Journal of Spectroscopy
Volume 2018 (2018), Article ID 1048157, 15 pages
https://doi.org/10.1155/2018/1048157

Research Article

Does the Intramolecular Hydrogen Bond Affect the Spectroscopic Properties of Bicyclic Diazole Heterocycles?

Paweł Misiak,¹ Alina T. Dubis,¹ and Andrzej Łapiński²

¹Institute of Chemistry, University of Bialystok, Ciołkowskiego 1K, 15-245 Bialystok, Poland
²Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznan, Poland

Correspondence should be addressed to Andrzej Łapiński; lapinski@ifmpan.poznan.pl

Received 28 November 2017; Revised 14 February 2018; Accepted 20 February 2018; Published 2 May 2018

Academic Editor: Renata Diniz

Copyright © 2018 Paweł Misiak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The formation of an intramolecular hydrogen bond in pyrrolo[1,2-a]pyrazin-1(2H)-one bicyclic diazoles was analyzed, and the influence of N-substitution on HB formation is discussed in this study. B3LYP/aug-cc-pVDZ calculations were performed for the diazole, and the quantum theory of atoms in molecules (QTAIM) approach as well as the natural bond orbital (NBO) method was applied to analyze the strength of this interaction. It was found that the intramolecular hydrogen bond that closes an extra ring between the C=O proton acceptor group and the CH proton donor, that is, C=O⋯H–C, influences the spectroscopic properties of pyrrolopyrazine bicyclic diazoles, particularly the carbonyl frequencies. The influence of N-substitution on the aromaticity of heterocyclic rings is also discussed in this report.

1. Introduction

Pyrrolo[1,2-a]pyrazin-1(2H)-ones are an important class of natural organic compounds synthesized by many grass-associated endophytic fungi [1, 2]. Symbiotic plants activate a defense reaction which allows the host plant to be protected against infection [3]. The ecological significance of pyrrolopyrazinones is related to their feeding deterrent activity. These alkaloids produced by endophytes provide protection of the host plant from herbivores as found in a large number of grass/endophyte associations [4]. A recent study has shown that peramine is transported from the endophyte into plant intercellular space where it is metabolized or removed via guttation fluid [2]. In the field of applied ecology, it is important to recognize natural chemical agents that control herbivorous insects [5]. Due to these properties, pyrrolopyrazinones can be used as structural models for studying the release mechanism, metabolism, structure of chemical compounds removed from plant tissues, and the mechanism of anti-insect activity [6].

An attempt has been made previously to identify spectroscopic properties of some pyrrolopyrazinones [7, 8]. The vibrational and electronic spectra of peramine and some of its derivatives were recorded, and assignments were made on the basis of B3LYP/aug-cc-pVDZ level calculations; FT-IR and ¹H NMR spectra indicated the conjugation of the pyrrolo and pyrazinone rings. These previous results also show that the ring modes are insensitive to the type of substituent introduced into the side chain of peramine.

We consider here a series of pyrrolopyrazinones (Scheme 1, Table 1) that is an extension of our previous work on N-substituted 2-acylpyrroles [9]. For some of the heterocyclic systems analyzed recently, short C=O⋯H–C intramolecular contacts are observed [10]. This observation inspired us to undertake a theoretical study on C=O⋯H–C intramolecular hydrogen bonds in pyrrolopyrazinone species.

Scheme 1: Schematic representation of the structure and atom numbering of pyrrolopyrazinone derivatives (2–22) where R₂ = CH₃, CH₂Cl, or CHCl₂; R₃ = H, Cl, CH₃, (CH₂)nCH₃, (CH₂)nCH₂Cl, (CH₂)nNH₂, NH₂, and (CH₂)₃NHC(NH)NH₂.

Scheme 2: Schematic representation of the endophyte-infected plant.

Table 1: Selected bond lengths of pyrrolo[1,2-a]pyrazin-1(2H)-ones (1–22), optimized at the B3LYP/aug-cc-pVDZ level of theory, HOMA indices, and calculated C=C and C=O stretching frequencies.

Compound

3,4-Dihydropyrrolopyrazinones

Pyrrolopyrazinones
Bond length [Å]

Pyrrole ring
Calculated
B3LYP/aug-cc-pVDZ
Calculated
B3LYP/aug-cc-pVDZ

Pyrrole ring
N5C9
C9C8
C8C7
C7C6
C6N5

HOMA
EN
GEO

νC=C (cm⁻¹)
Pyrrole ring stretching vibrations

1
Pyrrole
1.376
1.383
1.428
1.382
1.376

0.833
0.071
0.096

1568

1a
R₂ = CH₃, R₃ = H

1.383
1.390
1.418
1.390
1.383

0.876
0.082
0.043

1578

1b
R₂ = CH₂Cl, R₃ = H

1.384
1.392
1.416
1.391
1.384

0.882
0.082
0.036

1575

1c
R₂ = CHCl₂, R₃ = H

1.385
1.393
1.414
1.392
1.384

0.885
0.082
0.032

1573

2

R₂ = CH₃, R₃ = H
1.396
1.390
1.416
1.390
1.396

0.848
0.097
0.055

1564

3

R₂ = CH₂Cl, R₃ = H
1.396
1.391
1.415
1.390
1.396

0.852
0.095
0.053

1567

4

R₂ = CHCl₂, R₃ = H
1.389
1.393
1.413
1.393
1.388

0.875
0.091
0.034

1565

5

R₂ = CH₃, R₃ = Cl
1.394
1.391
1.415
1.391
1.393

0.859
0.095
0.046

1562

6

R₂ = CH₂Cl, R₃ = Cl
1.393
1.392
1.414
1.391
1.393

0.862
0.093
0.045

1565

7

R₂ = CHCl₂, R₃ = Cl
1.391
1.392
1.413
1.392
1.391

0.869
0.091
0.039

1564

8

R₂ = CH₃, R₃ = NH₂
1.391
1.395
1.412
1.395
1.390

0.873
0.098
0.029

1555

9

R₂ = CH₂Cl, R₃ = NH₂
1.390
1.394
1.412
1.394
1.390

0.875
0.095
0.030

1560

10

R₂ = CHCl₂, R₃ = NH₂
1.389
1.397
1.409
1.397
1.388

0.883
0.096
0.021

1555

11

R₂ = CH₃, R₃ = CH₃
1.392
1.392
1.415
1.391
1.391

0.863
0.095
0.042

1564

12

R₂ = CH₂Cl, R₃ = CH₃
1.391
1.392
1.392
1.392
1.391

0.905
0.053
0.042

1567

13

R₂ = CHCl₂, R₃ = CH₃
1.389
1.393
1.413
1.393
1.388

0.875
0.091
0.034

1565

14

R₂ = CH₃, R₃ = CH₂CH₂CH₂Cl
1.390
1.392
1.415
1.391
1.390

0.865
0.093
0.042

1565

15

R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂Cl
1.390
1.392
1.414
1.391
1.389

0.868
0.091
0.041

1568

16

R₂ = CHCl₂, R₃ = CH₂CH₂CH₂Cl
1.387
1.393
1.413
1.392
1.387

0.876
0.089
0.035

1567

17

R₂ = CH₃, R₃ = CH₂CH₂CH₂NH₂
1.390
1.392
1.415
1.392
1.390

0.864
0.095
0.040

1561

18

R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NH₂
1.390
1.392
1.414
1.392
1.389

0.869
0.092
0.039

1567

19

R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NH₂
1.388
1.393
1.413
1.393
1.387

0.877
0.090
0.033

1565

20

R₂ = CH₃, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
1.390
1.392
1.415
1.391
1.390

0.865
0.094
0.042

1564

21

R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
1.390
1.392
1.414
1.392
1.390

0.869
0.092
0.040

1568

22

R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
1.387
1.393
1.413
1.393
1.387

0.877
0.089
0.034

1566

Pyrazinone ring
C1N2
N2C3
C3-C4
C4N5
N5C9
C9C1
HOMA
EN
GEO
νC=O (cm⁻¹)
Pyrazine νC=C stretching vibrations(cm⁻¹)

1a
R₂ = CH₃, R₃ = H

1.390
1.462
1.525
1.453
1.383
1.470

1705

1b
R₂ = CH₂Cl, R₃ = H

1.404
1.467
1.525
1.455
1.384
1.463

1721

1c
R₂ = CHCl₂, R₃ = H

1.414
1.468
1.524
1.456
1.385
1.459

1726

1d
Pyrazine
1.338
1.338
1.400
1.338
1.338
1.400
0.985
0.010
0.005
—
1617

1e
2-Oxo-pyrazine
1.400
1.367
1.364
1.374
1.303
1.469
0.591
0.087
0.322
1743
1645

2

R₂ = CH₃, R₃ = H
1.406
1.388
1.349
1.391
1.396
1.456
0.466
0.199
0.335
1721
1695

3

R₂ = CH₂Cl, R₃ = H
1.421
1.396
1.346
1.392
1.396
1.452
0.414
0.209
0.376
1738
1705

4

R₂ = CHCl₂, R₃ = H
1.440
1.419
1.351
1.391
1.389
1.442
0.408
0.251
0.341
1741
1703

5

R₂ = CH₃, R₃ = Cl
1.420
1.390
1.351
1.390
1.394
1.450
0.470
0.210
0.320
1726
1686

6

R₂ = CH₂Cl, R₃ = Cl
1.435
1.400
1.348
1.391
1.393
1.447
0.416
0.224
0.360
1745
1694

7

R₂ = CHCl₂, R₃ = Cl
1.446
1.406
1.349
1.389
1.391
1.443
0.402
0.234
0.364
1744
1690

8

R₂ = CH₃, R₃ = NH₂
1.415
1.396
1.358
1.396
1.391
1.448
0.512
0.234
0.254
1734
1695

9

R₂ = CH₂Cl, R₃ = NH₂
1.431
1.407
1.354
1.396
1.390
1.445
0.444
0.250
0.306
1748
1711

10

R₂ = CHCl₂, R₃ = NH₂
1.445
1.414
1.356
1.395
1.389
1.438
0.440
0.268
0.292
1750
1703

11

R₂ = CH₃, R₃ = CH₃
1.411
1.401
1.354
1.392
1.392
1.451
0.487
0.225
0.288
1726
1693

12

R₂ = CH₂Cl, R₃ = CH₃
1.427
1.411
1.351
1.393
1.391
1.447
0.429
0.239
0.332
1742
1708

13

R₂ = CHCl₂, R₃ = CH₃
1.440
1.419
1.351
1.391
1.389
1.442
0.408
0.251
0.341
1741
1703

14

R₂ = CH₃, R₃ = CH₂CH₂CH₂Cl
1.413
1.404
1.355
1.392
1.390
1.450
0.488
0.229
0.282
1723
1692

15

R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂Cl
1.428
1.414
1.352
1.392
1.390
1.446
0.432
0.243
0.325
1740
1705

16

R₂ = CHCl₂, R₃ = CH₂CH₂CH₂Cl
1.441
1.422
1.352
1.391
1.387
1.442
0.407
0.255
0.339
1740
1700

17

R₂ = CH₃, R₃ = CH₂CH₂CH₂NH₂
1.411
1.403
1.356
1.390
1.390
1.451
0.495
0.229
0.276
1715
1683

18

R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NH₂
1.428
1.415
1.350
1.393
1.390
1.446
0.423
0.240
0.337
1740
1705

19

R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NH₂
1.441
1.423
1.351
1.391
1.388
1.441
0.400
0.253
0.347
1739
1699

20

R₂ = CH₃, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
1.412
1.405
1.355
1.392
1.390
1.450
0.487
0.229
0.284
1723
1691

21

R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
1.428
1.414
1.351
1.393
1.390
1.446
0.427
0.243
0.330
1741
1706

22

R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
1.441
1.423
1.352
1.391
1.387
1.441
0.404
0.256
0.340
1740
1700

In the first part of this study, we carried out a detailed analysis of the geometrical parameters of the pyrrolopyrazinone derivatives (Scheme 1). These species are divided into two groups according to QTAIM results; one group includes systems with short C=O⋯H–C contacts in which O…H bond paths with corresponding BCPs exist (all pyrrolopyrazines where R₂ = CHCl₂ are included here); the other group consists of systems in which there is no attractive C=O⋯H–C interaction and the H…O bond paths are not detected; all systems where R₂ = CH₂Cl are included in this group. There are also systems in which R₂ = CH₃ are dispersed into both these groups.

In the second part of this study, analysis of the aromaticity of the pyrrolopyrazinone derivatives was carried out to find the possible interplay between the existence of the hydrogen bonds and aromaticity of the heterocyclic rings. Aromaticity is a topic of scientific interest in the various areas of pyrrole derivative investigation. Numerous aromaticity concepts have been proposed to describe and evaluate this phenomenon. Criteria for establishing aromaticity of various species analyzed have been divided [10, 11] into energetic, [12] geometrical, [13] magnetic [14], and reactivity categories; the latter ones are mainly based on the chemical behavior of a system. There is also the harmonic oscillator model of aromaticity (HOMA) [15–18] that is classified as a geometrical index.

In general, the purpose of this study is to extend knowledge of physicochemical properties of pyrrolopyrazinones including spectroscopic properties of both heterocyclic rings. Theoretical analysis is performed using B3LYP/aug-cc-pVDZ calculations, the quantum theory of atoms in molecules (QTAIM) approach, and the natural bond orbital (NBO) method. The intramolecular C=O⋯H–C hydrogen bonds in the pyrrolopyrazinone molecules (1–22) are analyzed in terms of the NBO method, and orbital-orbital overlapping energy, ΔEn→σ, is discussed [19]. To the best of our knowledge, NBO, QTAIM, or HOMA approaches have not been applied so far to analyze the intramolecular C=O⋯H–C interactions in pyrrolopyrazinones (2–22).

2. Experimental FT-IR Spectra

The infrared spectrum of peramine 20 was investigated at room temperature in KBr pellets containing dispersed compounds. The FT-IR absorption spectrum was recorded in the range between 400 and 4000 cm⁻¹ with a Nicolet Magna-IR 550 Series II instrument.

3. Computational Details

The calculations were performed with the Gaussian 09 sets of codes [20]. The geometries of the investigated species (1–22) were fully optimized using the aug-cc-pVDZ Dunning’s correlation consistent basis set [21, 22] and B3LYP functional [23, 24]. Calculations of normal modes were performed with the use of the same level as that for the optimizations. The results of optimization correspond to energy minima since no imaginary frequencies were detected. The initial geometry of the pyrrolopyrazinone system was taken from X-ray data, and it was further applied in the geometry optimization [9]. The computed frequencies were multiplied by the uniform factor of 0.97 to obtain a good estimate of the experimental results and to eliminate known systematic errors related to anharmonicity [25].

Gaussian output wfn files were used as inputs for the AIM2000 [26] program to calculate topological properties of the systems investigated. The bond and ring critical points were located (BCPs and RCPs), and their properties, such as electron densities at critical points (ρBCP and ρRCP) and their Laplacians (∇²ρBCP and ∇²ρRCP), were calculated. The additional characteristics of BCPs were analyzed, such as total electron energy density at BCP (HBCP) and its components, potential electron energy density (VBCP), and kinetic electron energy density (GBCP).

Particularly, for the C-H...O hydrogen bond, these are the characteristics of the H...O bond critical point and the properties of the ring critical point that exist within the ring closed by the C=O⋯H–C intramolecular hydrogen bond. Relationships between topological parameters at the critical point are given by [27]

Kinetic electron energy density GBCP has a positive value, whereas potential electron energy density VBCP has a negative value. If the absolute value of VBCP is two times greater than the GBCP value, the Laplacian is negative. The classification of hydrogen bonds based on these parameters has been proposed by Rozas and coworkers [28]. and HBCP values are positive for weak and medium-strength HB interactions; is positive and HBCP is negative for strong hydrogen bonds; both these values are negative for very strong HBs. The electron density at H…B BCP, ρBCP, is often considered as a measure of A-H…B hydrogen bond strength since correlations between ρBCP and interaction energy or other HB strength descriptors have been found, especially for homogenous samples of interactions [29]. Similarly, in this study, ρBCP that corresponds to the H…O BCP of the C-H…O intramolecular hydrogen bond may be considered a descriptor of HB strength.

The NBO method [19] was applied to calculate nB→σAH interaction energies. nB designates the lone pair of the B proton acceptor, and σA-H is an antibonding orbital of the A-H bond. Interaction energy was calculated from second-order perturbation theory energy according to

where is the Fock matrix element, is the orbital energy difference, and nB is the population of the donor B orbital. The E⁽²⁾AB energy term can be considered a part of charge transfer energy or stabilization energy associated with delocalization.

The HOMA index is expressed by

where n is the number of bonds taken into account, α is an empirical constant chosen to give HOMA = 0 for a nonaromatic system and HOMA = 1 for a system with all bonds equal to the optimal value Ropt, and Ri is the individual bond length [30]. The HOMA index has a value between 1 for entirely aromatic molecules and 0 for nonaromatic systems. When the value of the HOMA index is less than zero, the structure is antiaromatic.

The Pauling bond number and virtual CC and CN bond lengths have been applied to the HOMA aromaticity index. This allows separation of HOMA into energetic and geometric contributions for heterocyclic π-electron systems [29]. The expression for the HOMA term is as follows:

where N is the number of bonds taken into calculation, Rav is the averaged bond length, and Ri is the virtual bond length calculated from the Pauling bond number [29]

According to the general formula,

4. Results and Discussion

4.1. Geometry of the C-H…O=C Intramolecular Contact

Scheme 1 presents pyrrolopyrazinone systems analyzed here, 2–22. Pyrrole, 1, and pyrazine, 1d, 1a–c, and 1e, which may be treated as fragments of these systems, are also analyzed for comparison. Selected geometrical parameters for all these species (1–22) are listed in Table 1. Three sets of samples of pyrrolopyrazinone systems which differ in the R₂ substituent may be selected here; the sample where R₂ = CH₃ (2, 5, 8, 11, 14, 17, and 20), R₂ = CH₂Cl (3, 6, 9, 12, 15, 18, and 21), and the sample where R₂ = CHCl₂ (4, 7, 10, 13, 16, 19, and 22).

For some of the systems analyzed, the existence of C-H…O intramolecular hydrogen bonds is observed which close additional five-membered rings. We can expect here weak hydrogen bonds which are formed when the hydrogen atom is covalently bonded to a slightly more electronegative atom relative to hydrogen; the electronegativity of carbon of 2.55 is only slightly higher than that of hydrogen, that is, 2.20, according to the Pauling electronegativity scale. The identification of the A-H…B hydrogen bond is often based on the A…B distance which should be lower than the sum of their van der Waals radii; this criterion can be applied for strong and medium strength interactions. It is inadequate for weaker hydrogen bonds that are mainly electrostatic in nature. This is why the criterion of the sum of van der Waals radii is more often applied for the H…B distances; however, it is also sometimes not fulfilled for weaker interactions. The most probable interpretation is that for weak hydrogen bonds the long-range electrostatic forces act far beyond the van der Waals radii cutoff [31, 32] while for strong and very strong interactions the additional forces related to electron density shifts are more important; these forces lead to the enormous shortening of the H…B hydrogen bond contact [31]. The role of electrostatic forces in hydrogen bonds and in other interactions, such as for example, halogen bonds, is in line with the σ-hole concept [33].

Table 2 presents the geometrical parameters corresponding to the C-H…O=C hydrogen bonds, H…O distances, dHO’s and ∠C-H…O angles. We can observe that among the C-H…O=C contacts there are systems with short H…O distances below the sum of vdW radii–2.72 Å (O, 1.52 Å and H, 1.20 Å), according to Bondi [34, 35]. One of the most important geometrical characteristics of hydrogen bonds is that the distance between the proton and the proton-accepting atom is shorter than the sum of their van der Waals radii. Additional generally accepted criterion is that the donor-proton-acceptor angle in hydrogen bond must be at least 90° [36]. For 3, 6, 9, 12, 15, 18, and 21, in which R₂ = CH₂Cl, the H...O distance varies from 2.19 to 2.27 Å. Systems 2, 5, 8, 11, 14,17, and 20, where R₂ is a methyl group (CH₃), are characterized by the H…O distance range of 2.17–2.24 Å and the ∠C-H…O angle range of 106–118° (Table 2). The systems with the R₂ = CHCl₂ group (4, 7, 10, 13, 16, 19, and 22) are characterized by the shortest H…O distances of 2.03–2.06 Å, much shorter than the sum of vdW radii of H and O atoms (2.68 Å); the ∠C-H…O angle range of 111–113° is observed here (Table 2). It is noted that the above values are within the range acceptable for intramolecular H-bonds since the accepted H…O distance range for the C-H…O hydrogen bonds is 2.0–2.7 Å [36]. Recent studies have also suggested the C-H…X angles up to 90° for acceptable hydrogen bonds [37].

Table 2: Geometrical parameters (dH…O in Å and ∠C-H…O in degrees) corresponding to the C-H…O intramolecular contacts obtained at B3LYP/aug-cc-pVDZ; QTAIM parameters (in a.u.) corresponding to the H…O bond critical points (BCPs), electron density at BCP, ρBCP; Laplacian of electron density at BCP∇²BCP; total electron energy density at BCP; HBCP and components of the HBCP value; kinetic electron energy density, GBCP; potential electron energy density, VBCP. Designation of species according to Scheme 2 where CHXY denotes R₂.

Compound

dH…O
∠C-H…O
dC-H
ρRCP
∇²ρRCP
ρBCP
∇²ρBCP
HBCP
V
G
ρBCP (C-H)
(C-H…O-C)

(Å)
(°)
(Å)

(a.u.)

2
R₂ = CH₃, R₃ = H
2.26
106.10
1.09

0.2844

3
R₂ = CH₂Cl, R₃ = H
2.27
103.44
1.09

0.2899

4
R₂ = CHCl₂, R₃ = H
2.17
107.67
1.09
0.0213
0.1078
0.0217
0.0840
0.0010
−0.0173
0.0191
0.2925

5
R₂ = CH₃, R₃ = Cl
2.20
108.38
1.09
0.0202
0.0925
0.0203
0.0839
0.0006
−0.0197
0.0203
0.2853

6
R₂ = CH₂Cl, R₃ = Cl
2.23
103.71
1.09

0.2898

7
R₂ = CHCl₂, R₃ = Cl
2.06
112.13
1.09
0.0241
0.1231
0.0253
0.1065
0.0005
−0.0255
0.0260
0.2933

8
R₂ = CH₃, R₃ = NH₂
2.21
106.89
1.09
0.0203
0.0882
0.0203
0.0862
0.0008
−0.0199
0.0207
0.2851

9
R₂ = CH₂Cl, R₃ = NH₂
2.24
102.82
1.09

0.2896

10
R₂ = CHCl₂, R₃ = NH₂
2.06
111.48
1.09
0.0244
0.1241
0.0255
0.1078
0.0006
−0.0257
0.0263
0.2931

11
R₂ = CH₃, R₃ = CH₃
2.19
108.16
1.09
0.0207
0.0939
0.0208
0.0860
0.0007
−0.0202
0.0209
0.2856

12
R₂ = CH₂Cl, R₃ = CH₃
2.23
102.80
1.09

0.2902

13
R₂ = CHCl₂, R₃ = CH₃
2.04
111.90
1.09
0.0248
0.1277
0.0261
0.1108
0.0006
−0.0265
0.0271
0.2938

14
R₂ = CH₃, R₃ = CH₂CH₂CH₂Cl
2.17
108.23
1.09
0.0211
0.0971
0.0213
0.0876
0.0007
−0.0206
0.0213
0.2861

15
R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂Cl
2.20
104.08
1.09

0.2905

16
R₂ = CHCl₂, R₃ = CH₂CH₂CH₂Cl
2.03
112.42
1.09
0.0257
0.1311
0.0269
0.1140
0.0006
−0.0273
0.0279
0.2943

17
R₂ = CH₃, R₃ = CH₂CH₂CH₂NH₂
2.20
106.73
1.09
0.0207
0.0922
0.0207
0.0868
0.0008
−0.0201
0.0209
0.2857

18
R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NH₂
2.19
104.19
1.09

0.2906

19
R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NH₂
2.03
112.18
1.09
0.0252
0.1307
0.0267
0.1138
0.0006
−0.0272
0.0278
0.2942

20
R₂ = CH₃, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
2.17
108.54
1.09
0.0211
0.0969
0.0212
0.0873
0.0006
−0.0206
0.0212
0.2860

21
R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
2.20
104.91
1.09

0.2906

22
R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
2.03
112.36
1.09
0.0253
0.1311
0.0268
0.1140
0.0006
−0.0273
0.0279
0.2942

The phenomenon which influences the geometry of C-H…O=C interactions is the acidity of the proton donating C-H group [38]. The main factor that controls both lengths and energies is the acidity of the C-H group. The acidity of the C-H group can sweep over a wide range of pKa values prompted by changes of the hybridization state of the carbon and for effect of electron-withdrawing substituents. The acidity of the C-H bond is increasing in the following order: sp³C-H, sp²C-H, and spC-H. For instance, pKa in water of CH₄, C₂H₄, and C₂H₂ decreases in the order 48, 44, and 26. The effects of the C-H acidity on the geometry of the C-H…O bonds have been studied by Desiraju [38]. It was found that C…O contact distances correlate with pKa values. Shorter bonds are associated with the more acidic C-H group [39, 40].

Replacement of the H atom from the group R₂ = CH₃ by Cl results in a reduction in the H…O distance [9]. This is also observed for the systems analyzed here; for example, the H…O distance is equal to 2.17, 2.03 Å for 20 (R₂ = CH₃) and 22(R₂ = CHCl₂), respectively (Table 2); it means that shorter H…O distances occur for more acidic C-H donors. The C-H…O angle varies from 102.8° in 12 (R₂ = CH₂Cl) to 104.91 in 21 (R₂ = CH₂Cl). For systems with R₂ = CH₃, the C-H…O angle varies from 106.1° in 2 to 112.42 in 22. For systems with R₂ = CHCl₂, the C-H…O angle varies from 107.67° in 4 to 108.54 in 20. It means that electron-withdrawing substituents affect CH…O bond geometry. It is observed that the introduction of two chlorine atoms where R₂ = CHCl₂ (4, 7, 10, 13, 16, 19, and 22) led to an increase of the C-H…O angle in comparison with molecules where R₂ = CH₃ as well as R₂ = CH₂Cl. It is interesting to compare the C-H…O angle of systems where R₂ = CH₃ and the C-H…O angle of systems where R₂ = CH₂Cl. Bond angle ∠C-H…O values for a system where R₂ = CH₃ are larger than ∠C-H…O for a system where R₂ = CH₂Cl.

For all molecules, under consideration (2–22), the H…O distances are within the range acceptable for intramolecular H-bonds. To find whether these H…O contacts may be classified as attractive hydrogen bonds, additional QTAIM and NBO analyses were performed here.

4.2. QTAIM Analysis

The quantum theory of atoms in molecules, QTAIM [27], is often applied to analyze different inter- and intramolecular interactions, such as A-H…B hydrogen bonds [41]. The existence of the H…B bond path as well as the characteristics of the corresponding bond critical point such as electron density, ρBCP, and its Laplacian, ∇²ρBCP, is often used as criteria for the existence of the hydrogen bond [42]. That is why QTAIM analysis was also performed here for pyrrolopyrazinones (2–22). Figure 1 presents molecular graphs of peramine derivatives 21 (X=H, Y=Cl) and 22 (X=Cl, Y=Cl) which are analyzed in this study; these are two examples of systems where the QTAIM approach confirms the existence of HB (22), or it does not confirm such interaction since the H…O intramolecular bond path was not detected (21). Based on QTAIM, there are no bond paths connecting the oxygen atom and the methylene hydrogen atom for 2, 3, 6, 9, 12, 15, 18, and 21, that is, for all systems where R₂ = CH₂Cl and for certain systems where R₂ = CH₃ (Scheme 1). The H atom = CH₃ is located at 2.6 Å distance from the hydrogen atom of the R₃ group and has no steric repulsion between the R₂ and R₃ electron clouds. This effect leads to the lack of attractive interaction of HB between the carbonyl group and the neighboring CH₃ group [9].

(a)

(b)

(c)

Figure 1: Molecular graphs (representation of bonding interactions according to QTAIM results) of the system analyzed in this study: 23 (a), 22 (b), and 21 (c). The dotted line corresponds to a bond path.

There is a bond path connecting C=O and C-H groups for systems 4, 7, 10, 13, 16, 19, 22, that is, for structures where R₂ = CHCl₂ (X=Cl, Y=Cl according to Table 2) and where the H…O distance is much shorter than the corresponding sum of the vdW radii (see the discussion in the previous section). There is also a subset of the group in which R₂ = CH₃ (5, 8, 11, 14, 17, and 20) where a bond path exists connecting the oxygen atom of the carbonyl group and the hydrogen atom of the CH₃ group (Table 2).

Table 2 presents selected QTAIM parameters for the systems analyzed here, that is, characteristics of the H…O BCP corresponding to the intramolecular hydrogen bond: electron density at the bond critical point, ρBCP , its Laplacian, ∇²ρBCP, and the energetic BCP characteristics (HBCP, VBCP, and GBCP), as well as the properties of the ring critical point corresponding to the ring closed by this hydrogen bond: electron density at the ring critical point, ρRCP, and its Laplacian, ∇²ρRCP. The typical topological parameters at the bond critical point for the hydrogen bond are 0.002–0.34 a.u. for electron density and 0.02–0.139 a.u. for its Laplacian [27]. The QTAIM analysis of electron densities at the H…O bond critical points of the systems under consideration (2–22) showed that ρBCP is in a range of 0.0269 to 0.0203 a.u., and Laplacian varies from 0.0839 to 0.114 a.u. It has been shown earlier that electron density and its Laplacian correlate with H-bond energy, especially for homogeneous samples of interactions [31, 40, 43]. The increase of HB strength is related to the increase of electron density at the BCP.

The largest electron density at the proton-acceptor (H…O) bond critical point is observed for 16 (R₂ = CHCl₂, R₃ = (CH₂)₃Cl), peramine derivative 19 (R₂ = CHCl₂, R₃ = (CH₂)₃NH₂), and 22 (R₂ = CHCl₂, R₃ = (CH₂)₃NHC(NH)NH₂), 0.0269, 0.0267, and 0.0268 a.u., respectively.

Figure 1(c) presents a molecular graph of system 22 where R₂ = CHCl₂. In this structure, shown in Figure 1(c), there is a bond path connecting oxygen atom and H8 atom of the R₂ group. There is also a bond path connecting atom Cl34 and atom H18 of methylene group as well as atom Cl35 and atom H33. The Cl34…H18 distance is 2.57 Å; the Cl34..H33 distance is 2.71 Å. We believe that carbon atom of the proton donor group (R₂ = CHCl₂) carries a more positive charge than the carbon atom of the CH₂Cl group. Furthermore, for these systems, the ∠C–H…O bond angle is closest to 120° compared with that of the other species (R₂ = CH₂Cl) in Table 2 and Figures 1(a) and 1(c). In such a case, the proton of R₂ group is located in the chelate ring plane. In spite of this results obtained, it seems that the path linking both C=O⋯H-C is an attractive interaction.

For the sample 21 where R₂ = CH₂Cl, the Cl…H distance is 2.81 Å, and the ∠C-H…O bond angle is 104.91°. In such a case, there is not a bond path connecting carbonyl oxygen with hydrogen of the R2 group (Figure 1(b)). This may be explained because of minimal nB→σAH overlap [44]. Hence, if hydrogen bonding is stronger, thus the C-H…O angle is closer to 120°.

It is seen that systems with R₂ = CHCl₂ correspond to the strongest interactions since it is also supported by other results collected in Table 2 that the shortest H…O distances are observed for the systems mentioned above. It is in agreement with the properties of the Cl atom as an electron-withdrawing substituent that enhances the proton-donating ability of the adjacent CH group. The latter was suggested in a previous study [45] that the strength of the C-H…B hydrogen bond strongly depends on the nature of the proton donor and increases when hydrogen atoms are replaced by electron-withdrawing substituents [9, 46].

The correlation between the length of the hydrogen bond and electron density at the corresponding bond critical point, ρBCP, which is often analyzed for samples of related species, is also observed here (Figure 2). Pyrrolopyrazinones analyzed here, where the H…O bond path corresponding to the intramolecular hydrogen bond was detected, can be divided into two groups (Figure 2); the group where R₂ = CHCl₂ and the group where R₂ = CH₃. For the first group, stronger interactions characterized by shorter H…O distances and greater ρBCP values are observed than those for the second group (Figure 2).

Figure 2: Correlation between electron density at the H-bond critical points ρBCP (in a.u.) and the H…O distance (in Å) was calculated at the B3LYP/aug-cc-pVDZ level. (4, 7, 10, 13, 16, 19, and 22; R₂ = CHCl₂) (5, 8, 11, 14, 17, and 20; R₂ = CH₃).

The properties of the ring critical point which is observed for the intramolecular hydrogen bonds often correlate with other measures of HB strength. It is noted that for the HBs analyzed here there is a linear correlation between the ρBCP and ρRCP values (R² = 0.998). The HBCP value is also useful to describe properties of hydrogen bonds. It is negative for interactions which are at least partly covalent in nature; for the systems analyzed here, it is positive and equal to ~0.001 a.u.

According to the latest studies on HB description, HB strength is related to the kinetic energy of electron density at the BCP and the decrease of potential energy and decrease of total electron energy density at the BCP [29]. G, V, and HBCP are the kinetic, potential, and total electron energy densities at critical point, respectively. G is a positive value, whereas V is a negative one. Rozas et al. have classified HB based on Laplacian of electron density at BCP and HBCP values [28]. Medium and week in strength HBs show positive value of Laplacian of electron density at BCP as well as H value. It is seen that for systems analyzed here, ∇²ρBCP is positive, which means that HBs could be classified as weak. For the highest ∇²ρBCP value of 0.1140, HBCP is 0.0006, while V is −0.0273. For the lowest ∇²ρBCP value of 0.0839, HBCP is 0.0006, while V is −0.0197.

4.3. NBO Analysis

The NBO method is a useful tool to analyze intra- and intermolecular interactions. There are two effects that are often attributed to A-H...B hydrogen bond formation: a hyper conjugative effect of A-H bond weakening and rehybridization-promoted A-H bond strengthening [47]. The hyper conjugative effect is related to electron charge transfer from the lone pair at the donor (B) into the antibonding σ orbital of the A-H bond. The interaction between these orbitals corresponds to the deviation of the molecule from the Lewis structure [48]. The EAB⁽²⁾ energy term mentioned earlier can be considered a part of charge transfer energy or the stabilization energy associated with the delocalization [49].

In NBO theory, a donor-acceptor picture of H-bonding is based on overlap-type ionic resonance. The resonance hybrid O…H-C ↔ OH⁺…C⁻ corresponds to a two-electron intermolecular donor-acceptor interaction of the form nO→σC-H in which electron density from the lone pair nO of Lewis base (oxygen atom) delocalizes into the unfilled σC-H hydride antibonding orbital of the Lewis acid (C-H) [44]. Such intermolecular delocalization corresponds to partial charge transfer from the Lewis base to the Lewis acid. The larger the E⁽²⁾ value, the more intensive is the interaction between the donor and electron acceptor and the greater the extent of conjugation of the systems.

Table 3 presents NBO parameters for the molecules considered in this study. The charge transfer energy contribution denoted by EAB⁽²⁾ that derives from the nO→σC-H orbital-orbital interaction is included. This energy ranges from 1.19 kcal/mol in system 12 to 2.87 kcal/mol in system 4. Table 3 indicates that the interaction energy E⁽²⁾ between the lone pair of oxygen atom LP(2)O-σC-H for 4 (R₂ = CHCl₂) and 2 (R₂ = CH₃) is 2.87 and 1.32 kcal/mol, respectively. Similarly, the interaction energy E⁽²⁾ between the lone pair of oxygen atom LP(2)O-σC-H for 22 (R₂ = CHCl₂) and 20(R₂ = CH₃) is 1.95 and 1.83 kcal/mol, respectively.

Table 3: Occupancy of natural orbitals (NBO), corresponding to the C-H…O intramolecular contacts, obtained at B3LYP/aug-cc-pVDZ; E⁽²⁾ means energy of hyperconjugative interactions; Ei-Ej is energy difference between donor and acceptor NBO orbitals. Designation of species according to Scheme 1.

Compound

Acceptor (A)
C-H
Donor (B)
C=O
E⁽²⁾AB
(kcal/mol)
Ei-Ej
(a.u.)

Type
Occupancy
Type
Occupancy
Hybrid (O)

2
R₂ = CH₃, R₃ = H
BD
0.00944
LP(2)
1.85498
s (0.00%), p 1.00 (99.67%), and d 0.00 (0.33%)
1.32
0.67

3
R₂ = CH₂Cl, R₃ = H
BD
0.01785
LP(2)
1.85014
s (0.00%), p 1.00 (99.66%), and d 0.00 (0.34%)
1.37
0.65

4
R₂ = CHCl₂, R₃ = H
BD
0.03173
LP(2)
1.84338
s (0.01%), p 1.00 (99.65%), and d 0.00 (0.34%)
2.87
0.67

5
R₂ = CH₃, R₃ = Cl
BD
0.01231
LP(2)
1.84837
s (0.01%), p 1.00 (99.66%), and d 0.00 (0.33%)
1.63
0.68

6
R₂ = CH₂Cl, R₃ = Cl
BD
0.01943
LP(2)
1.84368
s (0.01%), p 1.00 (99.64%), and d 0.00 (0.34%)
1.71
0.66

7
R₂ = CHCl₂, R₃ = Cl
BD
0.03248
LP(2)
1.84651
s (0.00%), p 1.00 (99.66%), and d 0.00 (0.34%)
2.65
0.67

8
R₂ = CH₃, R₃ = NH₂
BD
0.01129
LP(2)
1.85463
s (0.00%), p 1.00 (99.67%), and d 0.00 (0.33%)
1.48
0.68

9
R₂ = CH₂Cl, R₃ = NH₂
BD
0.01876
LP(2)
1.85009
s (0.00%), p 1.00 (99.66%), and d 0.00 (0.34%)
1.56
0.66

10
R₂ = CHCl₂, R₃ = NH₂
BD
0.03187
LP(2)
1.84175
s (0.01%), p 1.00 (99.65%), and d 0.00 (0.34%)
1.57
0.64

11
R₂ = CH₃, R₃ = CH₃
BD
0.01110
LP(2)
1.85514
s (0.00%), p 1.00 (99.67%), and d 0.00 (0.33%)
1.74
0.68

12
R₂ = CH₂Cl, R₃ = CH₃
BD
0.01830
LP(2)
1.85056
s (0.00%), p 1.00 (99.66%), and d 0.00 (0.34%)
1.19
0.66

13
R₂ = CHCl₂, R₃ = CH₃
BD
0.03176
LP(2)
1.84328
s (0.01%), p 1.00 (99.65%), and d 0.00 (0.34%)
1.41
0.64

14
R₂ = CH₃, R₃ = CH₂CH₂CH₂Cl
BD
0.01154
LP(2)
1.85466
s (0.00%), p 1.00 (99.67%), and d 0.00 (0.32%)
1.77
0.68

15
R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂Cl
BD
0.01891
LP(2)
1.85004
s (0.00%), p 1.00 (99.66%), and d 0.00 (0.34%)
1.86
0.66

16
R₂ = CHCl₂, R₃ = CH₂CH₂CH₂Cl
BD
0.03221
LP(2)
1.85237
s (0.01%), p 1.00 (99.66%), and d 0.00 (0.33%)
1.89
0.65

17
R₂ = CH₃, R₃ = CH₂CH₂CH₂NH₂
BD
0.01102
LP(2)
1.85699
s (0.00%), p 1.00 (99.67%), and d 0.00 (0.32%)
1.53
0.68

18
R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NH₂
BD
0.01866
LP(2)
1.85040
s (0.00%), p 1.00 (99.66%), and d 0.00 (0.34%)
1.62
0.66

19
R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NH₂
BD
0.03193
LP(2)
1.84319
s (0.01%), p 1.00 (99.65%), and d 0.00 (0.34%)
1.47
0.65

20
R₂ = CH₃, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
BD
0.01143
LP(2)
1.85483
s (0.00%), p 1.00 (99.67%), and d 0.00 (0.32%)
1.83
0.68

21
R₂ = CH₂Cl, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
BD
0.01838
LP(2)
1.85023
s (0.00%), p 1.00 (99.66%), and d 0.00 (0.34%)
1.92
0.66

22
R₂ = CHCl₂, R₃ = CH₂CH₂CH₂NHC(NH)NH₂
BD
0.03209
LP(2)
1.84293
s (0.01%), p 1.00 (99.65%), and d 0.00 (0.34%)
1.95
0.65

The s-character for the Lewis acid C-H increases in the order R₂ = CH₃, R₂ = CH₂Cl, R₂ = CHCl₂. For example, for 2, 3, and 4, C-H acceptor occupancy is equal to 0.0094, 0.0178, and 0.0317, respectively. This effect was observed previously for the hydrogen bonding complexes [50]. The increase of s-character is accompanied by the increase of polarization of the C-H bond. The electron density at the C-H BCP in R₂ = CH₃ is lower than the electron density at C-H BCP in R₂ = CHCl₂ (Table 2).

NBO results enable us to suggest the presence of an attractive C=O⋯H-C intramolecular interactions for all compound under study. Contrary to expectations, there is no QTAIM evidence of the existence of the hydrogen bond, 3, 6, 9, 12, and 15 (where R₂ = CH₂Cl), since the H…O bond path is not observed.

There was a similar earlier finding for the intramolecular dihydrogen bonds where for some systems the NBO method showed an orbital-orbital overlap typical for the intramolecular interaction while QTAIM did not show the corresponding bond path [51].

It is noted that the results presented here are partly consistent with AIM analysis. The greatest values of electron density at the H...O bond critical point are observed for moieties where R₂ = CHCl₂ (Table 2). The latter approximately corresponds to the greatest orbital-orbital nO→σC-H energies.

Interestingly, the lone pair electrons localized on the oxygen atom in the systems where R₂ = CHCl₂ point toward the C-H hydride atom as seen in Figure 3. For the systems where R₂ = CH₃, nO→σC-H orbitals are held much farther apart than in the former species where Cl substituents enhance the strength of the hydrogen bond. Figure 3 shows an overlap surface-rendered diagram for the interacting nO and σC-H orbitals in pyrrolepyrazinones 22 and 20. It reveals a propensity for the C-H…O=C bonding for pyrrolopyrazinone 22, whereas 20 (R₂ = CH₃) exhibits a weak nO→σC-H interaction with the backside of the CH antibond.

Figure 3: NBO overlap interaction surface plot for the bay region of pyrrolopyrazinones 22 (R₂ = CHCl₂) and 20 (R₂ = CH₃) showing stabilizing donor-acceptor nO→σC-H interaction.

It seems most likely that the changes observed in the H-bonding can be due to the steric repulsion between oxygen and chlorine atoms. The presence of H-bond depends on geometrical arrangement of the oxygen and hydrogen atoms determined by its repulsion. In R₂ = CHCl₂, two chlorine atoms are forced to be in the anticlinal configuration with respect to oxygen. Such behavior minimizes repulsion, and therefore the H atom of the CHCl₂ group is in a synperiplanar configuration that is favorable for H-bonding.

In R₂ = CH₂Cl, the minimal repulsion is present in the antiperiplanar configuration of the oxygen and chlorine atom. This phenomenon forces the synclinal conformation of two hydrogen atoms of R₂ with respect to O atom. It is much less favorable for H-bond formation between C=O and R2 = CH₂Cl.

4.4. Intramolecular Hydrogen Bond and HOMA Aromaticity Interrelation

Palusiak et al. [52] revealed the interplay between local aromaticity of a polycyclic aromatic hydrocarbon and the strength of the intramolecular HB. It is also interesting to recognize the role of substituents and the hydrogen bond to stabilize pyrrolopyrazinone molecules analyzed here, particularly the effect of these factors on local aromaticities. It is worth to mention that the local aromaticity analyzed for the numerous systems considered in this study characterizes the aromaticity of a particular ring of the system [53].

The HOMA indices calculated for pyrrole (1), 3,4-dihydropyrrolopyrazinones (1a–c), pyrazine (1d), 2-oxopyrazine (1e), and pyrrolopyrazinones (2–22) are shown in Table 1. There are substituents in 2 and 3 positions (R₂ and R₃) for the species analyzed here: 3,4-dihydropyrrolopyrazinones (1a–c) and pyrrolopyrazinones (2–22). Table 1 is divided into two sections; the first section shows the local aromaticity of the pyrrole ring whereas the second section lists the local aromaticity of the pyrazinone ring. C-C and C-N bond lengths and HOMA values as well as calculated νC=C and νC=O frequencies are also included.

The HOMA index of pyrrole (1) is 0.833, whereas local HOMAs of 3,4-dihydropyrrolopyrazinones (1a–c) range from 0.876 to 0.885. The aromaticity of the pyrrole ring in 2–22 moieties varies between 0.848 and 0.905 HOMA units. It is seen that the HOMAs of the pyrrole ring for structures 1c, 4, 7, 10, 13, 16, 19, and 22 where R₂ = CHCl₂ are higher than those for structures 1a, 2, 5, 8, 11, 14, 17, and 20, and 1b, 3, 6, 9, 12, 15, 18, and 21 where R₂ = CH₃ or CH₂Cl, respectively. For instance, the HOMA value for the pyrrole ring of peramine (20) where R₂ = CH₃ is 0.865, for the chloromethylene derivative (21) where R₂ = CH₂Cl is 0.869, and for the dichloromethylene derivative (22) where R₂ = CHCl₂ is 0.877 a.u.

The local HOMA indices of the pyrrole ring for 3,4-dihydropyrrolopyrazinones 1a, 1b, and 1c are higher than those of pyrrolopyrazinone 2, 3, and 4 (Table 1). For instance, the HOMA for pyrrolopyrazinones 2 and 3 is 0.848 and 0.852, respectively, while for 3,4-dihydropyrrolopyrazinone 1a and 1b, it is 0.876 and 0.882, respectively. An analogous situation is observed for residual pairs of pyrrolopyrazinone moieties (R₂ = CH₂Cl and R₂ = CH₃), such as 5 and 6, 8 and 9, 11 and 12, 14 and 15, 17 and 18, and 20 and 21, as compared with HOMA indices of the pyrrole ring for 3,4-dihydropyrrolopyrazinones 1a and 1b (Table 1). This means that the addition of a pyrazinone ring reduces the aromaticity of the pyrrole ring in a pyrrolopyrazinone system as compared with an isolated pyrrole molecule. Aside from the above-mentioned pairs of systems, the HOMA index for the pyrrole ring is typically higher for species with the CH₂Cl substituent than for those where R₂ = CH₃.

It is worth mentioning that the so-called Clar’s rules represent a qualitative description of the aromatic character of a particular ring in a molecule of polycyclic species. These rules classify rings according to their π-electron structure into aromatic sextets, empty rings, migrating rings, and those with localized double bonds [54]. The HOMA approach enables distinguishing Clar’s sextets (very high HOMA close to 1.00) and empty rings and those with a localized double bond (low HOMA values). This may be performed by HOMA partitioning in energetic (EN) and geometric (GEO) terms [18]. The EN and GEO contributions express the aromaticity contributions related to a decrease in resonance energy and to an increase in bond length alternation, respectively [29]. These contributions for the species analyzed here are shown in Table 1. It is seen that the GEO term varies significantly with the R₂ substituent, for example for the 2, 3, 4 and 5, 6, 7 triads where R₂ = CH₃, R₂ = CH₂Cl, and R₂ = CHCl₂, respectively. The formation of the C-H…O=C intramolecular hydrogen bond for systems where R₂ = CHCl₂ leads to a decreased GEO contribution and consequently an increase in the HOMA value (HOMA = 1 – GEO − EN).

It is concluded based on the results from Table 1 that the HOMA aromaticity of heterocyclic rings is directly related to the structural properties of the R₂ substituent and to the geometry of the H…O contact in the chelate ring. It should be noted that HOMA differences for the pair of compounds where R₂ = CH₂Cl or R₂ = CHCl₂ are small, ΔHOMA = 0.002–0.008. However, a trend is observed that HOMA is greater for species where R₂ = CHCl₂ than for the ones where R₂ = CH₂Cl. It may suggest that the relatively larger stability of the aromatic pyrrole ring in pyrrolepyrazinone moieties where R₂ = CHCl₂ compared to its R₂ = CH₂Cl counterpart results from the slightly larger aromatic character due to the formation of the HB chelate ring.

The HOMA index of pyrazine (1d) [55] is 0.985, whereas HOMA of 2-oxo-pyrazine (1e) is 0.591. Both heterocycles may be treated as reference moieties. Local aromaticity expressed by HOMA of the pyrazinone ring in moieties 2–22 varies in a range of 0.400–0.512. The HOMAs of the pyrazinone ring for structures 4, 7, 10, 13, 16, 19, and 22 where R₂ = CHCl₂ are lower than the HOMAs for structures 2, 5, 8, 11, 14, 17, and 20, and 3, 6, 9, 12, 15, 18, and 21 where R₂ = CH₃ or CH₂Cl, respectively. For example, the HOMA value for the pyrazinone ring of peramine (20) where R₂ = CH₃ is 0.487, while that for the chloromethylene derivative (21) where R₂ = CH₂Cl is 0.427. For the dichloromethylene derivative (22) where R₂ = CHCl₂, it is 0.404.

It is worth noting that the opposite relationship is observed for the local HOMA aromaticity index of the pyrrole ring; it is greater for R₂ = CHCl₂ than for R₂ = CH₃ or R₂ = CH₂Cl.

Some attention was paid previously to the intermolecular interactions affecting aromaticity of certain phenol derivatives [56, 57]. It was concluded that an increase in the H-bond strength of phenol derivatives resulted in a decrease in aromaticity. It was also stated that the main structural factor contributing to the decreased aromaticity of the ring resulted mostly from bond length alternations. The increase in GEO leads to a decrease in aromaticity (HOMA diminishes). For the species analyzed here, the local HOMA aromaticity of the pyrazinone ring decreases (Table 1), which is connected with the increase in the GEO and EN terms.

The electron-withdrawing substituents, such as –CHCl₂, lead to a local EN increase for pyrazinone that consequently results in the decrease in the corresponding local HOMA index. The lower local aromaticity of the pyrazinone ring may result from the methyl group electron-withdrawing properties that increase if hydrogen atoms are substituted by chlorine atoms. It is also noted, however, that the increase of stability of the other ring, pyrrole, is expressed in the increase of the corresponding local HOMA index. In other words, an increase in the aromaticity of one ring leads to lower aromaticity of the other ring. This result is consistent with the earlier findings for pyrrole and N-methylpyrrole reported by Dubis et al. [9].

Moreover, it is worth noting that the HOMA aromaticity index for the pyrazine ring, 1d, of 0.985 is greater than that calculated for 2-oxo-pyrazine, 1e, of 0.591. This may be compared with the pyrazinone ring HOMA values for 2, 3, and 4, equal to 0.466, 0.414, and 0.408, respectively. An analogous situation is observed for residual pairs of pyrrolopyrazine moieties.

These observations can be concluded in the following way. The C-H…O contact is shorter with higher local HOMA aromaticity of the pyrrole ring and lower HOMA aromaticity of the pyrazinone ring. These interrelated changes may be explained by a decrease in bond length alternation in the pyrrole ring confirmed by a decrease in GEO increments and a decrease in resonance energy of the pyrazinone ring confirmed by an increase in the EN increment to HOMA.

4.5. Vibrational Properties

Table 1 also shows the IR frequencies of the carbonyl group, νCO, which may be considered as an indicator of HB interaction. Conventional A-H…B hydrogen bonds include the bonds formed by main group elements such as N, O, F, Cl, and Br, whereas for weak H-bonds, C-H, P-H, and Si-H are often nonconventional proton-donating bonds. Such a situation occurs for the C-H…O hydrogen bonds analyzed here.

H-bond formation affects the stretching band of the A-H bond as well as the stretching vibrational mode of the proton-accepting center, that is, the C=O group in this study. Current computational studies reveal that the frequency of the C=O stretching mode of systems 2, 3, and 4 for which R₂ = CH₃, R₂ = CH₂Cl, and R₂ = CHCl₂ ranges from 1669 cm⁻¹ in 2 (R₂ = CH₃) without intramolecular C-H…O interactions to 1689 cm⁻¹ for system 4 (R₂ = CHCl₂).The frequency of the C=O stretching mode of systems 2, 5, 8, 11, 14, 17, and 20 for which R₂ = CH₃ ranges from 1674 cm⁻¹ in system 5 to 1664 cm⁻¹ in system 17.

The frequency of the C=O stretching mode of systems 3, 6, 9, 12, 15, 18, and 21 for which R₂ = CH₂Cl ranges from 1696 cm⁻¹ in system 9 to 1686 cm⁻¹ in system 3.

The formation of the hydrogen bond leads to an electron density shift from the Lewis base to the Lewis acid unit; for the C-H…O interactions analyzed here; from the lone pairs of oxygen (C=O group) to the C-H proton donor. It is expressed as the n(O)→σ(CH) orbital-orbital overlap in terms of the NBO approach. The latter causes weakening of the C=O bond, its elongation, and red shifting of the ν(C=O) stretching vibrational mode. The frequency of the C=O stretching mode of systems 4, 7, 10, 13, 16, 19, and 22 for which R₂ = CHCl₂ ranges from 1798 cm⁻¹ in system 13 to 1687 cm⁻¹ in system 19. ν(C=O) is lower for a system in which R₂ = CH₂Cl than for a system where R₂ = CHCl₂.

Figure 4 presents an experimental and theoretical spectrum of peramine (20) where R₂ = CH₃ (Figures 4(a) and 4(b)) and theoretical spectra of 21 and 22 (Figures 4(c) and 4(d)) where R₂ = CH₂Cl and CHCl₂, respectively.

Figure 4: Experimental (a, b) and calculated (c, d) IR spectra (B3LYP/aug-cc-pVDZ level of theory) of peramine 20 (R₂ = CH₃), 21 (R₂ = CH₂Cl), and 22 (R₂ = CHCl2) according to Scheme 1.

It has been found on the basis of the previous study [8] that bands within the spectral ranges 1671–1688 cm⁻¹ and 1640–1655 cm⁻¹are not simple C=O or C=C stretching modes, but they are the result of the mixing of C=O and C=C stretching vibrations. The mode να has C=O and C=C double bonds with stretching “out of phase” vibration, whereas νβ is the “in phase” mode (Figure 4(b)).

When R₂ = CHCl₂, an intramolecular CH…O=C hydrogen bond is formed. This effect causes the shift of να to higher frequencies (Δν~18 cm⁻¹) in comparison with peramine (20).

It seems that νC=O increases with the C-H…O=C distance decrease (Table 2). It could be explained as follows: the greater the chelate ring tension, the higher νC=O. The carbonyl group is sp² hybridized (120°). Bending the C-H…O toward each other from 116.63° in 20 to 112.91° in 22 results in changes in carbonyl carbon hybridization that leads to a strengthening of the C=O bond and weakening of the adjacent C-C bond.

5. Conclusions

Pyrrolo[1,2-a]pyrazin-1(2H)-ones as an important class of natural organic compounds were analyzed here. The emphasis was put on structures of these species and on factors which determine their unique properties and play a crucial role in numerous reactions, also those which are important in ecology.

For the pyrrolopyrazinone derivatives analyzed here, formation of the intramolecular C-H…O hydrogen bond is observed. In general, geometrical and NBO criteria confirm the existence of such interactions for all systems since the H…O distances for all of them are shorter than the corresponding sum of hydrogen and oxygen van der Waals radii as well as for all species in which nO→σC-H orbital-orbital overlap is observed with the corresponding interaction energy of 1.19–2.87 kcal/mol. However, for certain species (those with the R₂ = CH₂Cl substituent and some of the systems where R₂ = CH₃), the QTAIM approach does not detect the existence of the hydrogen bond; H…O bond paths are not observed for these systems. It is seen that the substitution of the hydrogen atoms by chlorine atoms enhances the strength of the hydrogen bond; the approximate strength order of the hydrogen bond is observed here according to the following types of R₂ groups: CHCl₂ > CH₂Cl > CH₃.

The changes observed in the H-bonding can be due to the steric repulsion between oxygen and chlorine atoms. The presence of H-bond depends on the geometrical arrangement of the oxygen and hydrogen atoms determined by its repulsion.

The aromaticity changes are discussed here in terms of the HOMA index and its EN and GEO components. The shortest C-H…O=C contact is related to a higher νC=O value.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

Calculations were carried out in the Warsaw Supercomputer Center (ICM) (G53-7).

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