {C-C}$ and $\hbox {C-N}$ bond axes, respectively. This is the only conformer without the type 6 IMHB. Each IMHB in this case is technically unique to $\delta \hbox {I}_{a}$: $\hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ (type 2), $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {O}$ (type 3), and $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {OH}$(type 5). However, as previously mentioned, type 4 and type 5 are highly similar. $\delta \hbox {I}_{a}$ is also unique in that it does not have any IMHBs $< 2.000$ Å in length, the NCI plot in Fig. 1 indicates no strongly attractive interactions, and all three IMHBs are weak electrostatic interactions ($k^a < 0.200$ mdyn/Å, BSO $n < 0.300$, $H (\mathbf {r}_b) > 0.000$ Hartree/Å$^3$, $\rho (\mathbf {r}_b) < 0.200$ e/Å$^3$). $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {OH}$ is 2.611 Å in length and has a $\hbox {O}{\cdots }\hbox {H} \varDelta q = 0.905$ e, $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {O}$ is 2.267 Å in length with $\hbox {O}{\cdots }\hbox {H} \varDelta q$ of 0.977 e, and $\hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ is 2.275 Å in length with $\hbox {N}{\cdots }\hbox {H} \varDelta q$ of 1.291 e. $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {OH}$ is the strongest IMHB in $\delta \hbox {I}_{a}$ ($k^a = 0.134$ mdyn/Å, BSO $n = 0.293$), followed by $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {O}$ ($k^a = 0.108$ mdyn/Å, BSO $n = 0.275$) and $\hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ ($k^a = 0.102$ mdyn/Å, BSO $n = 0.271$). The trend in $\rho (\mathbf {r}_b)$ is similar to $H (\mathbf {r}_b)$, where the strongest IMHB, $\hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {OH}$, has the largest $\rho (\mathbf {r}_b)$ value (0.177 e/Å$^3$), but $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {O}$ has slightly larger $\rho (\mathbf {r}_b)$ than $\hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {N}_{\alpha }$: 0.128 and 0.117 e/Å$^3$, respectively.

3.3 Relationship between intrinsic IMHB strength and relative stability

$\varepsilon \hbox {I} \hbox {I}_{a}$ is the most thermochemically stable conformer by 0.49, 1.44, and 2.72 kcal/mol compared to $\delta \hbox {I} \hbox {I}_{a}$, $\varepsilon \hbox {I} \hbox {I}_ b$, and $\delta \hbox {I}_{a}$, respectively, in accord with previous studies [12,13,14]. The small $\varDelta E$ values between the four conformers ($< 2.72$ kcal/mol) are in agreement with results from Kovačević et al. [85], and the 0.49 kcal/mol difference between the two most stable conformers, $\varepsilon \hbox {I} \hbox {I}_{a}$ and $\delta \hbox {I} \hbox {I}_{a}$, is near the 0.60 kcal/mol value previously reported by Huang et al [12]. In terms of cumulative IMHB force constants of each conformer: $\varepsilon \hbox {I} \hbox {I}_{a}> \delta \hbox {I} \hbox {I}_{a}> \varepsilon \hbox {I} \hbox {I}_ b > \delta \hbox {I}_{a}$, which matches the trend in $\varDelta E$ and supports IMHB strength being a primary factor in the conformational stability of HIS.

$\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ is present in $\varepsilon \hbox {I} \hbox {I}_{a}$, $\varepsilon \hbox {I} \hbox {I}_ b$, and $\delta \hbox {I} \hbox {I}_{a}$ but not in $\delta \hbox {I}_{a}$. Instead, $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {O}$ links $\hbox {CO}_{2}\hbox {H}$ to $\hbox {NH}_{2}$ in $\delta \hbox {I}_{a}$. The important difference between these two interactions is the donor/acceptor roles are reversed. The result being $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {O}$ is drastically weaker ($k^a =0.108$ mdyn/Å) and longer ($r = 2.267$ Å) than $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ by $\approx 0.150$ mdyn/Å and $\approx 0.380$ Å. Consequently, absence of $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ corresponds with $\delta \hbox {I}_{a}$ being the least stable conformer. In addition, $\varepsilon \hbox {I} \hbox {I}_{a}$ has the strongest type 6 IMHB with $k^a$ more than 10% larger than in $\varepsilon \hbox {I} \hbox {I}_ b$ and $\delta \hbox {I} \hbox {I}_{a}$.

Despite having only two IMHBs, $\varepsilon \hbox {I} \hbox {I}_ b$ is the third most stable HIS conformer, whereas $\delta \hbox {I} \hbox {I}_{a}$ has four IMHBs and is the second most stable. The most stable and least stable conformers each have three IMHBs, which indicates that the number of interactions is not as important as intrinsic nature and strength, type of interaction, and donor role. Although the number of IMHBs is not a primary stabilizing factor, a cooperative effect exists among IMHB networks with varying influence on the interactions individually. For example, the structure of $\varepsilon \hbox {I} \hbox {I}_{a}$ was modified to prevent $\hbox {OH}{\cdots }\hbox {N}_{\alpha }$ by rotating the OH bond away from $\hbox {NH}_{2}$, resulting in significant lengthening and weakening of the remaining two IMHBs, $\hbox {C}_{\beta }\hbox {H}{\cdots }\hbox {O}$ and $\hbox {N}_{\alpha }\hbox {H}{\cdots }\hbox {N}_{\delta }$ by 0.151 Å, 0.068 mdyn/Å and 0.267 Å, 0.075 mdyn/Å, respectively. Conversely, eliminating $\hbox {N}_{\alpha }\hbox {H}{\cdots }\hbox {N}_{\delta }$ by flipping the Im-ring and protonating $\hbox {N}_{\delta }$ instead of $\hbox {N}_{\varepsilon }$ resulted in a much smaller change to $\hbox {OH}{\cdots }\hbox {N}_{\alpha }$ ($+0.060$ Å, $-0.019$ mdyn/Å) and $\hbox {C}_{\beta }\hbox {H}{\cdots }\hbox {O}$ is shortened ($-0.103$ Å) and strengthened ($+0.016$ mdyn/Å). Optimizing the aforementioned structure also results in the Im ring flipping back to its original orientation, thus allowing for re-introduction of the $\hbox {N}_{\alpha }\hbox {H}{\cdots }\hbox {N}_{\delta }$ interaction. Another attempt to remove $\hbox {N}_{\alpha }\hbox {H}{\cdots }\hbox {N}_{\delta }$ was executed by rotating the $\hbox {C}_{\alpha }-\hbox {C}_{\beta }$ bond $\approx 180^{\circ }$, so $\hbox {H}_{\alpha }$ is forward-facing. This approach, however, leads to a transition state. Based on this example, $\hbox {OH}{\cdots }\hbox {N}_{\alpha }$ strengthens the IMHB network, whereas $\hbox {N}_{\alpha }\hbox {H}{\cdots }\hbox {N}_{\delta }$ and $\hbox {C}_{\beta }\hbox {H}{\cdots }\hbox {O}$ do so to a lesser degree, or not at all.

Table 2 Relative electronic plus zero-point energies ($\varDelta E$), electronic plus thermal enthalpies ($\varDelta H$), electronic plus thermal free energies ($\varDelta G$), CCSD(T) $\varDelta E$ corrections ($\varDelta E_\mathrm{corr}$), IMHB distances (r), local stretching force constants ($k^a$), and local mode frequencies ($\omega ^a$) of neutral and zwitterionic form of the most stable conformer in solution (water)

Depending on physiological properties such as pH and temperature, histidine exists in two different forms: a neutral and a zwitterionic form [4]. Our results show that the latter form is more favorable in water by 3.55 kcal/mol compared to the former (see Table 2). In water, the $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ (type 6) found in the zwitterionic form is by far stronger than the one found in the neutral form parallel to the thermodynamic results (see Table 2). The zwitterionic form is known to be more dominant in the solution as a result of gaining extra stabilization energy through interactions with the polar environment [10]. In the gas phase, the neutral form is more favorable compared to the zwitterionic form. However, neutral HIS has proven difficult to isolate and characterize experimentally due to its high melting point, low vapor pressure, and thermal instability [12, 13].

4 Conclusions

In this work for the first time, we quantified IMHB strength in neutral HIS and established a link between this property and structural stability/conformational preferences. Increase in bond strength and covalent properties correlate with increase in thermochemical stability. $\hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }$ (type 6) is the IMHB having the largest effect on structural stability due to increased bond strength, covalent character, and low susceptibility to cooperative effects. We also found donor/acceptor identity to play a major role in conformational stability, and not the number of IMHBs. Details of our major findings are summarized as follows:

• 1. Strength of the IMHB (BSO n, $k^a$, and $\rho (\mathbf {r}_b)$):

  $$\begin{aligned} \hbox {O}-\hbox {H}{\cdots }\hbox {N}_{\alpha }>> \hbox {HO/O}{\cdots } \hbox {H-C}_{\beta }\hbox {H}> \hbox {N}_{\delta }/\hbox {O}{\cdots } \hbox {H-N}_{\alpha }\hbox {H}> \hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {N}_{\alpha }>> \hbox {N}_{\delta }-\hbox {H}{\cdots }\hbox {O} > \hbox {HC}_{\delta }{\cdots }\hbox {H-N}_{\alpha }\hbox {H} \end{aligned}$$

• 2. Donor ability to increase BSO n: $\hbox {H}-\hbox {O}> \hbox {H}-\hbox {C}_{\beta }> \hbox {H}-\hbox {N}_{\alpha } > \hbox {H}-\hbox {N}_{\delta }$; acceptor plays a lesser role

• 3. Cumulative strength of IMHB networks correlates with $\varDelta E$:

  $$\begin{aligned} \varepsilon \hbox {I} \hbox {I}_{a}> \delta \hbox {I} \hbox {I}_{a}> \varepsilon \hbox {I} \hbox {I}_{a} > \delta \hbox {I}_{a} \end{aligned}$$

• 4. Observed donor–acceptor roles: $\hbox {CH}_{2}$ is a surprisingly capable donor, OH is a superior donor due to its polar nature, $\hbox {NH}_{2}$ and Im are surprisingly poor donors, and any combination of $\hbox {NH}_{2}$ donor/acceptor and Im donor/acceptor results in the weakest IMHBS

Future goals are to complete a comprehensive analysis of molecules capable of $\hbox {N}_{\alpha }-\hbox {H}{\cdots }\hbox {C}_{\delta }, \hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {OH}, \hbox {C}_{\beta }-\hbox {H}{\cdots }\hbox {O=C}$, and other HBs involving carbon to determine their similarities/differences between more well-studied and traditional HBs. The local mode analysis will play a key role because it provides a unique and quantitative measure of the intrinsic strength of a HB and any other weak chemical interaction or chemical bond.