1 Introduction

Tryptophan (Trp) is a kind of essential amino acid for humans and animals. Moreover, Trp has served as a useful probe of its local environment in proteins since the emission wavelength and excited-state lifetime depend on its environment. Trp is the only one amino acid which has both a complex structure and physiological and biochemical function in various amino acids.[1, 2] Trp was studied experimentally and theoretically in the ground and excited state[3, 4] because of its large absorption in the UV and its use as conformational fluorescence label in proteins. Most of the theoretical and experimental studies reported so far are devoted to the Trp and its various conformers. Levy and coworkers studied the UV spectroscopy of jet-cooled Trp and identified six different conformations in the resonantly enhanced two-photo ionization spectrum.[5] Five of the six conformers were confirmed nicely by the high-resolution vibronic spectra of Trp in 0.38 K cold helium droplets.[6] Compagnon et al. measured the permanent electric dipole of tryptophan isolated in a molecular beam at 85 K,[7] which gave different results from that of the Levy group. A systematic and extensive conformational search for the gas-phase tryptophan has been performed by Huang and Lin,[8] and the results support the conclusion drawn by Compagnon et al. that only one dominant isomer existed in the molecular beam at 85 K and add further evidence that the supersonic jet expansion or embedding helium droplets did not produce an equilibrium distribution. Recently, the photochemistry of the neutral and zwitterionic form with two water molecules were analysed with ab initio methods.[9]

In general, zwitterionic forms of amino acids are stabilized in the crystalline state and in a solution. On the other hand, the neutral form of amino acids is also found in the gas phase and low-temperature inert matrixes, which has stimulated extensive investigation of the transformation of Trp from the neutral form to the zwitterionic form. As previous researches have reported, eight or more water molecules may be necessary to render the zwitterionic structures of tryptophan-water (Trp-H2O) complexes.[9] The conformational picture of such Trp-H2O complexes is considerably complicated and the calculation would be prohibitively expensive. However, the Trp-H2O complexes may serve as a useful model system for the exploration of tryptophan-water complexes that are characteristic for hydrated zwitterionic Trp. Preliminary knowledge of these mechanisms will certainly be helpful for the future exploration of the nature of Trp in larger complexes. In this paper, the structures of Trp-H2O complexes formed by the hydrogen bonding interaction between Trp and water was studied. The energetic, vibrational frequencies of H-bonds were investigated. The quantum theory of atoms in molecules (QTAIM)[10–12] and natural bond orbital (NBO)[13] analyses were also carried out to study the nature of H-bonds in Trp-H2O complexes.

2 Computational details

All DFT calculations were performed with the Gaussian09[14] with the default convergence criteria without any constraint on the geometry. The ωB97XD functional[15] with the 6–311+ +G(d,p) basis set[16, 17] was used to investigate the electronic structure of the Trp-H2O systems. The ωB97XD functional includes empirical dispersion and can better treat hydrogen bonding and van der Waals interactions than conventional DFT. In the beginning, the geometries of the isolated Trp and water monomers were fully optimized. The complexes were constructed starting from the most stable Trp and water monomers. All complexes were also fully optimized at the same level. The harmonic vibrational frequencies were calculated with analytic second derivatives at the same level, which confirm the structures as minima and enable the evaluation of zero-point vibrational energies (ZPVE). To take into account the effects of the basis set superposition error (BSSE), the counterpoise (CP) correction[18] which was implemented in order to ensure that complexes and monomers are being computed with a consistent basis set. Finally, the interaction energies were calculated based on the ZPVE and BSSE corrections. In order to analyse the properties of the H-bond interactions in complexes, the QTAIM analyses were carried out using the wave functions obtained at ωB97XD at 6–311+ +G(d,p) level by the software AIM2000,[19] the bond critical point (BCP) of H-bonds and its electron density topologic information can help us to evaluate the nature of H-bond. To understand the nature of hydrogen bonding interaction in complexes, the localized molecular orbital energy decomposition analysis (LMOEDA)[20] were carried out using the Gamess electronic structure program code.[21]

3 Results and discussion

The proton transfer reaction mechanism in Trp moiety of Trp-H2O complex has been studied.[22] In this work, the Trp and water monomers were optimized at the ωB97XD/6–311+ +G(d,p) level and the molecular graphs were presented in figure 1. As shown in figure 1, Trp can offer several possible proton donor/acceptor sites to form H-bond. The hydroxyl or amino groups of Trp can donate proton to form H-bond. Moreover, the methylene of Trp also acts as a H–donor in some complexes. The oxygen atom of carbonyl is the major H-acceptor of Trp, and the nitrogen atom of amino can act as H-acceptor to form intramolecular H-bond in some complexes.

Figure 1
figure 1

Molecular graphs of free Trp monomer. Large circles correspond to attractors attributed to atomic positions: gray, H; blue, N; black, C; red, O. Small circles are attributed to critical points: red, bond critical point; yellow, ring critical point.

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3.1 Structures

In this article, different complexes were taken into account to analyse various types of H-bonds. All molecular graphs of optimized Trp-H2O complexes were shown in figure 2, and the structural parameters of H-bonds were listed in table 1. The vibrational frequency calculations confirmed that all optimized complexes have no imaginary frequencies and are stable structures. According to the QTAIM, both inter and intramolecular H-bonds can be characterized by the BCPs between H-donor (X–H) and H-acceptor (Y). Therefore, the existence of BCP and the electron density topological properties of BCP can be used to study the nature of H-bond. Ring critical point (RCP) can also be found when a ring structure was formed due to multiple H-bonds. There are two RCPs related with the benzene and indolyl rings of Trp, which have no relationship with H-bonds (figure 1). As shown in figure 1, due to the intramolecular O1H1T ⋯N1T H-bond in Trp monomer, a ring structure was formed and can be characterized by the BCP and corresponding RCP on the basis of QTAIM. Such intramolecular O1H1T⋯N1T H-bond are retained in all Trp-H2O complexes except TW5. The cleavage of the intramolecular O1H1T⋯N1T H-bond in TW5 indicates that the serious structural deformation occurred in TW5 than other complexes. The new intramolecular C5H7T⋯O2T H-bond seems to be formed in TW3 and TW5, respectively. In addition, one cage structure was formed by multiple H-bonds in TW2 and is characterized by cage critical point (CCP).

Figure 2
figure 2

Molecular graphs of Trp-H2O complexes. Large circles correspond to attractors attributed to atomic positions: gray, H; blue, N; black, C; red, O. Small circles are attributed to critical points: red, bond critical point; yellow, ring critical point.

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Table 1 Structural parameters (bond lengths in Å, angles in degree) of H-bonds in Trp-H2O complexes calculated at the ωB97XD/6–311+ +G(d,p) level.
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As shown in figure 2, only one intermolecular H-bond was formed between Trp and water in TW3 and TW4, respectively. However, because the distance between the centre of benzene ring and the proton of the hydroxyl of water in TW3 is about 2.520 Å, an π H-bond seems to be formed between the benzene ring and water molecule. When one water molecule is above the benzene ring, there is a tendency to form π H-bond between them because the sucking–electron ability of benzene is very strong. Unfortunately, neither QTAIM nor NBO analyses can give direct evidence for such π H-bond. For the other complexes (TW1, TW2 and TW5), multiple intermolecular H-bonds can be found, respectively.

Structural parameters of H-bonds can provide some rough information on the nature of H-bonds. It is well known that the H-bond formation is connected with the elongation of the proton donating X-H bond (except of the special case of so-called blue-shifted H-bonds) as well as the shortening of H⋯Y bond. The shorter H⋯Y bond or the longer X-H bond is, the stronger the interaction is, and vice versa. As shown in table 1, the H-bonds taking methylene as H–donor are very weak, which can be seen from the almost unchanged ΔRX − H and longer R H ·Y than about 2.2 Å. The other H-bonds involving the hydroxyl or amino as H-donor have positive ΔRX − H values and are red-shifted H-bonds. The largest ΔRX − H (0.025 Å) is found in the OH1W⋯N1T H-bond of TW5, which indicates that it seems to be the strongest intermolecular H-bond. It is worth noting that another intermolecular H-bond (O1H1T⋯OW) in TW5 is also very strong although its ΔRX − H (0.002 Å) is very small, moreover, and the intramolecular O1H1T⋯N1T H-bond was destroyed by the formation of such intermolecular H-bonds, which lead to a smaller ΔRX − H of the O1H1T⋯OW H-bond compared to that of the O1H1T⋯N1T H-bond. The shortest R H⋯Y (1.742 and 1.839 Å) of the two H-bonds in TW5 further confirms that they are the two strongest intermolecular H-bonds among all Trp-H2O complexes. However, such strong hydrogen bonding interactions in TW5 does not mean it is the most stable complex since the cleavage of the intramolecular O1H1T⋯N1T H-bond results in serious structural deformation which will be further discussed later.

The shorter H⋯Y bond means the stronger hydrogen bonding interaction. However, such a relationship is only a rough one, even if R H⋯Y concern similar species immersed into similar environments. In other words, if the considered sample of X–H⋯Y systems is homogeneous. The estimation of H-bond strength directly on the basis of R H⋯Y is not possible for a heterogeneous sample if H-bonds differ in the type of H-donor and/or H-acceptor. In view of the above difficulties, a H-bond parameter δRH⋯Y which allow one to unify interactions to estimate their strength even if different pairs of atoms is defined as[23]

$$ \label{eq1} \delta R_{\rm H \cdots Y} = R_{\rm H}^{\rm vDW} + R_{\rm Y}^{\rm vDW} - R_{\rm H \cdots Y} $$
(1)

where \(R_{\rm H}^{\rm vDW} \) and \(R_{\rm Y}^{\rm vDW} \) are van der Waals radii of H and Y atoms given by Bondi,[24] respectively, R H⋯Y is the distance between H-donor and H-acceptor. As shown in table 1, the δRH⋯Y of the intramolecular O1H1T⋯N1T H-bond in all Trp-H2O complexes except TW5 is larger than that of Trp monomer, which indicates that the intramolecular O1H1T⋯N1T H-bond was strengthened in complexes. The maximum of δRH⋯Y is 0.978 Å of the intermolecular O1H1T⋯OW H-bond in TW5, which seems to be the strongest H-bond. Of course, another intermolecular H-bond in TW5, OH1W ⋯N1T, is the second strongest H-bond due to the second largest δR H ⋯ Y (0.911 Å). It is worth noting that the δR H ⋯ Y of the H-bonds taking methylene as H-donor is small, which implies that the RH ⋯ Y is close to the sum of van der Waals radii of H and Y atoms. Therefore, from a structural viewpoint, the interaction between the methylene and Y atom is very weak and is the mixture of hydrogen bonding interaction and van der Waals interaction.

3.2 Vibrational frequencies

The harmonic vibrational frequencies and their shifts of H-bonds in Trp-H2O complexes and monomers calculated at the ωB97XD/6–311+ +G(d,p) level were listed in table 2. The red shifts in the X–H stretching vibrational frequency have been traditionally considered one of the main fingerprints of H-bonds, assuming that formation of an H-bond weakens an X–H single bond. The larger the shift value is, the stronger the H-bond is. However, it is not easy to calculate the shifts of X-H stretching vibrational modes if it mixes with other vibrational modes. For example, the intramolecular O1H1T ⋯N1T H-bond in Trp monomer lead to the mixture of the O-H stretching with symmetric NH2 stretching vibration modes, which are calculated to be 3556.2 and 3536.5 cm − 1, respectively. Similar things also happened in Trp-H2O complexes, so many ΔvX − H values may be given for one H-bond. As shown in table 2, the largest red-shifted values (about 380 ~ 490 cm − 1) are found in the OH1W ⋯N1T and O1H1T ⋯OW H-bonds in TW5, which shows that the two H-bonds are the strongest red-shifted ones. The OH1W ⋯O2T (TW1 and TW2) and N2H8T ⋯OW (TW4) H-bonds have larger red-shifted values of about 140 ~ 180 cm − 1, while other red-shifted H-bonds are tens of wavenumbers shift values. The C5H7T ⋯OW H-bond in TW1, is a red-shifted H-bond with negative Δv X − H of 28.6 cm − 1, while other H-bonds involving methylene are blue-shifted ones because of the positive shifts. Moreover, these H-bonds usually are weak since their shifts are small. In addition, the smaller Δv X − H values of the intramolecular O1H1T ⋯N1T H-bond do not mean that it is weak. On the contrary, it can seen from the negative Δv X − H values that the intramolecular O1H1T ⋯N1T H-bond was strengthened during the formation process of Trp-H2O complex.

Table 2 The X–H stretching vibrational frequencies (strength) of H-bonds in both Trp-H2O complexes and monomers.
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3.3 QTAIM analyses

To quantitatively study the nature of H-bond, the QTAIM analysis has been carried out to deepen the nature of the H-bond interactions. QTAIM has been proved to be a powerful tool and technique to investigate hydrogen bonding interactions.[23, 25–29] For example, the characteristics of critical points provide additional information on the nature of interactions. The topological criteria of the existence of hydrogen bonding were proposed by Koch and Popelier.[30] According to the criteria, H-bonds should have a relatively high value of the electron density at the H⋯Y BCP (ρ b ), in the range 0.002–0.034 a.u., and the Laplacian of the electron density at H⋯Y BCP (\(\nabla^{2}\) ρ b ) should be within the 0.024–0.139 a.u.[31] Therefore, both ρ b and \(\nabla^{2}\) ρ b at the H⋯Y BCP are good measures of the strength of H-bond. Moreover, the criteria provide a basis to distinguish hydrogen bonding interactions from van der Waals interactions and have been proved to be valid for standard and nonconventional H-bonds.

The other characteristics may be applied to describe the considered BCP and further the atom-atom interaction. There are well-known relationships resulting from the Virial theorem between energetic topological parameters and the Laplacian of electron density at BCP

$$ \left( {1 / 4} \right)\nabla^2\rho_b =2G_b +V_b $$
(2)
$$ \label{eq3} H_b =G_b +V_b , $$
(3)

where G b , V b and H b are the kinetic, potential, and total electron energy densities at critical point, respectively. G b is a positive value, whereas V b is a negative one. The sign of H b depends on which contribution, potential or kinetic, will locally prevail on the BCP. The Laplacian is negative if the modulus of the potential energy outweighs two times the kinetic energy, which implies the covalent character of interaction, and it may concern covalent bonds as well as very strong H-bonds. If the modulus of the potential energy only one time outweighs the kinetic energy, the Laplacian is positive, but H b is negative, which implies the partial covalent character of interaction and concerns strong H-bonds.[32, 33] Moreover, the \(\nabla^{2} \rho_{b}\) at the BCP is low and positive, which is typical of closed-shell interactions. Therefore, the following criterion of strength was proposed by Popelier:[30] for weak and medium in strength H-bonds, \(\nabla ^{2}\) ρ b  > 0 and H b  > 0; for strong H-bonds, \(\nabla ^{2}\) ρ b  > 0 and H b  < 0; for very strong H-bonds, \(\nabla ^{2}\) ρ b  < 0 and H b  < 0. This classification shows that weak H-bonds eventually merge with (weaker) van der Waals interactions whereas strong H-bonds merge, at the other end of the continuum, with covalent and polar bonds. The electronic topological properties at H⋯Y BCPs of H-bonds including electron density (ρ b ), the Laplacian of the electron density (\(\nabla^{2}\) ρ b ), kinetic energy density (G b ), potential energy density (V b ) and total electron energy density (H b ) of all complexes were listed in table 3.

Table 3 Electron density (ρ b ), Laplacian of the electron density (\(\nabla^{2} \rho_{b}\)), kinetic energy density (G b ), potential energy density (V b ) and total electron energy density (H b ) in a.u. at BCPs of H-bonds in both Trp-H2O complexes and Trp monomer by QTAIM analysis.
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As shown in table 3, the intramolecular O1H1T ⋯N1T H-bond in all the Trp-H2O complexes except TW5 is the strongest H-bond since it have negative H b and positive \(\nabla ^{2}\) ρ b values. Moreover, the value of ρ b is beyond the upper-limits of the range, which indicates that a partial covalent character is attributed to the intramolecular O1H1T ⋯N1T H-bond. The strength of the intramolecular O1H1T ⋯N1T H-bond in Trp-H2O complexes can also been learnt from the larger ρ b and \(\nabla^{2}\) ρ b as well as more negative H b compared to those of Trp monomer. Similarly, due to the negative H b (−0.00367 and −0.00199 a.u.) and positive \(\nabla ^{2}\) ρ b (0.10450 and 0.12730 a.u.), the OH1W ⋯N1T and O1H1T ⋯OW H-bonds in TW5 are the two strongest intermolecular H-bonds among all Trp-H2O complexes. Moreover, a partial covalent character is attributed to them since their ρ b values (0.04022 and 0.03986 a.u.) are beyond the upper-limits of the range. For the other H-bonds, both ρ b and \(\nabla ^{2}\) ρ b fall in the ranges proposed by Popelier, moreover, the H b values are positive, which indicates that these H-bonds are of weak or medium strengths. Especially, for the H-bonds taking methylene as H-donor, both ρ b and \(\nabla^{2}\) ρ b are close to the lower-limit of criteria proposed by Popelier, which shows that they are very weak and are regarded as the mixture of hydrogen bonding interaction and van der Waals interaction. Therefore, for such extreme case, the existence of BCP is not the unique criterion to verify weak H-bond, and other methods (such as NBO) should be applied to investigate the nature of such interaction. Another embarrassment is that no direct QTAIM evidence can be found for π H-bond formed between the benzene ring and the hydroxyl of water moiety in TW3.

To understand the relationship between δR H ⋯ Y and topological parameters of QTAIM (ρ b ~ δR H ⋯ Y and \(\nabla^{2}\) ρ b ~ δR H ⋯ Y) were shown in figure 3, and the linear relationships between them can be expressed as

$$ \label{eq4} \nabla^2\rho_{\rm b} =0.0113+0.1094\delta R_{\rm H\cdots Y} \,r=0.9784 $$
(4)
$$ \label{eq5} \rho_{\rm b} =0.0016+0.0375\delta R_{\rm H\cdots Y} \,r=0.9357 $$
(5)

It can be learnt that ρ b is a linearly correlate to δR H ⋯ Y substantially, while a better linear relationship exists between \(\nabla^{2}\) ρ b and δR H ⋯ Y.

Figure 3
figure 3

Correlation between δR H ⋯ Y and H-bond parameters of QTAIM. (a) δR \(_{\rm H \cdots Y} \sim \nabla ^{2}\) ρ b ; (b) δR H ~ ρ b .

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3.4 NBO and energy decomposition analyses

Generally, a certain amount of charge transfer (CT) from the H-acceptor to the H-donor is one of the characteristics attributed to H-bond, which lead to a rearrangement of electron density within each part of the molecule. Although QTAIM analysis can provide relevant information on the strength of H-bonds in Trp-H2O complexes, it cannot provide information on the CT. The NBO method[13] shows that for typical hydrogen bonding, a two-electron \(n_{B} \to \sigma_{XH}^\ast \) intermolecular donor-acceptor interaction exists where electron density from the lone pair n B of the H-acceptor delocalizes into the unfilled σ AH * anti-bonding orbital of the H-donor. The \(n_{B} \to \sigma _{XH}^\ast \) orbital overlap is characteristic for hydrogen bonding interaction. The hydrogen bond formation leads to an increase of the occupancy of the \(\sigma_{XH}^\ast \) antibond orbital and hence the weakening and lengthening of the X–H bond. This leads to the red-shifted ν X − H stretching frequency. Therefore, electron delocalization or CT effects between n B and \(\sigma_{XH}^\ast \)may be estimated by second-order perturbation theory:

$$ E\left( 2 \right)=-2\frac{\left\langle{n_B } \left|F\right| {\sigma _{XH}^\ast } \right\rangle^2}{\varepsilon \left( {\sigma_{XH}^\ast } \right)-\varepsilon \left( {n_B } \right)}, $$
(6)

where \(\left\langle {n_B } \right|F\left| {\sigma_{XH}^\ast } \right\rangle \) is the Fock matrix element between the n B and \(\sigma_{XH}^\ast \) orbitals, \(\varepsilon \left( {\sigma_{XH}^\ast } \right)-\varepsilon \left( {n_B } \right)\) is the orbital energy difference (the difference of diagonal Fock matrix element).[34] It is worth mentioning that the CT and the corresponding lowering of energy are attributed to hydrogen bonding interactions. In other words, the second-perturbation energies E(2) lowering is responsible for the orbital interaction of H-bond, the larger E(2) values correspond to stronger CT interaction occurred in the H-bond.

The result of NBO analysis was listed in table 4. As shown in table 4, the O atom involved as H-acceptor has two branches: one has ‘sp’ hybrid characteristics, and the other one has ‘p’ hybrid characteristics; they correspond to two E(2) values, respectively. On the contrary, the N atom involved as H-acceptor shows ‘sp’ characteristics. The sum of E(2) value of 59.51 kcal·mol − 1 in the N2H8T ⋯OW H-bond of TW4 is the largest, which indicates the strongest CT interaction is responsible for the H-bond. Similarly, strong CT interaction in the O1H1T ⋯OW H-bond of TW5 is also confirmed by the larger sum of E(2) value of 51.31 kcal·mol − 1. Moreover, such strong CT effects in the N2H8T ⋯OW (TW4) and O1H1T ⋯OW (TW5) H-bond further confirm the partial covalent character of these H-bonds, which is consistent with above discussion. For other H-bonds except the OH1W ⋯O2T H-bond in TW2, due to the smaller E(2) less than about 10.0 kcal·mol − 1, weaker CT interaction occurred in them. Especially, no E(2) values were found for the C5H7T ⋯O2T H-bond in TW3 and TW5, respectively, which indicates that the major contribution to such H-bond comes from non-CT interaction rather than CT interaction.

Table 4 The second-perturbation energies E(2) (in kcal·mol − 1) of H-bonds in both Trp-H2O complexes obtained by NBO analysis.
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The E(2) values of intramolecular O1H1T ⋯N1T H-bond in some complexes (TW1, TW2 and TW3) are significantly larger than that of Trp monomer, which shows that stronger CT effect occurred in these complexes due to the intermolecular H-bond. In other words, there exists a certain cooperative effects between the intramolecular O1H1T ⋯N1T H-bond and intermolecular H-bonds in these complexes (TW1, TW2 and TW3). There are structural evidences for such cooperativity. The positive ΔRX − H values of the intramolecular O1H1T ⋯N1T H-bond in some complexes (TW1, TW2 and TW3) implies that it was the strengthened due to the cooperativity between the intra- and inter-molecular H-bonds. On the contrary, without such cooperativity, the E(2) of the intramolecular O1H1T ⋯N1T H-bond in TW4 has a small change compared to that of Trp monomer since the intermolecular H-bond is away from the side chain of Trp, which can be seen from the unchanged ΔRX − H as well.

To explore the nature of hydrogen bonding interaction, an LMO–EDA20 calculations with the MP2 method was carried out, and the results were listed in table 5. In LMO–EDA, total interaction energy ΔE MP2 is decomposed into five terms:

$$ \label{eq7} \Delta E_{\rm MP2} =\Delta E_{\rm ele} +\Delta E_{\rm ex} +\Delta E_{\rm rep} +\Delta E_{\rm pol} +\Delta E_{\rm disp} , $$
(7)

where ΔE ele is the electrostatic energy, ΔE ex is the exchange energy, ΔE rep is the repulsion energy, ΔE pol is the polarization energy and ΔE disp is the dispersion energy. As shown in table 5, the total interaction energy (ΔE MP2) between Trp and H2O is in the range of about −3.86 ~ −10.41 kcal·mol−1. The ΔE MP2 (−10.41 kcal·mol − 1) of TW5 is the largest among all complexes. However, the cleavage of the intramolecular O1H1T ⋯N1T H-bond led to the serious structural deformation, which does not favour the stability of TW5. The largest stabilizing force in TW5 is the exchange interaction of −39.67 kcal·mol − 1, which is counteracted simultaneously by the repulsion energy of −73.637 kcal·mol − 1, so the exchang-repulsion energy is unfavourable for the stability of TW5. The second largest stabilizing force is the electrostatic energy of about −29.21 kcal·mol − 1. Although the polarization energy of −12.04 kcal·mol − 1 in TW5 is the largest among all complexes, ΔE pol makes a minor contribution to the total interaction energy between Trp and H2O. Similar trends were found in other Trp-H2O complexes except TW5, ΔE ele and ΔE ex makes major contributions to the total interaction energy (ΔE MP2) of complexes, while ΔE disp is the smallest component of the interaction energy.

Table 5 The LMO–EDA results of Trp-H2O complexes at the MP2/6–311+ +G(d,p) level.a
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4 Conclusions

In this paper, we studied the geometries, energies and IR characteristics of the H-bonds of Trp-H2O complexes at the ωB97XD/6–311+ +G(d,p) level. The intramolecular O1H1T ⋯N1T H-bond are retained in all complexes except TW5, and the cooperativity between the intra- and intermolecular H-bonds exist in TW1, TW2 and TW3, respectively. The intramolecular O1H1T ⋯N1T H-bond and the intermolecular H-bonds (OH1W ⋯N1T and O1H1T ⋯OW) in TW5 are strong and have partial covalent character. The H-bonds involving methylene of Trp as H-donors are weak ones, especially the C5H7T ⋯O2T H-bond in TW3 and TW5 are derived from non-CT interaction since no CT evidence provided by NBO analyses. There exists an π H-bond in TW3 which involves the benzene ring as the H-acceptor. Unfortunately, no direct NBO or QTAIM evidences confirm to such π H-bond. For all complexes, ΔE ele and ΔE ex makes major contributions to the total interaction energy (ΔE MP2), while ΔE disp is the smallest component of the interaction energy. Both hydrogen bonding interaction and structural deformation play important roles in the relative stabilities of the complexes. Regardless of strong H-bond, the stability of TW5 is weakened by the serious structural deformation. In conclusion, the variety of the hydrogen bonding motifs that occur in the studied complexes may be helpful to further understand the hydrogen bonding interactions between Trp and other small organic molecules.