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Original article
11 2022
:34;
102350
doi:
10.1016/j.jksus.2022.102350

Hydrogen bonds interactions in biuret-water clusters: FTIR, X-ray diffraction, AIM, DFT, RDG, ELF, NLO analysis

, , , , , , , ,
a Siberian Federal University, pr. Svobodny, 79, Krasnoyarsk 660041, Russia
b Institute of Chemistry and Chemical Technology, Krasnoyarsk Science Center, Siberian Branch, Russian Academy of Sciences, Akademgorodok, 50/24, Krasnoyarsk 660036, Russia
c Prof. V.F. Voino-Yasenetsky Krasnoyarsk State Medical University of the Ministry of Healthcare of the Russian Federation, St. Partizan Zheleznyak, Bld. 1, Krasnoyarsk 660022, Russia
d Laboratory of Quantum and Statistical Physics (LR18ES18), Faculty of Sciences, University of Monastir, Monastir 5079 Tunisia
e Department of Physics and Astronomy, College of Science, King Saud University, PO Box 2455, Riyadh 11451, Saudi Arabia
f IMD Laboratories Co, R&D Section, Lefkippos Technology Park, NCSR Demokritos PO Box 60037, 15130 Athens, Greece
g State Key Laboratory of Pulp and Paper Engineering, South China University of Technology, Guangzhou 510640, China

⁎Corresponding authors at: Siberian Federal University, pr. Svobodny, 79, Krasnoyarsk 660041, Russia. leo_lion_leo@mail.ru (Aleksandr S. Kazachenko), kazachenko.as@icct.krasn.ru (Aleksandr S. Kazachenko), omar@ksu.edu.sa (Omar Al-Dossary)

Received: , Accepted: ,
© The Author(s) 2022
Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

  • Biuret-(H2O)n (n = 1–10) clusters was calculated using DFT method.

  • Intermolecular interactions of Biuret with water discovered using AIM, ELF and RDG.

  • Biuret-(H2O) was investigated by FTIR and XRD.

  • Chemical reactivity was simulated via HOMO-LUMO, MEP.

Abstract

In this work, we studied intermolecular aqueous clusters of biuret, an important urea derivative. FTIR showed an increase in the intensity of absorption bands when water molecules are introduced into the biuret. X-ray diffraction analysis showed that the introduction of water molecules into the biuret structure significantly increases the intensity of the bands on the diffraction patterns in the range from 14 to 65 2˚⊖. Aqueous biuret clusters have also been studied in the gas phase by theoretical methods: density functional theory and Atoms in Molecules (AIM) using the DFT level B3LYP/6–31 + G (d, p). The nature of molecular interactions between water and biuret through hydrogen bonds was also investigated using the electron localization function (ELF) and non-covalent reduced density gradient (NC-RDG). The thermodynamic and Non-linear optical properties of biuret-water clusters were performed also.

Keywords

Biuret
Clusters
Water
DFT
QTAIM
RDG
1

1 Introduction

Urea is recognized as the first artificially synthesized organic molecule (Yokoya et al., 2021). This discovery provided an opportunity for the development of the field of synthetic organic chemistry, and the synthesis of very complex and / or strained molecules became possible (Nicolaou et al., 2005).

Urea derivatives using in engineering and chemical-catalytic processes (Bernhard et al., 2012), due to the increased use of urea as a reducing agent for the selective catalytic reduction of nitrogen oxides in the after treatment of diesel engine exhaust gases (Koebel et al., 2000), and new materials (Dong et al., 2011), due to recent studies of urea derivatives as precursors of carbon nitride materials (Liu et al., 2011).

Biuret (carbamylurea) is a chemical compound with the chemical formula [H2NC(O)]2NH, formed as a result of the condensation of two equivalents of urea (Hughes et al., 1961). Biuret is also used as a non-protein nitrogen source in ruminant feed (Kunkle et al., 2013), where it is converted to protein by intestinal microorganisms. (Oltjen et al., 1969) It is less preferred than urea due to its higher cost and lower digestibility, but the latter characteristic also slows down its digestion and thus reduces the risk of ammonia poisoning (Fonnesbeck et al., 1975).

In recent studies (Kazachenko et al., 2021), biuret has been investigated as a catalyst for the sulfation of polysaccharides with sulfamic acid, as an alternative to urea.

In aqueous solutions, the phenomenon of clustering of some organic and inorganic molecules is encountered, which has recently been actively studied, both theoretically and experimentally (Akman et al., 2020; Kazachenko et al., 2021). Water clusters are discrete hydrogen-bonded assemblies or clusters of molecules in water (Ludwig, 2001).

Water clusters of various classes of substances have been actively studied in recent years. Thus, water clusters of ozone in various water/ozone ratios were studied in (Yadav et al., 2017), and the maximum binding capacity of water clusters of various sizes with respect to ozone molecules was shown. In (Wang et al., 2015), the interaction of new polymers with a water cluster was studied. Water clusters in crystalline hydrates were studied in (Supriya and Das, 2003). In (Akman et al., 2020), aqueous thiourea clusters were studied by both experimental and theoretical methods. A similar work was presented for ammonium sulfamate (Kazachenko et al., 2021) and sulfamic acid (Kazachenko et al., 2022). It is shown that despite the similarity of the structure of ammonium sulfamate and sulfamic acid, their clustering with water occurs differently, which is affected by the presence of the ammonium cation in the sulfamate. The influence of urea on water, including in clusters, was actively studied by experimental and theoretical methods in (Lovrinčević et al., 2020; Carr et al., 2013) and others.

Based on all of the above, the importance of studying water clusters of various substances is obvious. This work is a systematic continuation of the previously started topic of the study of water clusters of some acids, salts and urea derivatives. In this regard, the combined use of experimental and theoretical methods allows us to obtain the most reliable picture.

In this work, we studied aqueous clusters of biuret by FTIR, X-ray diffraction, QTAIM, DFT, RDG, ELF, NLO.

2

2 Experimental

2.1

2.1 FTIR and XRD analysis

Samples of the Biuret-water cluster were obtained by dissolving biuret in distilled water at 70˚C, followed by precipitation of the cluster at room temperature.

Shimadzu IR Tracer-100 spectrometer (Japan) within the wavelength range of 400–4000 cm−1 was used for registration FTIR spectra of biuret and biuret-water cluster. OPUS program (version 5.0) was used for analysis spectral data. Solid samples for analysis were prepared in the form of pills in a KBr matrix (2 mg sample/1000 mg KBr).

DRON-3 X-ray diffractometer (CuKα monochromatized radiation (λ = 0.154 nm), voltage 30 kV, current 25 mA) was used for X-ray diffraction (XRD) phase analysis. The scanning step is 0.02 deg; intervals for 1 s per data point. The measurement was carried out in the interval of the Bragg angles 2Θ from 5.00 to 70.00 deg.

2.2

2.2 Computational details

Molecular stability of each biuret-Water cluster has been investigated by calculating the SCF energy of these different structures. The calculation was performed using B3LYP/6–31 + G(d,p) method via Gaussian 09 software (Frisch et al., 2013). The output of various theories shows similar results but DFT theory results was more accurate compared with experimental data, so we are mentioning the results of DFT theory only. DFT theory is an effective tool for performing chemical calculations of compounds, better representation of polar bonds and accretion of lower basis set can also be done (Petersson and Al‐Laham, 1991; Petersson et al., 1988). The initial configuration searches for the biuret-water clusters were based on two steps. Firstly, the isomer component of the ABCluster software (Zhang and Dolg, 2015) was used to generate the initial structures of biuret water clusters. Both 2D and 3D initial guesses have been considered to make sure we get the true global minima of each structure. Secondly, Each of the generated structure was then fully optimized by DFT using B3LYP functional with the polarized basis sets (6–31 + G(d,p)) by Gaussian 09 package to obtain the respective total energy and locate the most stable geometry for each cluster. The optimized geometry of the considered clusters was confirmed to be located at the local true minima on the potential energy surface, as indicated by the lack of imaginary frequencies in the vibrational mode calculation. In addition, molecular electrostatic potential (MEP) surface was plotted for the considered clusters by using B3LYP/6–31 + G(d,p) level of theory. The MEP and all the output files were visualized by means of GaussView software (Dennington et al., 2010). The important parameters was the energy gap which considered the differences between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO). This gap gives the stability and tells about hard and soft nature of cluster. Then, topological analysis was carried out to discover the non covalent interactions. The wavefunctions obtained at the B3LYP/6–31 + G(d,p) level were used to determine the electron density ρc and the Laplacien electron density (∇2ρc) at the bond critical points (BCPs). The AIM, RDG and ELF visual representations were generated throughout Multiwfn 3.8 program (Lu and Chen, 2012).

3

3 Results and discussions

3.1

3.1 FTIR and XRD analysis

The initial biuret and its water clusters were analyzed by FTIR spectroscopy (Fig. 1).

FTIR spectra: a - Biuret, b - Biuret water cluster.
Fig. 1
FTIR spectra: a - Biuret, b - Biuret water cluster.

Fig. 1 shows the spectra of biuret and water biuret cluster. Basic infrared spectral data of biuret and its water cluster are presented in Table 1.

Table 1 Assignment of absorption bands in the FTIR spectra of biuret and water biuret cluster.
Wavenumber, cm−1 Vibration type
Biuret Biuret-water
3413 3422 νas (NH2) + ν(H2O)/νas(NH2)
3211 3227 νas(NH2)
1724 1722 ν(C⚌O)
1585 1584 δ(NH2)
1496, 1404 1369 ν(C—N) + ν(C − NH2)
1281 1273 δ(N—H)
1139 1138 ν(C—N) + δ(N—H)
1072 1067 ν(C—N)
907 903 ν(C—N) + ν(C − NH2)
797 794 δ(C − NH2)
716 716 δ(C⚌O)

In the spectra of biuret and its water cluster, two bands are observed (3200–3420 cm -1) in the region of stretching vibrations of N—H. The former is alternatively referred to as bridging hydroxide, while the band of water hydration appears at about 3420 cm –1 (Wang et al., 2016). Bending N — H vibrations are observed at 1585 cm – 1 with significant intensity. It is reported that the frequencies of carbonyl stretching vibrations in compounds containing the CO-NH-CO group give two bands (Uno and Machida, 1962); the peak of the asymmetric stretching vibration appears above 1720 cm -1, and the peak of the symmetric vibration appears at about 1680–1695 cm -1 (Hajji et al., 2021; Hajji et al., 2021).

When coordination occurs, it determines the degree of electron delocalization in the N-CO-N system; thus, coordination through the oxygen atom will lead to a decrease in the nature of the double bond of the C⚌O bonds and will lead to a shift in the carbonyl extension mode to the region of lower frequencies (Udupa and Indira, 1975).

The peaks of stretching vibrations of C⚌O bonds are found at 1684, 1693, 1622 cm -1, respectively.

The peaks of bending vibrations of C⚌O bonds, found in the region of 624–671 cm -1, may indicate some coordination between water models and oxygen atoms in biuret.

In addition, for the aqueous biuret cluster, there is a significant increase in the signal intensity of almost all absorption bands in comparison with the initial biuret, which is consistent with the data (Akman et al., 2020; Kazachenko et al., 2021). The peak of intermolecular hydrogen bonds of OH groups is observed at 3500–3200 cm−1, and its intensity increases by about 5 times when passing from biuret to an aqueous biuret cluster.

According to Fig. 2, the background of the X-ray diffraction patterns is low, and the diffraction intensity is high, which indicates that the complex has a fine-crystalline state. The X-ray diffraction pattern of the original biuret has high intensity bands at 11,15,17,19,21,23,29,39 2⊖ (deg), which corresponds to the data given in (Udachin et al., 2011).

XRD data: a - Biuret, b - Biuret water cluster.
Fig. 2
XRD data: a - Biuret, b - Biuret water cluster.

The inclusion of water molecules in the biuret crystal leads to a significant increase in the intensity of most peaks in the range from 14 to 65 2⊖ (deg). A similar phenomenon was observed for thiourea (Akman et al., 2020), ammonium sulfamate (Kazachenko et al., 2021), which can also be explained by the specific effect of water molecules on the crystal structure of compounds (Volz and Clayden, 2011).

3.2

3.2 Structural analysis of Biuret -(H2O)n clusters (n = 1–10)

Urea and its derivatives, which have both acceptor and donor parts of the hydrogen bond, are an ideal structure for the formation of various intermolecular clusters (Yokoya et al., 2021), including water clusters (Akman et al., 2020). Recently, urea derivatives have attracted particular attention due to the fact that they contain important functional groups (Hammami et al., 2015).

To determine the interactions of the biuret molecule in water, the most stable clusters of biuret with water were identified. The most stable clusters are possible, such as Biuret -(H2O), Biuret -(H2O)2, Biuret -(H2O)3, Biuret -(H2O)4, Biuret -(H2O)5, Biuret -(H2O)6, Biuret -(H2O)7, Biuret -(H2O)8, Biuret-(H2O)9, Biuret-(H2O)10, have been optimized at the level of B3LYP theory with a 6–31 + G (d, p) basis set and are represented by atomic numbers in Fig. 3 (a-l).

The Optimized structures of Biuret-water clusters.
Fig. 3
The Optimized structures of Biuret-water clusters.

The optimized parameter such as bond lengths of Biuret-(H2O)(1−10) clusters were computed using the B3LYP theory with a 6–31 + G (d, p) method and compared with each other. The optimized bond parameters of the biuret water clusters (Biuret-(H2O)(1−10)) are shown in Table 2 and 3.

Table 2 The structural parameters of Biuret-water clusters: Biuret-(H2O), Biuret-(H2O)2, Biuret-(H2O)3, Biuret-(H2O)4, Biuret-(H2O)5.
Biuret-(H2O) Biuret-(H2O)2 Biuret-(H2O)3 Biuret-(H2O)4 Biuret-(H2O)5
C1-N8 1.3701 C1-N8 1.3632 O1-H2 0.9613 C1-N8 1.3567 O1-H2 0.9644
C1-N9 1.389 C1-N9 1.3958 O1-H3 0.9868 C1-N9 1.4013 O1-H3 0.9859
C1-O11 1.2319 C1-O11 1.2327 O1-H21 1.716 C1-O11 1.2348 O1-H24 1.7355
C2-N9 1.4036 C2-N9 1.3934 H3-O4 1.7221 C2-N9 1.3857 H3-O18 1.7639
C2-O10 1.3476 C2-O10 1.3474 O4-H5 0.9612 C2-N10 1.3463 O4-H5 0.9757
C2-O12 1.2385 C2-O12 1.2425 O4-H6 0.9836 C2-O12 1.2475 O4-H6 0.9846
H3-N8 1.0091 H3-N8 1.0134 H6-O18 1.7445 H3-N8 1.0166 O5-H22 1.9572
H4-N8 1.0087 H4-N8 1.0077 C7-N14 1.3579 H4-N8 1.0071 H6-O25 1.7929
H5-N9 1.0217 H5-N9 1.0201 C7-N15 1.3997 H5-N9 1.0259 C7-N14 1.3558
H6-N10 1.0157 H6-N10 1.0165 C7-O17 1.2264 H6-N10 1.0175 C7-N15 1.4022
H7-N10 1.0074 H7-N10 1.0074 C8-N15 1.393 H7-N10 1.0071 C7-O17 1.2343
O12-H15 1.8677 O13-H14 0.9891 C8-N16 1.3465 O12-H24 1.6408 C8-N15 1.3801
O13-H14 0.9642 O13-H15 0.965 C8-O18 1.2348 O13-H14 0.9642 C8-N16 1.3429
O13-H15 0.9828 O12-H17 1.7547 H9-N14 1.014 O13-H15 0.9805 C8-O18 1.2554
H14-O16 1.7497 H10-N14 1.0058 O13-H20 1.884 H9-N14 1.0157
O16-H17 0.9893 H11-N15 1.0188 H15-O22 1.8528 H10-N14 1.0071
O16-H18 0.964 H12-N16 1.0152 O16-H17 0.9643 H11-N15 1.0276
H13-N16 1.0058 O16-H18 0.98 H12-N16 1.0182
O19-H20 0.9621 O16-H21 1.8522 H13-N16 1.0074
O19-H21 0.9883 H18-O22 1.8754 O18-H20 1.9672
O19-H20 0.9793 O19-H20 0.9763
O19-H21 0.981 O19-H21 0.9749
O22-H23 0.9651 O19-H27 1.755
O22-H24 1.001 H21-O22 1.9877
O22-H23 0.9645
O22-H24 0.9903
O25-H26 0.9636
O25-H27 0.9893
Table 3 The structural parameters of Biuret-water clusters: Biuret-(H2O)6, Biuret-(H2O)7, Biuret-(H2O)8, Biuret-(H2O)9, Biuret-(H2O)10.
Biuret-(H2O)6 Biuret-(H2O)7 Biuret-(H2O)8 Biuret-(H2O)9 Biuret-(H2O)10
O1-H2 0.9853 O1-H2 1.0029 O1-H2 0.979 O1-H2 0.9755 O1-H2 0.9853
O1-H3 0.9648 O1-H3 0.9648 O1-H3 0.9784 O1-H3 0.9773 O1-H3 0.9874
O1-H27 1.7327 O1-H9 1.8579 O1-H9 1.6438 O1-H26 1.7459 O1-H6 1.9219
H2-O4 1.7939 O1-H26 1.9227 H2-H24 1.8715 H2-O4 1.9493 O1-H14 1.7329
O4-H5 0.9651 H2-H22 1.6563 H3-H25 1.8994 H3-O10 1.9145 H2-O7 1.8013
O4-H6 1.0059 O4-H5 0.9787 O4-H5 0.977 O4-H5 0.9653 H3-O40 1.7952
O4-H9 1.9351 O4-H6 0.9779 O4-H6 0.9789 O4-H6 0.9891 O4-H5 0.9764
H6-O28 1.6406 O4-H33 1.6563 O4-H29 1.6593 O4-H38 1.8858 O4-H6 0.9781
O7-H8 0.9862 H5-O21 1.8863 H5-O24 1.8893 H6-O24 1.7409 O4-H35 1.6905
O7-H9 0.9763 H6-O28 1.9058 H6-O25 1.8707 O7-H8 0.9647 H5-O31 1.9595
O7-H14 1.8288 O7-H8 0.9802 O7-H8 0.9647 O7-H9 1.0018 O7-H8 0.9639
H8-H14 2.0819 O7-H9 0.9802 O7-H9 1.0045 O7-H33 1.9216 O7-H9 0.9898
H8-O22 1.8322 O7-H14 1.8744 O7-H11 1.8428 O7-H39 1.8559 H9-O37 1.7538
C10-N17 1.361 H8-O31 1.8579 O7-H33 1.9138 H9-O28 1.6533 O10-H11 0.98
C10-N18 1.3973 C10-N17 1.3572 O10-H11 0.9805 O10-H11 1.0019 O10-H12 0.9807
C10-O20 1.2333 C10-N18 1.4011 O10-H12 0.9798 O10-H12 0.9649 O10-H29 1.999
C11-N18 1.3845 C10-O20 1.2341 H12-O34 1.853 O10-H32 1.8747 O10-H41 1.7914
C11-N19 1.3447 C11-N18 1.3836 C13-N20 1.3563 H11-O37 1.6594 H11-O27 1.9157
C11-O21 1.2504 C11-N19 1.3435 C13-N21 1.4021 C13-N20 1.3548 H12-O13 1.8985
H12-N17 1.0143 C11-O21 1.2518 C13-O23 1.2346 C13-N21 1.404 O13-H14 0.9946
H13-N17 1.0075 H12-N17 1.0158 C14-N21 1.385 C13-O23 1.2346 O13-H15 0.9814
H14-N18 1.0285 H13-N17 1.0072 C14-N22 1.3441 C14-N21 1.3765 H15-O31 1.8648
H15-N19 1.0173 H14-N18 1.0271 C14-O24 1.2505 C14-N22 1.3425 C16-N23 1.359
H16-N19 1.0075 H15-N19 1.0177 H15-N20 1.0171 C14-O24 1.2583 C16-N24 1.4007
O21-H24 2.0134 H16 -N19 1.0075 H16-N20 1.0072 H15-N20 1.0174 C16-O26 1.232
O21-H30 1.8644 O21-H23 1.8863 H17-N21 1.0256 H16-N20 1.0072 C17-N24 1.388
O22-H23 0.9753 O22-H23 0.9787 H18-N22 1.0179 H17-N21 1.0329 C17-N25 1.343
O22-H24 0.9756 O22-H24 0.9779 H19-N22 1.0076 H17-O25 1.8091 C17-O27 1.2499
H23-O25 1.9372 H24-O28 1.9061 O25-H26 0.9647 H18-N22 1.0185 H18-N23 1.0146
O25-H26 0.9647 O25-H26 0.9779 O25-H27 1.0003 H19-N22 1.0075 H19-N23 1.0076
O25-H27 0.9907 O25-H27 0.9779 H27-O31 1.6716 O24-H30 1.8866 H20-N24 1.0175
O25-H29 1.9415 O25-H29 1.6852 O28-H29 0.9998 O25-H26 0.9903 H21-N25 1.0174
O28-H29 0.9768 H27-O31 1.9219 O28-H30 0.9637 O25-H27 0.9792 H22-N25 1.0076
O28-H30 0.9799 O28-H29 0.9993 O28-H35 1.647 H27-O34 1.8597 O27-H38 1.9624
O28-H30 0.9645 O31-H32 0.979 O28-H29 0.9791 O28-H29 0.9744
O31-H32 0.9648 O31-H33 0.9777 O28-H30 0.9777 O28-H30 0.9795
O31-H33 1.0029 H32-O34 1.8825 H29-O34 1.8917 O28-H32 1.6752
O34-H35 1.0004 O31-H32 0.9799 H30-O34 1.9012
O34-H36 0.9649 O31-H33 0.9779 O31-H32 1.0007
O31-H36 1.6489 O31-H33 0.965
O34-H35 0.9651 O34-H35 0.9992
O34-H36 1.0033 O34-H36 0.9649
O37-H38 0.978 O34-H42 1.9657
O37-H39 0.9799 O37-H38 0.9757
H39-O40 2.0021
O40-H41 0.9855
O40-H42 0.9761

According to the data given in Tables 2 and 3, the bond lengths C1-N8, C2-O10, H4-N8, H5-N9, O13-H15 in a cluster of water biuret with one water molecule (Biuret- (H2O)) are slightly longer than in other water clusters, while the lengths of the C2-N9, C2-O12, C1-O11, and H3-N8 bonds in the Biuret- (H2O) cluster are shorter than in other clusters, that these bonds may be associated with greater sensitivity to hydration (Akman et al., 2020; Kazachenko et al., 2021).

The shortest bond length with a value of 0.9613 Å is observed for O1-H2 in the Biuret- (H2O)3 cluster. It should also be noted that a group of OH bonds with rather low values is observed for the Biuret- (H2O) 5 cluster: O22-H23 (0.9645 Å), O22-H24 (0.9903 Å), O25-H26 (0.9636 Å), and O25-H27 (0.9893 Å). The longest bond lengths H8-H14 (2.0819 Å) and O21-H24 (2.0134 Å) are observed for the Biuret cluster - (H2O) 6, H39-O40 (2.0021 Å) for the Biuret - (H2O) 10 cluster.

In the Biuret-(H2O)cluster (Fig. 3a, Table 4), the bonding energy is −58.45 kJ/mol (Table 5), and its is formed by one hydrogen bonds, such as, O13-H15…O12 with values X-H··· X 1.867. In the Biuret-(H2O)2cluster (Fig. 3b), the bonding energy is −111.45 kJ/mol, and its structure is formed by two hydrogen bonds, such as, O16- H17…O12, O13-H14…O16with values X-H··· X:1.750, 1.740, respectively. In the Biuret-(H2O)3 cluster (Fig. 3c), the bonding energy is −636.45 kJ/mol, and its structure is formed by three hydrogen bonds, such as, O4-H14…O16, O1-H3…O4, O19-H21…O1with values X-H··· X:1.74, 1.72, 1.71, respectively. It should be noted that the ring structure for aqueous biuret complexes is formed only for clusters with four water molecules and higher. In the Biuret-(H2O)4 cluster (Fig. 3d), the bonding energy is −242.45 kJ/mol, and its structure is formed by five hydrogen bonds, such as, O22-H24…O12, O16-H18…O22, O19-H21…O16, O13-H15…O22, O19-H20…O13 with values X-H··· X:1.64, 1.87, 1.85, 1.85, 1.88, respectively. In the Biuret-(H2O)5cluster (Fig. 3e), the bonding energy is −294.45 kJ/mol, and its ring structure is formed by six hydrogen bonds, such as, O1-H3…O18, O19-H20…O18, O22-H24…O1, O4-H5…O22, O4-H6…O25, O25-H27…O19with values X-H··· X:1.76, 1.96, 1.73, 1.95, 1.79, 1.75, respectively. In the Biuret-(H2O)6 cluster (Fig. 3f), the bonding energy is −347.45 kJ/mol, and its ring structure is formed by elevenhydrogen bonds, such as, N18-H14…O7, N18-H14…O8, O7-H9…O4, O1-H2…O4, O25-H27…O1, O28-H29…O25, O22-H23…O25, O4-H6…O28, O28-H30…O21, O22-H24…O21, O7-H8…O22 with values X-H··· X:1.82, 2.01, 1.93, 1.79, 1.73, 1.94, 1.93, 1.64, 1.86, 2.01, 1.83, respectively. In the Biuret-(H2O)7 cluster (Fig. 3g), the bonding energy is −426.45 kJ/mol, and its ring structure is formed by twelve hydrogen bonds, such as, N18-H14…O7, O7-H8…O31, O25-H27…O31, O4-H5…O21, O22-H23…O21, O31-H33…O4, O4-H6…O28, O22-H24…O28, O28-H29…O25, O25-H27…O31, O25-H26…O1, O1-H2…O22 with values X-H··· X:1.87, 1.85, 1.92, 1.88, 1.88, 1.65, 1.90, 1.96, 1.68, 1.92, 1.92, 1.65, respectively. In the Biuret-(H2O)8 cluster (Fig. 3h), the bonding energy is −478.45 kJ/mol, and its ring structure is formed by twelve hydrogen bonds, such as, O1-H2…O24, O4-H5…O24, O4-H6…O25, O25-H27…O31, O31-H32…O34, O10-H11…O7, O31-H33…O7, O10-H12…O34, O7-H9…O1, O1-H3…O25, O34-H35…O28, O28-H29…O4with values X-H··· X:1.87, 1.88, 1.87, 1.67, 1.88, 1.84, 1.91, 1.85, 1.64, 1.89, 1.64, 1.65, respectively. In the Biuret-(H2O)9 cluster (Fig. 3i), the bonding energy is −556.45 kJ/mol, and its ring structure is formed by fourteen hydrogen bonds, such as, O4-H6…O24, O1-H2…O4, O28-H30…O24, N21-H17…O25, O25-H27…O34, O28-H29…O34, O7-H9…O28, O34-H36…O31, O1-H3…O10, O31-H32…O10, O10-H11…O37, O37-H38…O4, O37-H39…O7, O25-H26…O1with values X-H··· X:1.74, 1.94, 1.88, 1.80, 1.85, 1.89, 1.65, 1.64, 1.91, 1.87, 1.65, 1.88, 1.85, 1.74, respectively. In the Biuret-(H2O)10cluster (Fig. 3j), the bonding energy is −583.45 kJ/mol, and its ring structure is formed by fifteen hydrogen bonds, such as, O37-H38…O27, O37-H39…O40, O7-H9…O37, O1-H2…O7, O1-H3…O40, O13-H14…O1, O28-H29…O10, O28-H30…O34, O40-H42…O34, O34-H35…O4, O4-H5…O31, O13-H15…O31, O31-H32…O28, O10-H12…O13, O4-H6…O1 with values X-H··· X:1.96, 2.00, 1.75, 1.80, 1.79, 1.73, 1.99, 1.90, 1.96, 1.69, 1.95, 1.86, 1.67, 1.89, 1.92, respectively.

Hydrogen bonds O ⋯ O between water molecules are also observed and, as was found, are shorter than hydrogen bonds NH … O, which indicates that the cyclic parts of aqueous biuret clusters with 6 (or more) water molecules are especially stabilized by OH … O hydrogen bonds, which is consistent with (Zumdahl, 2000). DFT calculations for aqueous biuret clusters with 6 (or more) water molecules show that a probable cluster is stabilized due to the formation of a ring structure around some parts of the central biuret molecule.

Intermolecular interaction energies of with hydrogen bonds calculated by the B3LYP / 6–31 + G (d, p) method (Table 4). The energies of intermolecular interaction with hydrogen bonds in the biuret water clusters calculated by the formula: ΔE = E(cluster)-[E(Biuret) + n*E(H2O)] (1).

Table 4 Hydrogen bonding interactions parameters of Biuret-water clusters.
H-Bond X-H…X X…X
Biuret-(H2O) O13-H15…O12 1.867 2.75
Biuret-(H2O)2 O16- H17…O12 1.75 2.73
O13-H14…O16 1.74 2.69
Biuret-(H2O)3 O4-H14…O16 1.74 2.72
O1-H3…O4 1.72 2.70
O19-H21…O1 1.71 2.69
Biuret-(H2O)4 O22-H24…O12 1.64 2.64
O16-H18…O22 1.87 2.82
O19-H21…O16 1.85 2.78
O13-H15…O22 1.85 2.79
O19-H20…O13 1.88 2.08
Biuret-(H2O)5 O1-H3…O18 1.76 2.74
O19-H20…O18 1.96 2.91
O22-H24…O1 1.73 2.69
O4-H5…O22 1.95 2.88
O4-H6…O25 1.79 2.74
O25-H27…O19 1.75 2.71
Biuret-(H2O)6 N18-H14…O7 1.82 2.83
N18-H14…O8 2.01 3.04
O7-H9…O4 1.93 2.87
O1-H2…O4 1.79 2.75
O25-H27…O1 1.73 2.70
O28-H29…O25 1.94 2.86
O22-H23…O25 1.93 2.87
O4-H6…O28 1.64 2.63
O28-H30…O21 1.86 2.83
O22-H24…O21 2.01 2.95
O7-H8…O22 1.83 2.77
Biuret-(H2O)7 N18-H14…O7 1.87 2.85
O7-H8…O31 1.85 2.80
O25-H27…O31 1.92 2.85
O4-H5…O21 1.88 2.85
O22-H23…O21 1.88 2.85
O31-H33…O4 1.65 2.65
O4-H6…O28 1.90 2.83
O22-H24…O28 1.96 2.83
O28-H29…O25 1.68 2.66
O25-H27…O31 1.92 2.85
O25-H26…O1 1.92 2.85
O1-H2…O22 1.65 2.65
Biuret-(H2O)8 O1-H2…O24 1.87 2.83
O4-H5…O24 1.88 2.85
O4-H6…O25 1.87 2.83
O25-H27…O31 1.67 2.66
O31-H32…O34 1.88 2.84
O10-H11…O7 1.84 2.79
O31-H33…O7 1.91 2.84
O10-H12…O34 1.85 2.82
O7-H9…O1 1.64 2.63
O1-H3…O25 1.89 2.83
O34-H35…O28 1.64 2.64
O28-H29…O4 1.65 2.65
Biuret-(H2O)9 O4-H6…O24 1.74 2.72
O1-H2…O4 1.94 2.90
O28-H30…O24 1.88 2.86
N21-H17…O25 1.80 2.79
O25-H27…O34 1.85 2.82
O28-H29…O34 1.89 2.84
O7-H9…O28 1.65 2.64
O34-H36…O31 1.64 2.64
O1-H3…O10 1.91 2.86
O31-H32…O10 1.87 2.82
O10-H11…O37 1.65 2.64
O37-H38…O4 1.88 2.84
O37-H39…O7 1.85 2.81
O25-H26…O1 1.74 2.72
Biuret-(H2O)10 O37-H38…O27 1.96 2.92
O37-H39…O40 2.00 2.89
O7-H9…O37 1.75 2.72
O1-H2…O7 1.80 2.73
O1-H3…O40 1.79 2.77
O13-H14…O1 1.73 2.71
O28-H29…O10 1.99 2.86
O28-H30…O34 1.90 2.84
O40-H42…O34 1.96 2.84
O34-H35…O4 1.69 2.67
O4-H5…O31 1.95 2.88
O13-H15…O31 1.86 2.80
O31-H32…O28 1.67 2.66
O10-H12…O13 1.89 2.87
O4-H6…O1 1.92 2.82

According to Table 5, the minimum value of Bonding energy (-58.45 kJ / mol) is observed for an aqueous biuret cluster with one water molecule. It should be noted that the maximum value of Bonding energy (-636.45 kJ / mol) is observed for the Biuret- (H2O) 3 cluster, which may be associated with some energy intensity of this structure. The ring structure is observed in Biuret- (H2O)n (n = 4–10). Bonding energy values for these clusters change almost linearly from R2 = 0.9924 (Fig. 4).

Table 5 Energy values of Biuret-water clusters computed at B3LYP/6–31 + G(d,p) level of theory.
Number of water molecules Energy (kJ/mol) Bonding energy ΔE (kJ/mol)
1 −1235219 −58.45
2 −1435939 −111.45
3 −1637131 −636.45
4 −1837404 −242.45
5 −2038123 −294.45
6 −2238843 −347.45
7 −2439589 −426.45
8 −2640308 −478.45
9 −2841053 −556.45
10 −3041747 −583.45
Influence of the number of water molecules in water clusters on: (a) - Energy, (б) - Bonding energy.
Fig. 4
Influence of the number of water molecules in water clusters on: (a) - Energy, (б) - Bonding energy.

For all water clusters of biuret, starting from Biuret- (H2O), with an increase in the number of molecules in the cluster, there is a linear change in the Energy value from −1235219 to −3041747 kJ / mol (Fig. 4, Table 5).

3.3

3.3 NLO and thermodynamic properties of biuret-water clusters

NLO properties are important for frequency shift, optical modulation, switching, laser, fiber, optical material logic, and optical memory for emerging technologies in areas such as telecommunications, signal processing, and optical interface. compounds (Noureddine et al., 2021).

Non-linear optical properties (NLO), such as dipole moment, hyperpolarizability and polarizability for biuret-water clusters were calculated using the DFT method (Table 6). The effect on polarizability (α0) of the water molecules numbers in biuret-water clusters is shown in Fig. 5.

Table 6 The Dipole moment (Debye), polarizability (10-24 e.s.u) and hyperpolarizability (10-31 e.s.u) of Biuret-water clusters.
Number of water molecule Dipole moment Polarisability Hyperpolarisability
1 1.758 9.429 6.139
2 2.068 10.080 7.460
3 1.796 12.376 9.667
4 3.112 13.614 9.609
5 2.896 14.664 12.771
6 2.500 15.931 8.501
7 1.212 17.281 10.868
8 2.215 19.004 10.405
9 1.567 20.659 6.170
10 2.031 21.462 7.787
The effect on polarizability of the number of water molecules in biuret-water clusters.
Fig. 5
The effect on polarizability of the number of water molecules in biuret-water clusters.

According to the data shown in Table 6, the values of the dipole moment change nonlinearly with an increase in the number of molecules in aqueous biuret clusters. The maximum value (3.112 Debye) of the dipole moment is observed for the Biuret- (H2O) 4 cluster, and the minimum value (1.212 Debye) is observed for the Biuret- (H2O) 7 cluster. Hyperpolarisability values change in the same way. Maximum value (12.771*10-31 e.s.u)Hyperpolarisability is observed for the Biuret- (H2O) 5 cluster, and the minimum value (6.139*10-31 e.s.u) - observed for the Biuret- (H2O) cluster.

At the same time, the polarisability values increase almost linearly with an increase in the number of water molecules in aqueous biuret clusters with an R2 value (0.9948). A similar phenomenon was observed in the case of thiourea (Akman et al., 2020) and ammonium sulfamate (Kazachenko et al., 2021).

Various thermodynamic functions are used to predict the reactivity of chemicals and to determine the likelihood of different reaction routes (Fazilath Basha et al., 2021).Standard thermodynamic functions such as zero-point energy correction, heat capacity, entropy (S) electronic energy (EE), thermal correction to energy, thermal correction to enthalpy, thermal correction to free energy, and other parameters were calculated using B3LYP methods with a basis set of 6–31 + G (d, p) (Table 7).

Table 7 The thermodynamic parameters calculated at 298.15 K for the different Biuret-water clusters using B3LYP/6–31 + G(d,p).
Parameters 1 2 3 4 5 6 7 8 9 10
E(RB3LYP) −470.4703 −546.9272 −623.5516 −699.8305 −776.2813 −852.7348 −929.1959 −1005.6473 −1082.1018 −1158.5479
Electronic Energy (EE) −470.4703 −546.9272 −623.5516 −699.8305 −766.2818 −852.7348 −929.1959 1005.6473 −1082.1018 −1158.5479
Zero-point Energy Correction 0.1159 0.1418 0.1664 0.19301 0.2187 0.2455 0.2722 0.2972 0.3237 0.3503
Thermal Correction to Energy 0.1260 0.1543 0.1819 0.2106 0.2388 0.2676 0.2960 0.3238 0.3532 0.3814
Thermal Correction to Enthalpy 0.1270 0.1553 0.1829 0.2116 0.2398 0.2685 0.2970 0.3247 0.3532 0.3823
Thermal Correction to Free Energy 0.0807 0.1031 0.1231 0.1474 0.1701 0.1948 0.2200 0.2412 0.2656 0.2890
EE + Zero-point Energy −470.3544 −546.7854 −623.3851 −699.6374 −776.0638 −852.4892 −928.9237 −1005.3499 −1081.7780 −1158.1976
EE + Thermal Energy Correction −470.3442 −546.7728 −623.3697 −699.6198 −766.0429 −852.4671 −928.8999 −1005.3234 −1081.7494 −1158.1665
EE + Thermal Enthalpy Correction −470.3433 −546.7719 −623.3687 −699.6188 −766.0419 −852.4662 −928.9888 −1005.3225 −1081.7485 −1158.1655
EE + Thermal Free Energy Correction −470.3896 −546.8241 −623.4285 −699.6830 −766.1117 −852.5399 −928.9758 −1005.4060 −108.8361 −1158.2588
E (Thermal) 79.12 96.881 114.186 132.201 149.91 167.933 185.779 203.209 221.080 239.348
Heat Capacity (Cv) 35.33 43.661 52.922 61.305 69.603 76.988 84.144 72.880 100.659 109.245
Entropy (S) 97.39 109.75 125.876 135.098 146.736 155.039 161.861 175.904 184.415 196.433

According to the data given in Table 7 and Fig. 6, the values of E (Thermal), Heat Capacity (Cv), Entropy (S) increase linearly as water molecules in the biuret cluster increase. For the change in E (Thermal) R2 = 1, which is high. For the dependence of the change in Heat Capacity (Cv) on the content of water molecules in the water cluster of biuret, R2 = 0.9939 is observed. For the dependence of the change in Entropy (S) on the content of water molecules in the aqueous biuret cluster, R2 = 0.9325 is observed.

The variation of thermodynamic parameters as a function of the water molecules numbers in the biuret-water clusters.
Fig. 6
The variation of thermodynamic parameters as a function of the water molecules numbers in the biuret-water clusters.

It should be noted that other thermodynamic characteristics also change almost linearly with a regular change in water molecules in the biuret cluster. A similar phenomenon was also observed in (Kazachenko et al., 2021).

3.4

3.4 HOMO-LUMO analysis and electronic parameters of Biuret-(H2O)n clusters

Frontier molecular orbitals (FMO) are a valuable practical model for describing chemical reactivity. This theory permit the identification of electrophilic and nucleophilic attacks which responsible to the formation of hydrogen bonding interactions. An important aspect of the theory of boundary electrons is the emphasis on the busiest and lowest unoccupied molecular orbitals (HOMO and LUMO). So, according to this theory, attention is paid to the localization of the HOMO orbital, because electrons from this orbital are most free to participate in the reaction. Likewise, the boundary orbit theory predicts that the location of the lowest unoccupied orbital (LUMO) is a good electrophilic site (Gatfaoui et al., 2019).

Using the energy gap between HOMO-LUMO, ionization potential (IP), electronegativity (χ), softness(ς),electron affinity (EA), electrophilicity index (ɷ),chemical potential (μ) (Table 8) were calculated (at B3LYP/6–31 + G(d,p) basis set, according (Fleming, 1976) by the following equations:

(2)
IP=-EHOMO
(3)
EA=-ELUMO
(4)
χ=-1/2ELUMO+EHOMO
(4)
μ=1/2ELUMO+EHOMO
(5)
η=1/2ELUMO-EHOMO
(5)
ζ=1η
(6)
ω=μ22η
Table 8 The electronic parameters of the different Biuret-water clusters.
EHOMO ELUMO Gap Ionisation energy Electron affinity Chemical potential Chemical hardness (η) Softness Electronegativity Electrophilicity
1 −7,33 −0,33 −7 7,33 0,33 −3,83 3,5 0,14 25,67 3,83
2 −7,76 −0,16 −7,6 7,76 0,16 −3,96 3,8 0,13 29,79 3,96
3 −7,76 −0,66 −7,1 7,76 0,66 −4,21 3,55 0,14 31,46 4,21
4 −7,58 −0,19 −7,39 7,58 0,19 −3,88 3,695 0,13 27,88 3,885
5 −7,68 −0,27 −7,41 7,68 0,27 −3,97 3,705 0,13 29,27 3,975
6 −7,75 −0,3 −7,45 7,75 0,3 −4,02 3,725 0,13 30,17 4,025
7 −7,76 −0,3 −7,46 7,76 0,3 −4,03 3,73 0,13 30,28 4,03
8 −7,73 −0,32 −7,41 7,73 0,32 −4,02 3,705 0,13 30,01 4,025
9 −7,77 −0,82 −6,95 7,77 0,82 −4,29 3,475 0,14 32,05 4,295
10 −7,93 −0,44 −7,49 7,93 0,44 −4,18 3,745 0,13 32,79 4,185

A small band gap indicates that the molecule has high polarization, chemical reactivity and biological activity, and low kinetic stability (Bader, 1990). Based on the lower energy gap, it should be noted that the biuret cluster with nine water molecules has a higher chemical stability than other clusters.

According to the data presented in Table 8, the Softness values practically do not change with an increase in the number of water molecules in the biuret cluster and are 0.13–0.14. The Electronegativity values change nonlinearly with an increase in the number of water molecules in the biuret cluster, while the minimum Electronegativity (25.67) corresponds to the minimum number of water molecules in the biuret cluster, and the maximum Electronegativity (32.79) corresponds to the maximum number of water molecules (in the us spaces (1–10)). Electrophilicity values also change non-linearly. The minimum Electrophilicity value (3.83) corresponds to the Biuret- (H2O) cluster, and the maximum Electrophilicity value (4.295) corresponds to the Biuret- (H2O) 9 cluster. Other characteristics, such as Ionisation energy, Electron affinity, Chemical potential and Chemical hardness, change nonlinearly with an increase in the amount of water in the water clusters of biuret.

3.5

3.5 AIM, RDG and ELF topological analysis

The theory of atoms in molecules (AIM) is actively used to determine the types of interactions in various molecular systems (Johnson et al., 2010). Topological parameters such as electron density ρ (r), the Laplacian of electron density ∇2ρ (r), potential energy density V (r), Lagrangian kinetic energy G (r), Kinetic energy of Hamiltonian H (r) = G (r) + V (r) and the binding energy Eint = V (r) / 2 can help to understand the properties of hydrogen bonds between compounds (Akman et al., 2020). The Molecular diagram of the Biuret-water clusters is shown in Fig. 7.

AIM graphical visualization of Biuret-water clusters.
Fig. 7
AIM graphical visualization of Biuret-water clusters.

According to (Johnson et al., 2010), the interactions of hydrogen bonds can be defined as follows:

  • (1)

    ∇2ρ (r) > 0 and H (r) > 0 = Weak hydrogen bonds;

  • (2)

    ∇2ρ (r) > 0 and H (r) < 0 = Moderate hydrogen bonds;

  • (3)

    ∇2ρ (r) < 0 and H (r) < 0 = Strong hydrogen bonds.

The electron density ρ (r) and its Laplacian ∇2ρ(r) help determine the nature of interactions. On the whole, large values of the electron density ρ (r) and its Laplacian ∇2ρ(r) show the power of hydrogen interactions. Negative values of the Laplacian ∇2ρ(r) indicate a strong covalent character, while positive values indicate a decrease in the charge in the internuclear region (Akman et al., 2020; Kazachenko et al., 2021).

In the Biuret-(H2O) cluster, three types of interactions were observed: O13-H15…O12, N9-H5…O13, N10-H6…O11, where the electron density values are 0.0312, 0.0256, 0.0290a. u. and the Laplacian values are 0.0887, 0.0775, 0.0912a. u. respectively. As clearly seen from Table 9, the first hydrogen bond (O13-H15…O12) was matched to the biggest binding energy with value equal to 62.16 kcal/mol. In the Biuret-(H2O)2 cluster, five H-bonds interactions were observed: N8-H3…O13, N9-H6…O13, O16-H17…O12, O13-H14…O16, N10-H6…O11, where the electron density values are 0.0139, 0.0267, 0.0380, 0.0390, 0.0288a. u. and the Laplacian values are 0.0445, 0.0742, 0.1122, 0.1171, 0.0898a. u. respectively. The major interaction energy value corresponds to the fourth hydrogen bond with 76.85 kcal/mol. In the Biuret-(H2O)3 cluster, three types of interactions were observed: N14-H9…O19, N15-H11…O19, N16-H12…O17, O19-H21…O1, O1-H3…O4, O4-H6…O18, where the electron density values are 0.0211, 0.0226, 0.0290, 0.0421, 0.0411, 0.0367a. u. and the Laplacian values are 0.0807, 0.0792, 0.1103, 0.1347, 0.1347, 0.1308a. u. respectively. In the Biuret-(H2O)4 cluster, three types of interactions were observed: N18-H3…O19, O19-H20…O13, N9-H5…O19, O19-H21…O16, O13-H15…O22, O22-H24…O12, N10-H6…O11, where the electron density values are 0.0216, 0.0289, 0.0300, 0.0313, 0.0308, 0.0487, 0.0308a. u. and the Laplacian values are 0.0654, 0.0847, 0.0822, 0.0913, 0.0903, 0.1459, 0.0960a. u. respectively. Concerning Biuret-(H2O)5 cluster, three types of interactions were observed: N16-H12…O17, N15-H11…O4, N14-H9…O4, O4-H5…O22, O25-H27…O19, O1-H3…O18, O19-H20…O18, O22-H24…O1, O4-H6…O25, where the electron density values are 0.0307, 0.0321, 0.0195, 0.2451, 0.0398, 0.0361, 0.0232, 0.0402, 0.0349a. u. and the Laplacian values are 0.0956, 0.0857, 0.0597, 0.0710, 0.1139, 0.1113, 0.0677, 0.1195, 0.1053a. u. respectively. The EH…O energy value of these interactions were ranging from 40 to 77 kcal/mol. Regarding Biuret-(H2O)6 cluster, three types of interactions were observed: N17-H12…O7, N18-H14…O7, O28-H30…O21, O22-H24…O21, O1-H2…O4, O4-H6…O28, O25-H27…O1, O7-H8…O22, O7-H9…O4, O28-H29…O25, O22-H23…O25, O22-H23…O21, where the electron density values are 0.0140, 0.0358, 0.0284, 0.0220, 0.0355, 0.0523, 0.0408, 0.0337, 0.0259, 0.0256, 0.0254, 0.0220a. u. and the Laplacian values are0.0447, 0.0693, 0.0864, 0.0608, 0.0141, 0.1407, 0.1197, 0.0941, 0.0472, 0.0736, 0.0740, 0.0608a. u. respectively. In the Biuret-(H2O)7 cluster, twelve hydrogen bonding interactions were identified: N17-H12…O7, N18-H14…O7, N19-H15…O20, O4-H5…O21, O22-H23…O21, O31-H33…O4, O4-H6…O28, O22-H24…O28, O25-H27…O31, O1-H2…O22, O25-H26…O1, O7-H9…O1,where the electron density values are 0.0200, 0.0322, 0.0302, 0.0272, 0.0272, 0.0501, 0.0275, 0.0275, 0.0269, 0.0501, 0.0268, 0.0306a. u. and the Laplacian values are0.0607, 0.0877, 0.0940, 0.0817, 0.0818, 0.1372, 0.0800, 0.0799, 0.0768, 0.1372, 0.0767, 0.0893a. u. respectively. In the Biuret-(H2O)8 cluster, three types of interactions were observed: N20-H15…O10, N21-H17…O10, N22-H18…O23, O1-H2…O24, O4-H5…O24, O10-H12…O34, O10-H11…O7, O31-H32…O34, O31-H33…O7, O25-H27…O31, O1-H3…O25, O4-H6…O25, O34-H35…O28, O28-H29…O4, O7-H9…O1,where the electron density values are0.0228, 0.0290, 0.0309, 0.0279, 0.0263, 0.0305, 0.0315, 0.0292, 0.0273, 0.0483, 0.0280, 0.0296, 0.0494, 0.0492, 0.0518a. u. and the Laplacian values are0.0688, 0.0786, 0.0963, 0.0853, 0.0816, 0.0897, 0.0928, 0.0830, 0.0782, 0.1337, 0.0810, 0.0863, 0.1429, 0.1378, 0.1404a. u. respectively. In the Biuret-(H2O)9 cluster, three types of interactions were observed: N20-H15…O25, N21-H17…O25, N22-H18…O23, O4-H6…O24, O28-H30…O24, O28-H29…O34, O25-H27…O34, O37-H38…O4, O1-H3…O10, O10-H11…O37, O31-H32…O10, O31-H33…O7, O37-H39…O7, O7-H9…O28, O34-H36…O31, O25-H26…O1,where the electron density values are 0.0214, 0.0372, 0.0309, 0.0379, 0.0273, 0.0285, 0.0303, 0.0286, 0.0272, 0.0502, 0.0296, 0.0268, 0.0306, 0.0502, 0.0511, 0.0402a. u. and the Laplacian values are 0.0641, 0.1023, 0.0959, 0.1168, 0.0809, 0.0812, 0.0887, 0.0829, 0.0774, 0.1374, 0.0851, 0.0765, 0.0899, 0.1394, 0.1396, 0.1153a. u. respectively.In the Biuret-(H2O)10 cluster, three types of interactions were observed: N25-H21…O26, N24-H20…O13, N23-H18…O13, O10-H11…O27, O37-H38…O27, O37-H39…O40, O40-H42…O34, O4-H6…O1, O28-H29…O10, O13-H15…O31, O4-H5…O31, O28-H30…O34, O40-H41…O10, O13-H14…O1, O1-H2…O7, O7-H9…O37, O34-H35…O4,where the electron density values are 0.0294, 0.0243, 0.0157, 0.0229, 0.0270, 0.0213, 0.0246, 0.0261, 0.0216, 0.0302, 0.0248, 0.3371, 0.0372, 0.0423, 0.0347, 0.0394, 0.0464a. u. and the Laplacian values are 0.0917, 0.0718, 0.0455, 0.0675, 0.0779, 0.0658, 0.0717, 0.00786, 0.0679, 0.0879, 0.0700, 1.8245, 0.1045, 0.1175, 0.1032, 0.1133, 0.1282a. u. respectively. As it is shown in Table 9, the O28-H30…O34 bond was associated to the bigger interaction energy which is in the range 1449.22 kcal/mol.

Table 9 The topological parameters of H-bond interactions at BCP calculated for the various clusters.
H-bonds ρ Δρ H VBCP EH…O
1 O13-H15…O12 0.0312 0.0887 −0.7661 0.10-3 −0.0237 62.16
N9-H5…O13 0.0256 0.0775 −0.1145 0.10-3 −0.0196 51.41
N10-H6…O11 0.0290 0.0912 −0.1751 0.10-3 −0.0231 60.59
2 N8-H3…O13 0.0139 0.0445 0.0002 −0.0107 28.06
N9-H6…O13 0.0267 0.0742 −0.8114. 10-3 −0.0201 52.72
O16-H17…O12 0.0380 0.1122 0.1598. 10-3 −0.0278 72.92
O13-H14…O16 0.0390 0.1171 −0.1390. 10-4 −0.0293 76.85
N10-H6…O11 0.0288 0.0898 −0.2422. 10-3 −0.0229 60.06
3 N14-H9…O19 0.0211 0.0807 0.0025 −0.0151 39.6
N15-H11…O19 0.0226 0.0792 0.0019 −0.0159 41.7
N16-H12…O17 0.0290 0.1103 0.0021. 10-2 −0.0233 61.11
O19-H21…O1 0.0421 0.1347 −0.0026 −0.0388 101.77
O1-H3…O4 0.0411 0.1347 −0.0020 −0.0376 98.62
O4-H6…O18 0.0367 0.1308 −0.1208. 10-3 −0.0329 86.29
4 N18-H3…O19 0.0216 0.0654 −0.2954. 10-3 −0.0169 44.32
O19-H20…O13 0.0289 0.0847 −0.3305. 10-3 −0.0218 57.18
N9-H5…O19 0.0300 0.0822 −0.0012 −0.0220 57.7
O19-H21…O16 0.0313 0.0913 −0.3356. 10-3 −0.0230 60.32
O13-H15…O22 0.0308 0.0903 −0.1315. 10-3 −0.0220 57.7
O22-H24…O12 0.0487 0.1459 −0.8494. 10-3 −0.0381 99.9
N10-H6…O11 0.0308 0.0960 −0.2685. 10-3 −0.0240 62.95
5 N16-H12…O17 0.0307 0.0956 −0.2765. 10-3 −0.0244 64
N15-H11…O4 0.0321 0.0857 −0.0012 −0.0238 62.42
N14-H9…O4 0.0195 0.0597 −0.1891. 10-3 −0.0153 40.13
O4-H5…O22 0.2451 0.0710 −0.4564. 10-3 −0.0186 48.78
O25-H27…O19 0.0398 0.1139 −0.5233. 10-3 −0.0295 77.37
O1-H3…O18 0.0361 0.1113 0.4838. 10-3 −0.0268 70.29
O19-H20…O18 0.0232 0.0677 −0.0360. 10-3 −0.0176 46.16
O22-H24…O1 0.0402 0.1195 −0.1286. 10-3 −0.0299 78.42
O4-H6…O25 0.0349 0.1053 0.1354. 10-3 −0.0260 68.19
6 N17-H12…O7 0.0140 0.0447 0.1762. 10-3 −0.0108 28.32
N18-H14…O7 0.0358 0.0693 −0.0011. 10-3 −0.0265 69.51
O28-H30…O21 0.0284 0.0864 0.2467. 10-3 −0.0211 55.34
O22-H24…O21 0.0220 0.0608 −0.7184. 10-3 −0.0166 43.54
O1-H2…O4 0.0355 0.0141 −0.1166. 10-3 −0.0262 68.72
O4-H6…O28 0.0523 0.1407 −0.0029 −0.0411 107.80
O25-H27…O1 0.0408 0.1197 −0.1788. 10-3 −0.0302 79.21
O7-H8…O22 0.0337 0.0941 −0.7059. 10-3 −0.0249 65.31
O7-H9…O4 0.0259 0.0472 −0.5059. 10-3 −0.0195 51.14
O28-H29…O25 0.0256 0.0736 −0.5354. 10-3 −0.0194 50.88
O22-H23…O25 0.0254 0.0740 −0.4054. 10-3 −0.0193 50.62
O22-H23…O21 0.0220 0.0608 −0.0718. 10-3 −0.0166 43.54
7 N17-H12…O7 0.0200 0.0607 −0.2761. 10-3 −0.0157 41.18
N18-H14…O7 0.0322 0.0877 −0.0010 −0.0204 53.50
N19-H15…O20 0.0302 0.0940 −0.2657. 10-3 −0.0240 62.95
O4-H5…O21 0.0272 0.0817 0.7739. 10-3 −0.0202 52.98
O22-H23…O21 0.0272 0.0818 0.7847. 10-3 −0.0202 52.98
O31-H33…O4 0.0501 0.1372 −0.0022 −0.0388 101.77
O4-H6…O28 0.0275 0.0800 −0.3986. 10-3 −0.0208 54.55
O22-H24…O28 0.0275 0.0799 −0.3995. 10-3 −0.0207 54.29
O25-H27…O31 0.0269 0.0768 −0.5550. 10-3 −0.0203 53.24
O1-H2…O22 0.0501 0.1372 −0.0022 −0.0388 101.77
O25-H26…O1 0.0268 0.0767 −0.5565. 10-3 −0.0202 52.98
O7-H9…O1 0.0306 0.0893 −0.2426. 10-3 −0.0228 59.80
8 N20-H15…O10 0.0228 0.0688 −0.3425. 10-3 −0.0178 46.68
N21-H17…O10 0.0290 0.0786 −0.0010 −0.0217 56.91
N22-H18…O23 0.0309 0.0963 −0.2652. 10-3 −0.0246 64.52
O1-H2…O24 0.0279 0.0853 0.2338. 10-3 −0.0208 54.55
O4-H5…O24 0.0263 0.0816 0.2973. 10-3 −0.0198 51.93
O10-H12…O34 0.0305 0.0897 −0.8836. 10-4 −0.0226 59.28
O10-H11…O7 0.0315 0.0928 −0.1378. 10-3 −0.0234 61.37
O31-H32…O34 0.0292 0.0830 −0.4410. 10-3 −0.0216 56.65
O31-H33…O7 0.0273 0.0782 −0.5124. 10-3 −0.0205 53.77
O25-H27…O31 0.0483 0.1337 −0.0017 −0.0369 96.78
O1-H3…O25 0.0280 0.0810 −0.4246. 10-3 −0.0211 55.34
O4-H6…O25 0.0296 0.0863 −0.2494. 10-3 −0.0220 57.70
O34-H35…O28 0.0494 0.1429 −0.0014 −0.0385 100.98
O28-H29…O4 0.0492 0.1378 −0.0017 −0.0380 99.67
O7-H9…O1 0.0518 0.1404 −0.0027 −0.0406 106.49
9 N20-H15…O25 0.0214 0.0641 −0.3824. 10-3 −0.0168 44.06
N21-H17…O25 0.0372 0.1023 −0.0010 −0.0277 72.65
N22-H18…O23 0.0309 0.0959 −0.3016. 10-3 −0.0245 64.26
O4-H6…O24 0.0379 0.1168 0.5208. 10-3 −0.0281 73.70
O28-H30…O24 0.0273 0.0809 −0.3776. 10-3 −0.0203 53.24
O28-H29…O34 0.0285 0.0812 −0.4496. 10-3 −0.0212 55.60
O25-H27…O34 0.0303 0.0887 −0.1957. 10-3 −0.0225 59.01
O37-H38…O4 0.0286 0.0829 −0.2831. 10-3 −0.0213 55.87
O1-H3…O10 0.0272 0.0774 −0.5441. 10-3 −0.0204 53.50
O10-H11…O37 0.0502 0.1374 −0.0023 −0.0389 102.03
O31-H32…O10 0.0296 0.0851 −0.3996. 10-3 −0.0220 57.70
O31-H33…O7 0.0268 0.0765 −0.5232. 10-3 −0.0201 52.72
O37-H39…O7 0.0306 0.0899 −0.1787. 10-3 −0.0228 59.80
O7-H9…O28 0.0502 0.1394 −0.0021 −0.0391 102.56
O34-H36…O31 0.0511 0.1396 −0.0025 −0.0399 104.65
O25-H26…O1 0.0402 0.1153 −0.5262. 10-3 −0.0298 78.16
10 N25-H21…O26 0.0294 0.0917 −0.2402. 10-3 −0.0234 61.37
N24-H20…O13 0.0243 0.0718 −0.4222. 10-3 −0.0158 41.44
N23-H18…O13 0.0157 0.0455 −0.2542. 10-3 −0.0118 30.95
O10-H11…O27 0.0229 0.0675 −0.1948. 10-3 −0.0172 45.11
O37-H38…O27 0.0270 0.0779 −0.5162. 10-3 −0.0205 53.77
O37-H39…O40 0.0213 0.0658 −0.1644. 10-3 −0.0167 43.80
O40-H42…O34 0.0246 0.0717 −0.5626. 10-3 −0.0190 49.83
O4-H6…O1 0.0261 0.00786 −0.2814. 10-3 −0.0202 52.98
O28-H29…O10 0.0216 0.0679 −0.1086. 10-3 −0.0172 45.11
O13-H15…O31 0.0302 0.0879 −0.3318. 10-3 −0.0226 59.28
O4-H5…O31 0.0248 0.0700 −0.6309. 10-3 −0.0187 49.05
O28-H30…O34 0.3371 1.8245 −0.5043. 10-3 −0.5525 1449.22
O40-H41…O10 0.0372 0.1045 −0.7301. 10-3 −0.0275 72.13
O13-H14…O1 0.0423 0.1175 −0.0010 −0.0315 82.62
O1-H2…O7 0.0347 0.1032 −0.1245. 10-3 −0.0260 68.19
O7-H9…O37 0.0394 0.1133 −0.3466. 10-3 −0.0203 53.24
O34-H35…O4 0.0464 0.1282 −0.0014 −0.0350 91.80

The Reduced Density Gradient (RDG) function is used to understand non-covalent interactions as a wide range of real space in a molecule. Its value is determined by the electron density ρ (r) and the first derivative (Contreras Aguilar et al., 2019):

(7)
RDGr=123π21/3∇ρrρr4/3

The peaks of the two-dimensional plots of the dependence of the reduced gradient on the sign of (λ2) ρ, that is, non-covalent interactions appear in areas of low density and low gradient. The sign of the second sign of the Hessein eigenvalue (λ2) is introduced to distinguish between different types of non-covalent interactions, and the density ρ represents the strength of interactions (Becke and Edgecombe, 1990). The force interactions in the molecular system, which indicate a stronger attractiveness of blue and a push of red, is analyzed using Multiwfn and VMD software.

The RDG scatter graphs of Biuret-(H2O)(1−10) clusters were indicated in Fig. 8. Based on the color scale of RDG and VMD visual representation, we can identify each type of interaction. The red, the green and the blue colors were respectively matched to steric effect, van der Waals interaction and hydrogen bonding contact. As clearly seen from RDG graphs, the hydrogen interactions appear in the range (-0.05)-(-0.02) a.u. The van der Waals interaction ranging from −0.02 to 0.01 a.u. While to range between 0.01 and 0.05 a.u was concerned to ring steric effect.

RDG map along with VMD representation of the different clusters.
Fig. 8
RDG map along with VMD representation of the different clusters.
RDG map along with VMD representation of the different clusters.
Fig. 8
RDG map along with VMD representation of the different clusters.
RDG map along with VMD representation of the different clusters.
Fig. 8
RDG map along with VMD representation of the different clusters.

Important methods for studying the electronic structure of molecules free from an arbitrary choice of molecular orbitals are topological analysis of the electron density by Bader (AIM) (Johnson et al., 2010) and topological analysis of ELF (Michalski et al., 2019). The electronic structure of a molecule described by ELF is represented by maxima (attractors) and its field localization region η (r), which characterize covalent bonds, lone pairs, nuclear regions, and valence shells in atoms (Fuster et al., 2000).

The spatial position of these attractors makes it possible to differentiate the core basins and the valence basins (Kazachenko et al., 2021). Heart basins are located around nuclei (except for the hydrogen atom). The valence basins are classified according to their connectivity with the core basins. Topological analysis of the localization function of electrons constitutes the suitable mathematical model for the characterization of chemical bonds. The electron density, ELF diagrams of the different biuret-water clusters are shown in Fig. 9. The ELF color code range between blue and red, as shown in Fig. 9. The minimum Pauli repulsion correspond to blue regions. While the areas with maximum Pauli repulsion were colored by the red. In addition, the charge delocalization regions with ELF < 0.5 were mapped as blue spots. Whereas, the red electron localization areas with ELF > 0.5 were associated to covalent bonds.

2D ELF representation of Biuret-water clusters.
Fig. 9
2D ELF representation of Biuret-water clusters.
2D ELF representation of Biuret-water clusters.
Fig. 9
2D ELF representation of Biuret-water clusters.

3.6

3.6 Electrostatic potential (ESP) analysis of Biuret-water clusters

Calculation of the electronic characteristics of various materials is important for understanding their functionality and reactivity (Timmer and Mooibroek, 2021).

Electrostatic potential (ESP) or molecular electrostatic potential (MEP) has been actively used in scientific research for several decades (Sharma and Tiwari, 2016). Surface analysis by electrostatic potential (ESP) is one of the factors that can play an important role in the design of various substances (Drissi et al., 2015). Molecular electrostatic potential is the potential that a single positive charge will experience at any point surrounding a molecule, due to the distribution of electron density in the molecule. Electrostatic potential is considered to be a predictor of chemical reactivity, since areas of negative potential are expected to be sites of protonation and nucleophilic attack, while areas of positive potential may indicate electrophilic sites [50].

Different electrostatic potential values are indicated by different colors in the ESP (Fig. 10). A decreasing order potential is expressed as follows: blue > green > yellow > orange > red. Negative values are shown in red and are associated with the area of electrophilic attack and mainly with oxygen atoms in biuret, water, and the biuret-water cluster. The nucleophilic attack area (positive area) is shown in blue and is mainly associated with the hydrogen and nitrogen atoms in the biuret and the biuret-water cluster. As clearly seen from Fig. 10, the oxygen atoms of biuret-water cluster were colored with red color (nucleophilic sites). Whereas, the electrophilic sites were localized on hydrogen atoms (blue color).

The electrostatic potential (ESP) analysis of biuret, water and biuret-water cluster (with 1 water molecule).
Fig. 10
The electrostatic potential (ESP) analysis of biuret, water and biuret-water cluster (with 1 water molecule).

4

4 Conclusions

In this work, water clusters of biuret (n = 1–10) were investigated by FTIR, XRD, AIM, DFT, RDG, ELF, NLO methods. It is shown that the introduction of water molecules into the biuret cluster leads to an increase in the intensity of the FTIR spectra. The inclusion of water molecules in a biuret crystal leads to a significant increase in the intensity of most peaks in the range from 14 to 65 2⊖ (deg). All calculations of biuret clusters - (H2O) (1–10) were carried out in the gas phase at the level of the B3LYP / 6–31 + G (d, p) theory. The strength of hydrogen bond interactions is discussed using the AIM topological analysis. We also studied the NLO properties for each cluster using the RB3LYP functionality. It was shown that the values of E (Thermal), Heat Capacity (Cv), Entropy (S) increase linearly with an increase in water molecules in the biuret cluster.

Declarations

Compliance with ethical standards.

5

5 Ethics approval

N/A. In the course of work on this article, the authors did not conduct research on animals and humans in any form.

Acknowledgments

Experimental work was conducted within the framework of the budget plan # 0287-2021-0017 for Institute of Chemistry and Chemical Technology SB RAS using the equipment of Krasnoyarsk Regional Research Equipment Center of SB RAS. Theoretical work was supported Researchers Supporting Project number (RSP -2021/61), King Saud University, Riyadh, Saudi Arabia. The authors are grateful to G.N. Bondarenko for the X-ray study and E.V. Elsuf’ev for recording the FTIR spectra.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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