Advances in Condensed Matter Physics
Volume 2019 (2019), Article ID 4246810, 22 pages
https://doi.org/10.1155/2019/4246810

Research Article

Electronic Structure, Spectroscopic (IR, Raman, UV-Vis, NMR), Optoelectronic, and NLO Properties Investigations of Rubescin E (C₃₁H₃₆O₇) Molecule in Gas Phase and Chloroform Solution Using Ab Initio and DFT Methods

Richard Arnaud Yossa Kamsi,1,2 Geh Wilson Ejuh,2,3,4 Fidèle Tchoffo,¹ Pierre Mkounga,⁵ and Jean-Marie Bienvenu Ndjaka1,2

¹University of Yaounde I, Faculty of Science, Department of Physics, P.O. Box 812, Yaounde, Cameroon
²CETIC (Centre d’Excellence Africain en Technologies de l’Information et de la Communication), Université de Yaoundé I, B.P. 8390, Yaoundé, Cameroon
³University of Bamenda, National Higher Polytechnic Institute, Department of Electrical and Electronic Engineering, P. O. Box 39, Bambili, Cameroon
⁴University of Dschang, IUT Bandjoun, Department of General and Scientific Studies, P.O. Box 134, Bandjoun, Cameroon
⁵University of Yaounde I, Faculty of Science, Department of Chemistry, P.O. Box 812, Yaounde, Cameroon

Correspondence should be addressed to Richard Arnaud Yossa Kamsi; richardkamsi@yahoo.fr

Received 12 October 2018; Accepted 28 November 2018; Published 2 January 2019

Academic Editor: Jörg Fink

Copyright © 2019 Richard Arnaud Yossa Kamsi 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.

Quantum chemical methods were used to study the electronic structure and some physicochemical properties of Rubescin E molecule. Good agreement with experiment was found for coupling constant, IR, ¹H NMR, and ¹³C NMR. The excitation energy and oscillator strength calculated by TD-DFT also complement with experiment. Large values were obtained for dipole moment, polarizability, first static hyperpolarizability, electric susceptibility, refractive index, and dielectric constant, meaning that Rubescin E has strong optical and phonon application and can be a good candidate as NLOs material. The 3D analysis of the title molecule leads us to the conclusion that electron can easily be transferred from furan to tetrahydrofuran ring. The global reactivity descriptors were evaluated. Mulliken, ESP, and NBO charges comparisons were carried out and described.

1. Introduction

Many molecules from plant research were found nowadays to have application in the field of medicine, where there are use for the treatment of many diseases among which we found malaria caused by plasmodium falciparum. The new limonoid name Rubescin E (C₃₁H₃₆O₇), extracted from the roots of Trichilia Rubescens, collected from Cameroon, has been evaluated against erythrocytic stages of strain 3D7 plasmodium falciparum and also exhibited significant antiplasmodial in vitro activity with IC₅₀ value of 1.13μM [1]. The FT-IR performed on Rubescin E molecule revealed the presence of α, β-unsaturated carbonyl moiety at 1720 cm⁻¹ and 1664 cm⁻¹. These values can be obtained theoretically by performing the vibrational frequencies calculation on the title molecule and used to explain the different motion of atoms or group of atoms in a molecular system. The 1D (¹H, ¹³C NMR) and 2D NMR spectra were run on a Bruker AV spectrometer [1] in order to predict the structure of the title molecule and were done in this work in order to take out similarities between experiment done previously and theoretical calculation performed here.

In this work, quantum chemical calculation was performed in order to take out the electronic structure (energy gap, charge distributions, NLO properties, vibrational frequencies, NMR, and UV-vis calculation) and some physicochemical properties ( chemical coupling-coupling constant, the global reactivity descriptors, and some geometrical parameters such as bonds lengths and bonds angles) of Rubescin E molecule. To the best of our knowledge, no theoretical study was performed yet on the title molecule, that is what motivated us to investigate the electronic structure, the spectroscopic, and some physicochemical properties of Rubescin E molecule. Except for NMR, UV-vis, chemical coupling-coupling constant, and the vibrational frequencies obtained for the two α, β-unsaturated carbonyl moiety, most of our results were not compared and we are optimistic that it can be used as threshold for future experimental or theoretical research. Hartree Fock and DFT (using B3LYP and B3PW91 functionals) methods were used for these purposes. These properties were calculated by employing the triple split valence basis set along with polarization functions with and without diffuse functions as implemented in Gaussian 09, Rev. A02 in both gas phase and in a solution of chloroform. The methods and basis sets used are among the most widely used [2–5] and provide excellent results which are generally very close to experiments [6–8].

2. Computational Methods

Theoretical calculations were performed on Rubescin E using HF and DFT methods at the B3LYP and B3PW91 levels as implemented in Gaussian 09W code [9]. All these calculations were done in gas phase and in a solution of chloroform. No geometry restriction was applied during the optimization procedure. The solvent effects were treated within the conductor-like polarizable continuum model (CPCM). For the geometry optimization, the 6-311G(d,p) and 6-311++G(d,p) basis set were used in both gas and solvent. Convergence criteria in which both the maximum force and displacement are smaller than the cut-off of 0.000015 and 0.000060 and RMS force and displacement less than the cut-off values of 0.000010 and 0.000040 were used in the calculations in order to increase the accuracy of our results. The chemical proton-proton coupling constant function of angle between two C-H vectors was calculated from the optimization output using the original Karplus equation [10]. The optimized form of our molecule was then used to determine the global reactivity descriptors, electronic and NLOs properties. The net charges were also evaluated using MPA, ESP, and NBOs methods at the three levels mentioned above, and all this was done in both gas phase and chloroform with the 6-311++G(d,p) basis set. In order to confirm the stability of our molecule, the vibrational frequencies (IR and Raman) were evaluated at the 6-311G(d,p) and no imaginary frequencies were found leading us to the results that our molecule was stable at the levels and basis set considered. The time dependent density functional theory (TD-DFT) field was used in gas phase with the 6-311++G(d,p) basis in order to understand the electronic transition of our molecule and the obtained results were compared to experiment. The GIAO (gauge independent atomic orbital) method was used on the optimized form of our molecule in a solution of chloroform to determine the ¹H and ¹³C NMR spectra parameters at the three levels and with the 6-311++G(d,p) basis set. In order to compare the calculated values of ¹H and ¹³C chemical shift with experimental results, the reference and widely used molecule TMS (tetramethylsilane) for this purpose were exploited at the same level, at the same phase, and with the same basis set.

3. Results and Discussion

3.1. Optimized Structure

The optimized geometry of Rubescin E obtained using the B3LYP/6-311++G(d,p) method in chloroform is shown in Figure 1. The value of the total electronic energy of the molecule obtained at the B3LYP shows that Figure 1 is the most stable structure of the molecule. The total electronic energy calculated within the two methods in gas and in a solution of chloroform with the 6-311++G(d,p) is given in Table 1.

Table 1: Optimized geometric parameters in gas phase and in chloroform solution of Rubescin E at the RHF, B3LYP, and B3PW91 level with the 6-311++G (d,p) basis sets.

Levels
RHF
B3LYP
B3PW91
Theory[11], [12], [13]

Basis set
Gaz
CDCl3
Gaz
CDCl3
Gaz
CDCl3

Bond length

R1 (C₁-C₂)
1.5503
1.5490
1.5603
1.5583
1.5521
1.5500

R2 (C₁-C₃)
1.5698
1.5672
1.5811
1.5777
1.5719
1.5684

R3 (C₁-C₂₀)
1.5167
1.5157
1.5221
1.5215
1.5153
1.5147

R4 (C₁-C₂₂)
1.5474
1.5481
1.5510
1.5509
1.5439
1.5438

R5 (C₂=O₇)
1.1900
1.1948
1.2167
1.2213
1.2152
1.2197

R6 (C₂-C₃₄)
1.5041
1.4992
1.4966
1.4910
1.4920
1.4867

R7 (C₃-C₄)
1.5898
1.5887
1.5973
1.5968
1.5866
1.5860

R8 (C₃-C₄₀)
1.4814
1.4800
1.4972
1.4958
1.4931
1.4918

R9 (C₃-O₅₉)
1.3994
1.4024
1.4311
1.4335
1.4236
1.4256

R10 (C₄-C₅)
1.5515
1.5518
1.5549
1.5548
1.5473
1.5471

R11 (C₄-C₁₂)
1.5707
1.5733
1.5756
1.5787
1.5676
1.5707

R12 (C₄-C₃₆)
1.5501
1.5503
1.5543
1.5543
1.5471
1.5472

R13 (C₅-C₆)
1.5428
1.5442
1.5477
1.5487
1.5401
1.5410

R14 (C₅-C₄₆)
1.4556
1.4553
1.4720
1.4717
1.4686
1.4684

R15 (C₅-O₆₁)
1.4206
1.4235
1.4568
1.4590
1.4473
1.4492

R16 (C₆-C₂₆)
1.5259
1.5260
1.5306
1.5307
1.5246
1.5248

R17 (C₆-C₄₂)
1.5352
1.5350
1.5373
1.5373
1.5298
1.5298

R18 (C₆-C₅₁)
1.5703
1.5708
1.5810
1.5814
1.5724
1.5728

R19 (C₈-C₁₆)
1.5423
1.5424
1.5477
1.5481
1.5405
1.5408

R20 (C₈-C₂₀)
1.5256
1.5244
1.5348
1.5335
1.5276
1.5264

R21 (C₈-C₂₉)
1.5405
1.5402
1.5479
1.5468
1.5416
1.5406

R22 (C₈-C₃₂)
1.5036
1.5036
1.5010
1.5010
1.4958
1.4960

R23 (C₉-O₁₁)
1.4120
1.4133
1.4389
1.4411
1.4304
1.4324

R24 (C₉-C₁₂)
1.5288
1.5302
1.5357
1.5373
1.5311
1.5329

R25 (C₉-C₂₀)
1.4997
1.4993
1.5044
1.5042
1.4999
1.4998

R26 (O₁₁-C₂₉)
1.4261
1.4287
1.4530
1.4551
1.4438
1.4457

R27 (C₁₂-O₆₀)
1.4104
1.4131
1.4339
1.4369
1.4255
1.4283

R28 (C₁₄-C₅₁)
1.5035
1.5041
1.5003
1.5010
1.4953
1.4959

R29 (C₁₄-C₅₃)
1.4493
1.4505
1.4428
1.4438
1.4387
1.4397

R30 (C₁₄=C₅₇)
1.3411
1.3410
1.3621
1.3619
1.3614
1.3614

R31 (O₁₅-C₅₅)
1.3382
1.3412
1.3609
1.3638
1.3548
1.3574

R32 (O₁₅-C₅₇)
1.3467
1.3496
1.3659
1.3686
1.3592
1.3616

R33 (C₂₆-C₄₀)
1.5162
1.5158
1.5190
1.5181
1.5137
1.5129

R34 (C₃₂=C₃₄)
1.3270
1.3285
1.3431
1.3445
1.3422
1.3436

R35 (C₄₀-O₅₉)
1.4010
1.4054
1.4353
1.4395
1.4282
1.4320

R36 (C₄₆-C₄₈)
1.5086
1.5076
1.5135
1.5123
1.5088
1.5077

R37 (C₄₆-O₆₁)
1.4005
1.4051
1.4326
1.4376
1.4254
1.4297

R38 (C₄₈-C₅₁)
1.5407
1.5405
1.5478
1.5475
1.5408
1.5405

R39 (C₅₃=C₅₅)
1.3381
1.3381
1.3567
1.3567
1.3559
1.3559

R40 (O₆₀-C₆₂)
1.3485
1.3397
1.3805
1.3700
1.3743
1.3650

R41 (C₆₂-C₆₃)
1.5033
1.5030
1.4998
1.5000
1.4956
1.4952

R42 (C₆₂=O₆₅)
1.1810
1.1873
1.2059
1.2113
1.2046
1.2098

R43 (C₆₃=C₆₄)
1.3222
1.3230
1.3402
1.3403
1.3394
1.3398

R44 (C₆₃-C₇₁)
1.5153
1.5159
1.5127
1.5135
1.5071
1.5083

R45 (C₆₄-C₆₇)
1.5001
1.5002
1.4954
1.4959
1.4898
1.4901

Bond angles

A1 (C₂-C₁-C₃)
115.3869
115.1538
115.3519
115.0591
115.3042
114.9661

A2 (C₂-C₁-C₂₀)
104.9116
105.2360
104.8861
105.3058
105.0195
105.4353

A3 (C₂-C₁-C₂₂)
104.6632
104.8093
104.8467
105.0548
104.7619
105.0065

A4 (C₃-C₁-C₂₀)
105.4487
104.9239
106.0693
105.3428
105.9491
105.1727

A5 (C₃-C₁-C₂₂)
110.0598
110.4677
109.3407
109.9326
109.4774
110.1062

A6 (C₂₀-C₁-C₂₂)
116.6507
116.5134
116.6409
116.4160
116.6212
116.4196

A7 (C₁-C₂-O₇)
122.6712
122.1731
122.5890
122.0461
122.6012
122.0599

A8 (C₁-C₂-C₃₄)
118.8294
119.0297
118.5520
118.8580
118.5112
118.8095

A9 (O₇-C₂-C₃₄)
118.3115
118.6060
118.6750
118.9135
118.6899
118.9368

A10 (C₁-C₃-C₄)
117.4677
117.2546
117.5179
117.3499
117.4703
117.2908

A11 (C₁-C₃-C₄₀)
120.4116
120.3391
120.5229
120.3696
120.4781
120.3201

A12 (C₁-C₃-O₅₉)
113.5239
113.6346
113.2288
113.4708
113.2740
113.5007

A13 (C₄-C₃-C₄₀)
119.7989
119.8618
119.6777
119.7275
119.7605
119.8264

A14 (C₄-C₃-O₅₉)
110.9192
111.3348
110.6687
111.0566
110.7288
111.1433

A15 (C₃-C₄-C₅)
108.2815
108.0767
108.5292
108.3020
108.4460
108.1898

A16 (C₃-C₄-C₁₂)
116.9097
116.9148
116.6545
116.8466
116.8336
117.0260

A17 (C₃-C₄-C₃₆)
107.3533
107.5825
107.2145
107.3890
107.2213
107.3820

A18 (C₅-C₄-C₁₂)
110.9502
111.2590
110.8879
111.1131
111.0310
111.3284

A19 (C₅-C₄-C₃₆)
108.2096
108.3900
108.2857
108.5557
108.0890
108.3471

A20 (C₁₂-C₄-C₃₆)
104.7402
104.2361
104.883
104.2585
104.7988
104.1530

A21 (C₄-C₅-C₆)
122.3963
122.5160
122.2095
122.2513
122.2181
122.2697

A22 (C₄-C₅-C₄₆)
126.1434
126.0858
126.2488
126.1993
126.1315
126.0739

A23 (C₄-C₅-O₆₁)
113.7557
113.5947
113.7382
113.6922
114.0173
113.9553

A24 (C₆-C₅-C₄₆)
108.4092
108.4312
108.2407
108.2667
108.2513
108.2900

A25 (C₆-C₅-O₆₁)
109.3436
109.1575
109.7850
109.6384
109.6935
109.5481

A26 (C₅-C₆-C₂₆)
106.9225
107.1323
107.1725
107.3025
107.1359
107.2931

A27 (C₅-C₆-C₄₂)
114.7934
114.8607
114.4807
114.5006
114.5313
114.5541

A28 (C₅-C₆-C₅₁)
101.8612
101.8830
101.9281
102.0115
101.8916
101.9777

A29 (C₂₆-C₆-C₄₂)
108.8679
108.6162
109.1102
108.9149
109.1443
108.9314

A30 (C₂₆-C₆-C₅₁)
113.8205
113.8653
113.9931
114.0014
113.9406
113.9367

A31 (C₄₂-C₆-C₅₁)
110.5307
110.4727
110.1102
110.0888
110.1443
110.1222

A32 (C₁₆-C₈-C₂₀)
117.8467
117.8806
117.5220
117.5381
117.3986
117.3974

A33 (C₁₆-C₈-C₂₉)
108.3950
108.5431
108.4117
108.5195
108.5270
108.6672

A34 (C₁₆-C₈-C₃₂)
109.5455
109.4283
109.5034
109.3293
109.6190
109.4415

A35 (C₂₀-C₈-C₂₉)
96.3773
96.4321
96.6032
96.6193
96.4146
96.4285

A36 (C₂₀-C₈-C₃₂)
106.3315
106.2487
106.4280
106.3876
106.432
106.3732

A37 (C₂₉-C₈-C₃₂)
118.2843
118.2659
118.3155
118.4200
118.3462
118.4575

A38 (O₁₁-C₉-C₁₂)
113.2108
113.1065
113.2048
113.2060
113.1493
113.1724

A39 (O₁₁-C₉-C₂₀)
103.3360
103.1494
103.8285
103.6622
103.8971
103.7399

A40 (C₁₂-C₉-C₂₀)
109.2549
109.4574
108.7908
108.9954
108.4814
108.6640

A41 (C₉-O₁₁-C₂₉)
111.1841
111.2217
109.8976
109.9018
109.8190
109.8362

A42 (C₄-C₁₂-C₉)
110.4259
110.6951
110.0123
110.3980
109.8110
110.1418

A43 (C₄-C₁₂-O₆₀)
111.1499
111.4570
110.9644
111.4849
111.3257
111.9073

A44 (C₉-C₁₂-O₆₀)
109.0864
108.7044
108.7314
108.2508
108.4512
107.9972

A45 (C₅₁-C₁₄-C₅₃)
126.042
126.0928
126.1043
126.1692
126.2986
126.3771

A46 (C₅₁-C₁₄-C₅₇)
129.3418
129.1716
128.8385
128.6558
128.7371
128.5448

A47 (C₅₃-C₁₄-C₅₇)
104.5893
104.7043
105.0493
105.1666
104.9597
105.0728

A48 (C₅₅-O₁₅-C₅₇)
107.1084
107.1499
106.7602
106.8013
106.8133
106.8678

A49 (C₁-C₂₀-C₈)
121.1479
121.0073
120.9097
120.7705
120.9914
120.8439

A50 (C₁-C₂₀-C₉)
118.7226
118.5220
118.7478
118.3732
118.6818
118.2898

A51 (C₈-C₂₀-C₉)
103.8120
103.9439
104.2023
104.3600
104.0389
104.2216

A52 (C₆-C₂₆-C₄₀)
111.4945
111.6304
111.4804
111.5216
111.4199
111.4969

A53 (C₈-C₂₉-O₁₁)
104.4386
104.4819
104.6594
104.594
104.6712
104.6043

A54 (C₈-C₃₂-C₃₄)
120.4664
120.4528
120.5688
120.4387
120.4312
120.2925

A55 (C₂-C₃₄-C₃₂)
125.2907
124.9802
125.5569
125.2584
125.5114
125.1913

A56 (C₃-C₄₀-C₂₆)
124.7594
125.1561
124.3752
124.7373
124.3541
124.7241

A57 (C₂₆-C₄₀-O₅₉)
116.1404
115.9652
116.0868
116.0753
115.9905
115.9607

A58 (C₅-C₄₆-C₄₈)
110.0006
110.0212
109.8202
109.8537
109.6430
109.6699

A59 (C₄₈-C₄₆-O₆₁)
111.5740
111.5456
111.7313
111.7203
111.8859
111.8641

A60 (C₄₆-C₄₈-C₅₁)
102.6704
102.7788
102.8570
103.0253
102.6915
102.8703

A61 (C₆-C₅₁-C₁₄)
116.8638
116.8705
116.6829
116.6156
116.3993
116.3329

A62 (C₆-C₅₁-C₄₈)
104.4966
104.5425
104.2867
104.3539
104.3511
104.4332

A63 (C₁₄-C₅₁-C₄₈)
114.9685
114.8714
115.2826
115.1809
115.2757
115.1468

A64 (C₁₄-C₅₃-C₅₅)
106.1668
106.2381
106.7966
106.8606
106.6618
106.7168

A65 (O₁₅-C₅₅-C₅₃)
110.7484
110.6455
110.3339
110.2350
110.4305
110.3331

A66 (C₁₄-C₅₇-O₁₅)
111.3857
111.2607
111.0591
110.9356
111.1339
111.0086

A67 (C₁₂-O₆₀-C₆₂)
123.1805
123.4264
122.4520
122.2629
121.8099
121.5920

A68 (O₆₀-C₆₂-C₆₃)
118.3342
119.1473
118.6681
119.4932
118.6273
119.3485

A69 (O₆₀-C₆₂-O₆₅)
118.3753
117.9395
117.5454
117.1467
117.6414
117.2568

A70 (C₆₃-C₆₂-O₆₅)
123.0766
122.6884
123.4720
123.0718
123.4069
123.1015

A71 (C₆₂-C₆₃-C₆₄)
116.9655
117.1950
116.2922
116.7661
116.1754
116.6519

A72 (C₆₂-C₆₃-C₇₁)
117.8479
117.3833
119.4971
118.5815
119.7175
119.0158

A74 (C₆₄-C₆₃-C₇₁)
125.0717
125.2904
124.1105
124.5124
123.9876
124.1815

A75 (C₆₃-C₆₄-C₆₇)
127.2664
127.2197
127.2301
127.2514
126.9123
126.7855

Total energy (Hartree)
-1719.15539
-1719.17648
-1729.82917
-1729.84726
-1729.17724
-1729.19498

Figure 1: Ground state geometry of Rubescin E at B3LYP/6-311++G(d,p) in chloroform solution.

3.2. Structural Properties

A part of the optimized geometrical parameters (bond length, bond angle) and total electronic energy of the title molecule both in gas and in a solution of chloroform are given in Table 1 using the three levels and with the 6-311++G(d,p) basis set. The total description of the molecular geometry of Rubescin E molecule in gas phase and in a solution of chloroform using ab initio (RHF) and DFT (B3LYP and B3PW91) methods with the 6-311++G(d,p) basis set can be obtained from Supplementary Material S1.

The atom numbering scheme adopted for this purpose is the same as in Figure 1. The energy differences between the two used phases increase when we move from B3PW91 to B3LYP and to RHF and are found to be approximatively 0.48 eV, 0.49 eV, and 0.57 eV, respectively. The optimized bond length and bond angle of Rubescin E are also listed in Table 1 with some specific experimental values [12–14] found in the literature for some groups of compounds such as furan, ethylene oxide, and tetrahydrofuran present in our molecule. It can be observed from Table 1 that the values of the bond length obtained at B3LYP are slightly higher than those obtained at the B3PW91 level. These differences are found between 0.0034 Å and 0.0107 Å for C-C; 0.0061 Å and 0.0095 Å for C-O; and 0.0007 Å and 0.0013 Å for C=C in gas phase. The value of C=O bond length is better at the DFT methods since its values are closer to 2.10 Å found in literature [11]. It can also been observed that the calculated bonds length using Hartree Fock and DFT methods are very close to the values found in literature for the specific groups of compounds present in our molecule. These observed differences varied from 0.0012 Å at the B3LYP level to 0.0363 Å at the RHF level; from 0.0002 Å at the B3PW91 level to 0.0288 Å at the B3LYP level; and from 0.0019 Å at the B3LYP level to 0.0259 Å at the RHF level for C-C, C-O, and C=C bonds both in gas phase and in chloroform solution, respectively.

The bonds angles of the studied molecule are slightly different when we move from one phase to another at each level with larger values obtained at the RHF level. From our results, it can be seen that the C-C-C bond angle varies from 96.3773° to 129.3418°, from 96.6032° to 128.8385°, and from 96.4146° to 128.7371° at the gas phase, respectively, at the RHF, B3LYP, and B3PW91 level of the theory. In CDCl3, the C-C-C bond angles are similar to those obtained at the gas phase. The smallest value of C-C-C bond angle was C₂₀-C₈-C₂₉ bond angle and the largest C₅₁-C₁₄-C₅₇ bond angle. For the C-C-O angle, the smallest value was 104.4386° obtained at the RHF and the largest value was 123.472° obtained at the B3LYP level both in the gas phase. The C-O-C bond angle was found between 107.1084° and 123.4264° obtained at the RHF level. These bonds angles compared to some known values found in literature [12, 14] for specific compound present in our structure show good similarities. The little differences are found between 0.0268° and 1.5507° for C-C-C bond, between 0.0595° and 3.0614° for C-C-O bond, and between 0.0202° and 0.781° for C-O-C bond. These observed differences are due to the fact that these groups of compounds were not isolated.

3.3. Calculated Coupling Constant

The chemical proton-proton coupling constant was calculated using the original Karplus [10] equation in gas and solvent and its results compared to experimental values [1] obtained by extracting Rubescin E in a solution of chloroform. From our results, we found that the calculated parameters both in gas and in chloroform are all similar at all the levels used. These obtained results are also very close to experiment. As predicted in literature [10], we observed from Table 2 that when the angles between the two C-H vectors are close enough to 0⁰ or 180⁰, the value of coupling constant is greater (with ) and is very small when the angle is close to 90⁰.

Table 2: Experimental and calculated proton-proton coupling constant of Rubescin E in gas phase and in chloroform solution.

PARAMETERS
RHF
B3LYP
B3PW91
EXP [1]

Gaz
CDCl3
Gaz
CDCl3
Gaz
CDCl3

Angles(°)
(Hz)
Angles(°)
(Hz)
Angles(°)
(Hz)
Angles(°)
(Hz)
Angles(°)
(Hz)
Angles(°)
(Hz)

H₁₀-C₉-C₁₂-H₁₃
45.5506
6.20
43.8143
6.49
48.1393
5.79
45.9537
6.14
48.3285
5.76
46.1662
6.10
4.0

H₁₀-C₉-C₂₀-H₂₁
169.5395
12.65
169.8194
12.67
168.824
12.61
168.658
12.59
168.5
12.58
168.2201
12.56
12.0

H₂₇-C₂₆-C₄₀-H₄₁
-11.0718
10.65
-12.0311
10.59
-10.1794
10.70
-10.89
10.66
-10.4324
10.69
-11.298
10.64
6.5

H₂₈-C₂₆-C₄₀-H₄₁
105.3029
2.96
103.995
2.83
106.3433
3.07
105.3319
2.96
106.1668
3.05
104.964
2.92
1.3

H₃₃-C₃₂-C₃₄-H₃₅
-0.2873
11
-0.123
11
-0.5893
11
-0.366
11
-0.566
11
-0.3331
11
10.0

H₄₇-C₄₆-C₄₈-H₄₉
-61.3614
3.82
-61.1286
3.85
-61.9356
3.74
-61.8438
3.75
-61.5482
3.79
-61.4875
3.80
4.2

H₄₇-C₄₆-C₄₈-H₅₀
58.7437
4.17
58.7503
4.17
58.0428
4.27
57.8579
4.30
58.534
4.20
58.3044
4.24
4.2

H₄₉-C₄₈-C₅₁-H₅₂
-42.5704
6.69
-42.1786
6.75
-43.9616
6.46
-43.3642
6.56
-44.5718
6.36
-43.9227
6.47
4.2

H₅₀-C₄₈-C₅₁-H₅₂
-164.093
12.21
-163.817
12.18
-165.22
12.32
-164.673
12.27
-165.874
12.37
-165.259
12.32
11

H₅₄-C₅₃-C₅₅-H₅₆
-0.3838
11
-0.2856
11
-0.3275
11
-0.2429
11
-0.3921
11
-0.3074
11

H₆₆-C₆₄-C₆₇-H₆₈
-177.906
12.99
-177.979
12.99
178.4674
12.99
178.7874
13
178.4147
12.99
178.548
12.99

H₆₆-C₆₄-C₆₇-H₆₉
-56.9125
4.43
-56.9428
4.43
-60.3746
3.95
-59.9903
4
-60.4007
3.95
-60.1923
3.97
7.0

H₆₆-C₆₄-C₆₇-H₇₀
60.6324
3.91
60.4696
3.94
56.6811
4.47
56.9449
4.42
56.6504
4.47
56.7234
4.46
7.0

3.4. Electronic Properties

3.4.1. Mulliken, ESP, and Natural Charge Distribution

The Mulliken atomic charges of our molecule calculated at all the levels in gas phase and chloroform show positive charge for all the hydrogen atoms. The net charge on all the atoms varies from -1.109653e to 1.980512e, from -1.164916e to 1.904034e, and from -0.891775e to 1.524787e, respectively, in gas phase at the RHF, B3PW91, and B3LYP levels. In a solution of chloroform, the charges varied from -1.064962e to 1.826589e, from -1.206706e to 1.904292e, and from -0.945041e to 1.550492e with some oxygen atoms charges being positive and can be explained by the fact that the oxygen is related to extremely negative carbon atoms. The most positive charge atoms are C₆₃, C₅, C₈ and the most negative charge atoms are C₇₁, C₆₂, C₆₇.

The electrostatic charges were evaluated in this work using the CHelpG scheme of Breneman model. We found from our results that the most positive charges atom is C₄ followed by C₆₂ and C₂ and the most negative charge atom is C₁₂ followed by C₅ and C₇. The observation made at all levels and basis set in gas phase and in a solution of chloroform is that the most positive charge atoms are directly related to the most negative charge atoms.

The natural atomic charges, obtained using the natural bonding orbital method, were also used to evaluate the atomic charge of Rubescin E. Positive and negative charges were found for all hydrogen and oxygen atoms, respectively. In this case, all carbon atoms directly linked to hydrogen atoms were found to have negative charges except for those linked to oxygen atoms. The most negative charge atom was calculated using HF method and was observed for O₆₅ (-0.69456e) and O₆₀ (-0.68330e), respectively, in chloroform and gas phase. The most positive charge atom was found to be C₆₂ in both gas (0.97067e, 0.80601e, and 0.81407e, respectively, at the RHF, B3PW91, and B3LYP levels) and solvent (0.98887e, 0.81804e, and 0.82650e, respectively, at the RHF, B3PW91, and B3LYP levels); this is due to the fact that C₆₂ is related to negative charge atoms (O₆₅, O₆₀, and C₆₃). Mulliken, electrostatic, and natural atomic charge distributions are graphically shown in Figure 2. From Figure 2, one can observe that, for almost all the methods used for charge description, the most positive and negative charge atoms were calculated at the RHF level in both gas and chloroform and this is due to the fact that the effect of electron correlation is not well described in HF method.

Figure 2: Charge distribution on Rubescin E calculated at the RHF, B3PW91, and B3LYP levels in both gas phase and chloroform solution and with the 6-311++G(d,p) basis set.

3.4.2. Global Reactivity Descriptors

In order to understand the relationships between structure, stability, and reactivity of Rubescin E molecule, the global reactivity descriptors parameters such as chemical hardness (H), chemical potential (), chemical softness (s), electronegativity (), and electrophilicity index () were calculated. The finite difference equation given by (1) was used to calculate the ionization potential and electron affinity, which are generally used to calculate the above cited parameters.

The IP and EA calculated from (1) were then used to calculate , , s, , and using equations found in the literature [15–17]. All these parameters calculated using the two methods in gas phase are presented in Table 3. A high value of and characterizes a good electrophile, while a small value stands for good nucleophile.

Table 3: Global reactivity descriptors of Rubescin E at the RHF, B3LYP, and B3PW91 levels in gas phase and in chloroform solution using the 6-311++G(d,p) basis set.

RHF
B3LYP
B3PW91

Gas
Chloroform
Gas
Chloroform
Gas
Chloroform

IP (eV)
7.151
5.662
7.875
6.819
7.861
6.819

EA (eV)
-0.841
0.684
0.461
1.804
0.450
1.825

(eV)
-3.155
-3.173
-4.168
-4.312
-4.156
-4.322

X (eV)
3.155
3.173
4.168
4.312
4.156
4.322

H (eV)
3.996
2.489
3.707
2.508
3.706
2.497

s (eV)⁻¹
0.250
0.402
0.270
0.399
0.270
0.400

(eV)
1.245
2.022
2.343
3.707
2.330
3.740

The calculated vertical IP values in gas phase are bigger than their corresponding values in solvent. From Table 3, we also found that putting the molecule in solvent increases its electron affinity. From the calculated IP and EA values, one can conclude that solvent effect increases the capacity of molecule of gaining an electron compared to donating it. It also reduces the harness of our molecule and increases the softness. Hence, the presence of solvent increases the reactivity of the molecule Rubescin.

3.4.3. Frontier Molecular Orbitals

The frontier molecular orbitals of Rubescin E were evaluated using the ab initio and DFT methods. The 6-311G(d,p) and 6-311++G(d,p) basis sets were used for this purpose in gas phase and in chloroform solution. The results show that the energy gap of our molecule decreases when diffuse functions are added onto all the atoms. We also found that whenever the basis set and methods used, the energy gap is greater than 4, showing that our molecule is hard and can be used as insulator in many electronic devices. In Figure 3, the 3D plots of the HOMO and LUMO orbitals computed at the RHF, B3PW91, and B3LYP levels with the 6-311G(d,p) basis set are illustrated in gas phase. We observed that the HOMO of Rubescin E is located over the furan ring at the three levels and also at the C-C of cyclohexane ring and C-O of oxiran ring. By contrast, the LUMO orbital is located over the cyclohex-2-enone ring, C-C and C-O bond of tetrahydrofuran ring. We can therefore conclude that electron can easily be transferred from furan ring to tetrahydrofuran ring.

Figure 3: Molecular orbital and the HOMO and LUMO energy of Rubescin E in gas phase.

The total density of states (DOS) spectrum of Rubescin E at the gas phase and in chloroform is given in Figure 4 for each level at the 6-311++G(d,p) basis set. These DOSs spectra presented in Figure 4 were obtained from Gauss-Sum 3.0 program [18] which was used in order to show the contributions of different group to molecular orbital (HOMO and LUMO). From Figure 4, we observe that the HOMO-LUMO energy gap is smaller when we move from RHF to B3PW91 and from B3PW91 to B3LYP level, respectively, for both gas and chloroform phases, with larger values obtained in chloroform.

Figure 4: Total density of state (DOS) spectrum of Rubescin E at the RHF, B3PW91, and B3LYP levels in both gas and chloroform phase and with the 6-311++G(d,p) basis set.

3.4.4. UV-Vis Spectra Analysis

Time dependent density functional theory (TD-DFT) was used in gas phase at the two levels B3PW91 and B3LYP with the 6-311++G(d,p) basis set in order to determine the first six excited states to investigate the UV-vis absorption spectra of the molecule. The excitation energy (E), wavelength (λ), and oscillator strength (f) along with their major contributions are given in Table 4 and their results are compared to experiment.

Table 4: Theoretical absorption wavelength (λ), excitation energy (E), and oscillator strengths of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.

Excited states
Exp [1]
B3PW91
B3LYP

λ (nm)
λ (nm)
E (eV)
f
Major contributions
λ (nm)
E (eV)
f
Major contributions

1
365
360.27
3.4415
0.0014
H-1 → L (93%)
358.31
3.4603
0.0014
H-1 → L (93%)

2

312.18
3.9715
0.0000
H → L (99%)
313.69
3.9524
0.0000
H → L (99%)

3
254
275.92
4.4934
0.0043
H-4 → L (24%)
274.77
4.5123
0.0041
H-4 → L (28%)

4

272.66
4.5473
0.0006
H-4 → L (50%)
272.27
4.5538
0.0004
H-4 → L (44%)

5

269.56
4.5994
0.0001
H-4 → L (19%)
268.47
4.6182
0.0001
H-4 → L (20%)

6

261.21
4.7465
0.0000
H → L+1 (100%)
263.16
4.7113
0.0000
H → L+1 (100%)

Two intense electronic transitions were predicted at 4.4934 eV (275.92 nm) and 3.4415 eV (360.27 nm) with oscillator strengths of 0.0043 and 0.0014, respectively, at the B3PW91 level and 4.5123 eV (274.77 nm) and 3.4603 eV (358.31 nm) with oscillator strengths of 0.0041 and 0.0014, respectively, at the B3LYP level. We observed from the spectra that the maximum absorption wavelength corresponds to the electronic transition from HOMO to LUMO+1 with 100% contribution followed by the electronic transition from HOMO to LUMO with 99% contribution at the two levels. The experimental absorption spectra of the title molecule predict two bands at 254 nm and 365 nm. The error between the theoretical and experimental results range from - 4.73 nm to 21.92 nm at the B3PW91 and from - 6.69 nm to 20.77 nm at the B3LYP level. These errors are due to the fact that only one molecule was considered for simulation. The theoretical UV-vis absorption spectra of Rubescin E in gas phase are shown in Figure 5.

Figure 5: Theoretical absorption spectra of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.

3.4.5. Dipole Moment (μDM), Average Polarizability (α), First Static Hyperpolarizability (β), and Anisotropy of Polarization

In this work, the dipole moment , average polarizability α, first static hyperpolarizability β, and anisotropy of polarizability Δα of Rubescin E were evaluated in both gas phase and chloroform solution in order to define the nonlinearity of Rubescin E. The finite-field approach was used for this purpose. Equations (2), (3), (4), and (5) were used to calculate the polarizability, dipole moment, anisotropy of polarizability, and first static hyperpolarizability, respectively, using the components obtained from Gaussian 09 W output. The calculated parameters were presented in Table 5 at the three levels with the 6-311++G(d,p) basis set.

The calculated values of polarizability and first static hyperpolarizability obtained from Gaussian output are in atomic unit. These values were then converted into electrostatic unit (esu) for comparison purpose (for α: 1 a.u = 0.1482 x 10⁻²⁴ esu, for β: 1 a.u = 8.6393 x 10⁻³³ esu) [19–22]. From a giving molecule, when these values ( and β) are greater than those of urea, the molecule is said to have good active NLO properties. We observed from our results that the values of α, β, and are higher in solvent than their corresponding value in gas phase. β and of Rubescin E calculated at the 6-311++G(d,p) basis set using different methods were greater than those of urea. These values calculated using the HF/6-311D(d,p) method ( and esu) were also higher than those of urea ( and esu), obtained using the same method and basis set [21]. Hence Rubescin E can be considered to have good active NLO properties and this is due to the delocalize electron on the furan ring.

Table 5: Electric dipole moment, polarizability, anisotropy of polarization, first-order hyperpolarizability, and molar refractivity of Rubescin E at the RHF, B3LYP, and B3PW91 levels with the 6-311G (d, p) and 6-311++G (d, p) basis sets.

RHF
B3LYP
B3PW91

Gas
Chloroform
Gas
Chloroform
Gas
Chloroform

(D)
5.3966
7.0953
5.2074
6.7654
5.1176
6.6663

352.266
421.425
387.992
470.193
384.258
465.488

17.3299
24.2341
19.6436
29.6995
19.3544
29.0512

336.148
424.889
374.795
479.493
371.091
475.445

1.50612
0.677331
0.715703
-0.411779
0.795242
-0.371934

3.39268
-1.23142
4.44903
0.0306216
4.53244
0.450373

278.550
371.379
305.049
415.461
301.619
411.131

(10⁻²⁴ esu)
47.7036
60.0729
52.6799
67.3473
52.1438
66.7018

Δα (10⁻²⁴ esu)
10.9240
9.8814
12.5387
11.6890
12.4723
11.5857

58.5850
116.324
77.8905
117.687
82.0568
124.840

-34.3404
-40.3762
-33.9536
-66.5203
-29.0441
-60.4155

22.5993
15.4126
-29.6091
-106.843
-36.6541
-122.127

92.3349
129.004
27.6922
-58.5834
26.8972
-63.6805

-16.3605
-23.5326
-55.0267
-81.7313
-58.0975
-89.6785

-8.72859
-0.242861
-11.9414
10.3722
-12.8764
6.24556

-38.9332
-65.6523
-107.633
-207.304
-108.216
-214.866

-14.4537
-58.3711
-7.34826
-70.3072
-7.94692
-69.1599

-50.8004
-109.450
-77.7921
-196.200
-71.2685
-182.588

-6.38532
23.9632
-16.7476
-0.675756
-9.68167
5.78764

β (10⁻³³ esu)
787.4783
866.9154
1747.7167
3772.6270
1678.8815
3743.0498

3.4.6. Optoelectronic Properties

In order to recognize the optoelectronic nature of Rubescin E for different devices applications, some parameters such as electric field (E), electric polarization (P), electric susceptibility (), permittivity (ℰ), refractive index (η), and electric displacement (D) were calculated using equations given in the literature [23–25]. We observed from Table 6 that the results of the calculated parameters are slightly different when we move from one level to another and also when the medium changes. The value of electric field is greater in a solution of chloroform than its corresponding value in gas phase. This is because the polarizability increases in presence of a solvent. The values of electric susceptibility, dielectric constant, and refractive index are greater at B3LYP level compared to their corresponding value at the RHF. All the calculated parameters of optoelectronic properties obtained at the B3LYP level are similar to those obtained at the B3PW91 level. None of these parameters have been determined before either theoretically or experimentally.

Table 6: Calculated values of polarization density (P), average electric field (E), electric susceptibility (), refractive index (), dielectric constant (), magnitude of the displacement (D), and molar refractivity (MR) of Rubescin E molecule obtained at the RHF, B3LYP, and B3PW91 levels with the 6-311++G(d,p) basis set.

Parameters
RHF
B3LYP
B3PW91

Gas
Chloroform
Gas
Chloroform
Gas
Chloroform

E (V.m⁻¹) 10⁹
3.3873
3.5365
2.9597
3.0078
2.9386
2.9924

P (C.m⁻²)10⁻²
8.3339
10.7944
7.5778
8.6086
8.3117
7.9130

2.7787
3.4473
2.8916
3.2324
3.1945
2.9865

10⁻¹¹
3.3458
3.9377
3.4457
3.7475
3.7139
3.5297

η
1.9439
2.1089
1.9727
2.0573
2.0480
1.9966

D (C.m⁻²)10⁻²
0.1133
0.1393
0.1020
0.1127
0.1091
0.1056

MR (esu.mol⁻¹)
120.3345
151.5366
132.8875
169.8866
131.5351
168.2585

One of the central goals of this study is to understand the underlying structure–property relationships which might form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics. The molar refractivity of our molecule, known to be an important parameter in quantitative structure–property relationship analysis was calculated for this purpose. The value of the molar refractivity was calculated at the three levels, in both gas and chloroform using the 6-311++G(d,p) basis set. The Lorenz-Lorentz equation was used for this calculation [26, 27] and its results are listed in Table 6.

The high values of molar refractivity, polarizability, anisotropy of polarizability, and first static hyperpolarizability of Rubescin E molecule show that the molecule has good quantitative structure–property relationship analysis and might therefore form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics.

3.5. NMR Study of Rubescin E

After the optimization of the Rubescin E molecule, the ¹H and ¹³C chemical shifts were calculated at the RHF, B3LYP, and B3PW91 levels of the theory using the 6-311++G(d,p) basis set. In order to compare the calculated values of ¹H and ¹³C chemical shifts with experimental results, we also need to calculate the absolute shielding value of ¹H and ¹³C for the tetramethylsilane (TMS) using the same methods above. The GIAO (Gauge Invariant Atomic Orbitals) approach known to provide satisfactory chemical shifts for different nuclei with larger molecules [28] was used for this purpose and the following equation:

where is the atom type and was used to convert the chemical shielding to chemical shifts.

The experimental and calculated chemical shifts of ¹H along with their corresponding error are listed in Table 7. From our results we observed that all the methods provide results which are very close to experiment since the errors between the experimental and calculated results are smaller.

Table 7: Experimental and calculated ¹H NMR chemical shifts (ppm) of Rubescin E at the RHF, B3LYP, and B3PW91 levels in chloroform solution using the 6-311++G(d,p) basis set.

Nuclei
Calculated (ppm)
Experimental (ppm) [1]
Nuclei
Calculated (ppm)
Experimental (ppm) [1]

RHF
B3LYP
B3PW91
RHF
B3LYP
B3PW91

H10
3,6354
4,4787
4,5162
4,44
H41
3,2764
3,8070
3,7375
3,97

H13
3,7599
4,5046
4,4656
5,5
H43
0,0206
0,1390
0,1217
-

H17
1,1735
1,3264
1,2850
-
H44
0,5304
0,6752
0,6653
0,65

H18
1,4006
1,4842
1,5205
1,34
H45
1,1410
1,2581
1,2916
-

H19
0,8843
0,9632
0,9055
-
H47
2,9441
3,4299
3,3665
3,45

H21
2,2212
3,1228
3,2220
2,9
H49
1,8799
2,0794
2,0578
2,11

H23
0,7480
0,8702
0,8499
-
H50
1,6401
2,0098
2,0019
1,51

H24
0,9682
1,2471
1,2747
1,43
H52
2,1382
2,6231
2,6453
2,52

H25
1,6905
1,7201
1,7225
-
H54
6,4241
6,4756
6,5064
6,23

H27
1,7833
2,0352
1,9975
1,9
H56
7,6008
7,6737
7,6347
7,34

H28
1,7575
2,1239
2,1319
1,9
H58
7,2432
7,2352
7,1892
7,24

H30
3,1956
3,7283
3,7158
3,77
H66
6,5053
6,5963
6,7294
6,73

H31
3,3513
3,5791
3,5410
3,55
H68
1,9939
2,0486
2,0556
-

H33
7,4298
7,4428
7,5055
7,07
H69
1,6905
1,8891
1,9108
1,82

H35
5,9894
6,1274
6,1740
5,95
H70
1,7037
1,8508
1,8560
-

H37
0,3741
0,4953
0,4827
-
H72
1,3371
1,5726
1,5006
-

H38
1,4776
1,8588
1,8632
1,22
H73
1,7489
1,8289
1,8340
1,87

H39
0,7281
1,2414
1,3276
-
H74
2,1737
2,2617
2,2408
-

In order to compare experimental and theoretical results, a linear correlation of ¹H-NMR chemical shifts was established as shown in Figure 6. The regression line was plotted using the following equations: , , and , respectively, at the RHF, B3PW91, and B3LYP levels of the theory. The theoretical results obtained from using the 6-311++G(d,p) basis set show good correlation with experiment since, and the calculated R-square values are found to be close to 1 at each level as shown by Figure 6.

Figure 6: Comparison of experimental and theoretical ¹H chemical shifts of Rubescin E calculated at the RHF, B3PW91, and B3LYP using the 6-311++G(d,p) basis set in chloroform.

The calculated and experimental ¹³C chemical shifts of our molecule are given in Table 8 and their comparison can be found in Figure 7. The linear regression line plotted in Figure 7 shows that theoretical results are in good agreement with experiment. This is confirmed by the linear correlation coefficient calculated here as R-square at the RHF, B3PW91, and B3LYP levels using the 6-311++G(d,p) basis set.

Table 8: Experimental and calculated ¹³C NMR chemical shift (ppm) of Rubescin E at the RHF, B3LYP, and B3PW91 levels in chloroform solution using the 6-311++G(d,p) basis set.

Nuclei
Calculated (ppm)
Experimental (ppm) [1]
Nuclei
Calculated (ppm)
Experimental (ppm) [1]

RHF
B3LYP
B3PW91
RHF
B3LYP
B3PW91

C1
44,217875
56,667075
53,80495
47,5 s
C34
134,341675
139,383575
138,51605
131,3 d

C2
206,549275
213,070575
210,62615
200,3 s
C36
21,545175
24,454275
24,23345
22,7 q

C3
56,393275
73,459075
70,54015
64,6 s
C40
53,124275
65,723775
64,21635
60,3 d

C4
43,854075
56,324675
52,83685
44,9 s
C42
22,468475
24,495375
24,17495
21,5 q

C5
60,103575
77,293875
74,30925
68,3 d
C46
48,923175
61,540375
59,53515
55,2 d

C6
39,115675
49,868075
47,23345
41,3 s
C48
29,511075
34,706875
33,33385
31,1 t

C8
39,020275
51,568975
49,31465
41,3 s
C51
38,272375
48,003275
46,38035
38,8 d

C9
65,951775
79,364675
77,38455
71,4 d
C53
117,347375
119,574075
118,57695
110,8 d

C12
72,763675
87,369975
84,63375
74,7 d
C55
149,815075
151,680375
149,71195
142,9 d

C14
130,650675
133,767875
131,73785
123,1 s
C57
144,528075
147,708875
145,91185
139,2 d

C16
21,641175
23,522875
22,88275
21,1 q
C62
178,475775
182,888075
180,33025
167,4 s

C20
44,504575
54,261975
53,16905
50,6 d
C63
132,986175
138,281375
136,47755
128,8 s

C22
16,680575
18,585575
18,72435
17,5 q
C64
148,221575
150,697975
151,11665
138,3 d

C26
34,988975
41,161875
39,99065
35,4 t
C67
15,275775
17,096475
17,51975
14,6 q

C29
71,816475
83,425975
81,35795
79,5 t
C71
13,518375
15,400475
15,47155
12,6 q

C32
164,415875
166,172275
165,17515
151,6 d

Figure 7: Comparison of experimental and theoretical ¹³C chemical shifts of Rubescin E calculated at the RHF, B3PW91, and B3LYP using the 6-311++G(d,p) basis set.

The following regression line plotted for each level using the general equation , where a and b are given in Figure 7, shows that the calculated ¹³C chemical shifts correlate very well with experiment. The linear correlation coefficient calculated as R-square found in Figure 7 also confirms this.

3.6. Vibrational Frequencies Analysis

The vibrational frequencies of our molecule were computed by using B3LYP/6-311G(d,p) method in both gas phase and chloroform. The experimental IR vibrational frequencies obtained for the two carbonyl moiety present in our structure along with the calculated scaled and unscaled vibrational frequencies, IR, and Raman frequencies with their approximate descriptions are given in Table 9. The rest of the vibrational parameter of Rubescin E molecule which is not described in Table 9 can be obtained from Supplementary Material S2. The scale factor was determined as the mean value of the scale factor that matches correctly for the C=O stretching and the given experimental value. The obtained scale factor was 0.9706. No imaginary frequencies were found showing that structure of the molecule Rubescin E is stable in both gas and solvent. Figure 8 gives the representation of the scaled IR intensity and Raman scattering activity.

Table 9: Some calculated scaled and unscaled vibrational frequencies (cm⁻¹), IR (km.mol⁻¹), and Raman scattering activities (Å⁴.amu⁻¹) of Rubescin E in gas phase and chloroform solution obtained at the B3LYP/6-311G(d,p) level.

Gas phase
Chloroform solution

Vibrational frequencies

Vibrational frequencies

Exp. [1]
Unscaled
Scaled
IR
Raman
Unscaled
Scaled
IR
Raman
Approximate descriptions

3277.8244
3179.489668
0.1483
154.454
3277.3381
3179.017957
0.2265
260.5952
Sym C-H groups on furan ring

3272.9127
3174.725319
1.6469
66.8185
3272.4528
3174.279216
1.0819
83.7804
Asym C-H groups on furan ring

3240.2105
3143.004185
0.9505
45.7116
3240.612
3143.39364
1.6053
100.3155
Asym of (C₅₃-H₅₄; C₅₅-H₅₆)

3189.511
3093.82567
3.5332
66.4094
3189.3244
3093.644668
8.3712
160.0412
C₄₀-H₄₁

3175.4637
3080.199789
11.8025
201.1091
3175.3082
3080.048954
19.8811
372.2174
Sym (C₃₄-H₃₅; C₃₂-H₃₃)

3172.7225
3077.540825
4.8286
43.2929
3170.4225
3075.309825
12.9561
111.1091
Asym of CH₃ (C₃₆)

3164.5342
3069.598174
5.4628
42.0037
3160.4647
3065.650759
13.1398
103.7241
C₆₄-H₆₆

3140.7401
3046.517897
10.7253
48.1146
3141.8739
3047.617683
28.9110
111.4035
Asym of CH₃ (C₃₆. C₂₂)

3096.4047
3003.512559
37.8710
128.8493
3103.9325
3010.814525
53.3513
256.448
Asym of (C₂₉-H₃₀; C₂₉-H₃₁)

3087.0614
2994.449558
18.8484
62.1458
3094.289
3001.46033
37.2141
110.584
Asym of CH₃ (C₇₁); C₁₂-H₁₃

3056.0169
2964.336393
13.0488
74.2148
3062.0737
2970.211489
17.9489
162.7148
Sym of CH₃ (C₂₂)

3055.6408
2963.971576
14.4803
142.8654
3056.849
2965.14353
21.0392
234.8621
Asym of (C₆₇-H₆₉; C₆₇-H₇₀)

3023.1661
2932.471117
14.1323
120.9272
3029.0714
2938.199258
23.4132
269.1079
Sym of CH₃ (C₇₁)

3016.7818
2926.278346
23.9892
318.0136
3018.0608
2927.518976
25.8983
486.6073
Sym of CH₃ (C₆₇)

2999.7383
2909.746151
1.0004
31.9507
2998.9246
2908.956862
3.4528
89.9972
of C₂₀-H₂₁

1720
1779.5912
1726.203464
172.5832
16.0679
1753.6214
1701.012758
326.2675
24.7567
of C₆₂=O₆₅ and of C₆₂-C₆₃=C₆₄-C₆₇

1664
1742.8596
1690.573812
191.5410
32.6047
1719.1678
1667.592766
374.9763
96.2937
of C₂=O₇ and of C₁-C₂-C₃₄-H₃₅

1699.8624
1648.866528
90.7515
127.5998
1692.7491
1641.966627
159.0973
264.4437
C₆₃=C₆₄; H₆₆-C₆₄-C₆₇-H₆₈ and C₆₂-C₆₃-C₇₁-H₇₂

1655.4051
1605.742947
20.9946
48.7257
1648.5716
1599.114452
54.0221
158.0979
C₃₄=C₃₂; of H₃₃-C₃₂-C₈ and of H₃₅-C₃₄-C₂

1627.2588
1578.441036
1.1593
11.251
1625.9499
1577.171403
1.4847
24.0532
Asym of C=C on furan ring

1532.8277
1486.842869
17.3545
52.0428
1530.1712
1484.266064
23.5845
101.1704
Sym of C=C on furan ring

1531.0536
1485.121992
4.3738
6.1013
1522.5028
1476.827716
5.4574
13.4777
of (C₂₉-H₃₀; C₂₉-H₃₁)

1518.4514
1472.897858
13.9129
13.9129
1514.0912
1468.668464
12.9483
27.3727
of CH₃ (C₂₂; C₁₆) and of (C₂₉-H₃₀; C₂₉-H₃₁)

1503.6728
1458.562616
9.8386
5.7612
1498.5877
1453.630069
19.7850
13.2898
of CH₃ (C₁₆; C₂₂; C₃₆)

1499.3956
1454.413732
5.1940
7.4533
1492.6161
1447.837617
9.3270
17.4033
of CH₃ (C₄₂); of (C₂₆-H₂₇; C₂₆-H₂₈) and of (C₄₈-H₄₉; C₄₈-H₅₀)

1488.4029
1443.750813
0.9776
2.8672
1485.682
1441.11154
6.7043
7.8167
of CH₃ (C₁₆; C₂₂; C₃₆) and of C₂₀-H₂₁

1485.5561
1440.989417
2.9100
5.2938
1481.7402
1437.287994
4.3280
14.1082
of (C₄₈-H₄₉; C₄₈-H₅₀) and of CH₃ (C₄₂)

1483.6563
1439.146611
0.4862
7.8554
1478.0624
1433.720528
1.4889
21.2082
of (C₂₆-H₂₇; C₂₆-H₂₈) and of CH₃ (C₄₂)

1479.4465
1435.063105
7.9832
38.0149
1470.3189
1426.209333
12.7942
58.6094
of CH₃ (C₆₇; C₇₁)

1463.5075
1419.602275
2.5457
1.0126
1459.7847
1415.991159
4.0997
2.0734
of H₂₁-C₂₀-C₉-H₁₀ and of CH₃ (C₂₂)

1442.8169
1399.532393
5.3126
6.5726
1441.0254
1397.794638
8.4482
14.8596
of C₃-C₄₀; of C₅-C₄₆; of (C₂₆-H₂₇; C₄₀-H₄₁) and of H₁₀-C₉-C₂₀-H₂₁

1422.4074
1379.735178
42.8712
4.011
1420.5762
1377.958914
63.3216
10.8875
Sym CH₃ umbrella mode

1418.7082
1376.146954
0.6510
1.2396
1416.3711
1373.879967
0.6332
11.5796
Asym CH₃ umbrella mode; (C₃₄-H₃₅;C₃₂-H₃₃); C₅₁-H₅₂

1417.9087
1375.371439
6.7934
3.5193
1414.8341
1372.389077
5.2808
12.6492
of C₁₄-C₅₃; of H₅₂-C₅₁ and sym CH₃ umbrella mode

1411.6946
1369.343762
3.6967
24.766
1405.5801
1363.412697
6.3221
38.7377
asym CH₃ umbrella mode (C₆₇; C₇₁) and of H₆₆-C₆₄

1404.0182
1361.897654
5.7921
1.3462
1402.0625
1360.000625
12.7684
4.8755
of (H₃₅-C₃₄; C₃₂-H₃₃); CH₃ umbrella mode (C₂₂; C₁₆) and of H₂₁-C₂₀-C₉-H₁₀

1399.4114
1357.429058
7.3054
2.6928
1399.317
1357.33749
5.4113
6.6084
of H₁₀-C₉-C₂₀-H₂₁; of (H₃₅-C₃₄; C₃₂-H₃₃) and of H₁₃-C₁₂-O₆₀

1392.7814
1350.997958
4.4872
7.7674
1393.9199
1352.102303
8.7259
13.1186
of H₁₀-C₉-C₂₀-H₂₁; of (H₃₅-C₃₄; C₃₂-H₃₃) and of H₁₃-C₁₂-O₆

1381.3486
1339.908142
0.8619
1.6091
1378.5237
1337.167989
2.7575
3.5116
of (C₂₉-H₃₀; C₂₉-H₃₁); of H₁₀-C₉-C₂₀-H₂₁; of H₁₃-C₁₂-C₉ and CH₃ umbrella mode (C₁₆)

1373.7055
1332.494335
4.3307
9.0916
1371.0783
1329.945951
5.0163
17.666
of C₆₃-C₇₁; CH₃ umbrella mode (C₆₇; C₇₁); of C₆₄-H₆₆ and of H₁₀-C₉-C₂₀-H₂₁

1368.9888
1327.919136
4.4971
10.4931
1367.4102
1326.387894
5.4518
20.2257
of (H₅₆-C₅₅; C₅₃-H₅₄); of C₅₁-H₅₂; of (C₄₈-H₄₉; C₄₈H₅₀) and of (C₂₆-H₂₇; C₂₆H₂₈)

1365.648
1324.67856
4.2088
1.0219
1364.8154
1323.870938
6.4354
2.7506
of H₁₀-C₉-C₁₂-H₁₃; of C₆₄-H₆₆; (H₃₅-C₃₄; C₃₂-H₃₃); of (C₂₉-H₃₀; C₂₉H₃₁) and CH₃ umbrella mode (C₁₆; C₃₆)

1351.6819
1311.131443
2.3942
1.8233
1351.4078
1310.865566
3.8793
2.9367
of (C₂₆-H₂₇; C₂₆-H₂₈); of C₅₁-H₅₂

1343.0612
1302.769364
0.8245
6.8235
1343.2284
1302.931548
0.0396
7.8405
of H₁₀-C₉-C₂₀-H₂₁; of C₁₂-H₁₃; of C₅₁-H₅₂

1326.3406
1286.550382
6.0965
5.2766
1322.4392
1282.766024
7.9781
13.8929
of C₃-C₄₀; of C₄₀-H₄₁

1301.2149
1262.178453
4.1883
6.2643
1301.7097
1262.658409
7.1261
6.9678
of C₅-C₆; of (C₂₆-H₂₇; C₂₆-H₂₈); of (C₄₈-H₄₉; C₄₈-H₅₀); of H₄₇-C₄₆-C₅; of (H₅₆-C₅₅; C₅₃-H₅₄)

1297.0244
1258.113668
1.7948
7.1956
1297.4084
1258.486148
1.3878
21.5171
of C₉-C₁₂; of (C₄₈-H₄₉; C₄₈-H₅₀); of H₄₇-C₄₆-C₄₈; of C₅₁-H₅₂; of (C₂₆-H₂₇; C₂₆-H₂₈)

1288.4675
1249.813475
3.5313
1.5262
1287.909
1249.27173
1.5765
14.1367
of C₄₆-H₄₇; of C₁₂-H₁₃; of H₁₀-C₉-C₂₀-H₂₁ and of (C₂₆-H₂₇; C₂₆-H₂₈)

1278.2074
1239.861178
1.4763
18.6173
1278.0044
1239.664268
2.9774
29.5326
of C₁₄-C₅₁; of C₅₇-H₅₈; of (C₄₈-H₄₉; C₄₈-H₅₀) and of C₅₁-H₅₂

1273.4643
1235.260371
3.1680
10.1375
1271.8325
1233.677525
4.2401
20.9966
of C₄₆-H₄₇; of C₁₂-H₁₃; of C₅₇-H₅₈; of H₁₀-C₉-C₂₀-H₂₁ and of (C₂₆-H₂₇; C₂₆-H₂₈)

1266.8541
1228.848477
3.8717
5.3878
1266.4233
1228.430601
6.8831
16.4996
of H₁₀-C₉-C₂₀-C₈ and of C₃₂-H₃₃

1253.2129
1215.616513
59.1657
19.3282
1253.6896
1216.078912
120.7089
57.0914
of (C₃₂-H₃₃; C₃₄-H₃₅) and of C₂-C₁-C₂₀-C₉

1252.2694
1214.701318
0.7185
4.8164
1251.9233
1214.365601
0.6008
8.7087
of CH on furan ring; of (C₄₈-H₄₉; C₄₈-H₅₀); of (C₂₆-H₂₇; C₂₆-H₂₈) and of H₅₂-C₅₁-C₆-C₄₂

1245.9092
1208.531924
177.9705
5.7457
1246.65
1209.2505
254.8417
9.1404
of C₆₂C₆₃; of H₆₆-C₆₄-C₆₇-H₆₈; of (C₂₉-H₃₀; C₂₉H₃₁)

1237.0891
1199.976427
12.8957
8.0876
1236.5792
1199.481824
11.7625
18.8578
of (C₂₉-H₃₀; C₂₉-H₃₁); of H₂₁-C₂₀-C₈-C₁₆ and of (C₃₂-H₃₃; C₃₄-H₃₅)

1220.0711
1183.468967
14.9312
3.1637
1219.3148
1182.735356
19.5929
7.8591
of (C₂₆-H₂₇; C₂₆-H₂₈) and of (C₄₈-H₄₉; C₄₈-H₅₀); of C₅₁-H₅₂; of C₅₅-H₅₆ and of C₆-C₅-C₄-C₃₆

1201.9071
1165.849887
3.4760
6.7455
1199.1897
1163.214009
8.0422
13.5718
of C₄₀-H₄₁; of C₄₆-H₄₇ and of H₁₃-C₁₂-C₄-C₃

1185.406
1149.84382
15.4074
0.3306
1180.1007
1144.697679
18.7873
1.4104
of (C₄₈-H₄₉; C₄₈-H₅₀); of H₅₂-C₅₁-C₁₄-C₅₇; of (C₅₅-H₅₆; C₅₃-H₅₄)

1179.6911
1144.300367
1.9628
1.119
1178.2209
1142.874273
2.8925
1.7435
of (C₄₈-H₄₉; C₄₈-H₅₀); of H₂₈-C₂₆-C₄₀-H₄₁; of C₅₁-H₅₂ and of C₄₂-C₆-C₅-C₄

1166.7314
1131.729458
14.6259
5.1602
1164.8183
1129.873751
9.3342
9.3366
C₁-C₂₀-C₈-C₃₂   of (C₂₉-H₃₀; C₂₉-H₃₁); C₃-C₄-C₁₂-C₉

1157.5523
1122.825731
15.5290
4.7107
1156.1874
1121.501778
28.1722
11.6347
of (C₃₂-H₃₃; C₃₄-H₃₅); of C₉-H₁₀ and C₁₂-C₄-C₅-C₆

1148.5582
1114.101454
146.5450
3.5872
1149.5402
1115.053994
200.0358
6.6811
of C₆₂-O₆₀ and C₆₃-C₆₄-C₆₇-H₆₈

1144.341
1110.01077
178416
3.5877
1144.4015
1110.069455
27.0332
7.8819
of (C₂₆-H₂₇; C₂₆-H₂₈); C₄-C₅-C₆-C₄; C₁₀-C₉-C₂₀-C₈

1136.9705
1102.861385
1.6907
9.6148
1134.337
1100.30689
2.0658
19.6536
H₂₈-C₂₆-C₄₀-H₄₁; H₃₇-C₃₆-C₄₆-C₄₇; (C₃₂-H₃₃; C₃₄-H₃₅)

1122.8634
1089.177498
21.5468
4.0892
1120.5923
1086.974531
35.6177
10.2656
H₃₃-C₃₂-C₈-C₂₀; C₉-C₁₂-C₄-C₃₆; C₄₁-C₄₀-C₂₆-C₂₈ and C₄₂-C₆-C₅₁-C₄₈

1099.4941
1066.509277
48.0338
2.0757
1096.2182
1063.331654
62.1695
5.261
C₁₂-O₆₀; of C₄₆-H₄₇; of C₅₁-H₅₂; C₉-C₂₀-C₁-C₂₂ and of (C₄₈-H₄₉; C₄₈-H₅₀)

1091.4985
1058.753545
28.1743
1.6861
1085.2223
1052.665631
29.9371
3.0875
C₅₇-O₁₅ and of (C₅₃-H₅₄; C₅₅-H₅₆)

1080.7072
1048.285984
92.4087
0.7097
1080.9064
1048.479208
144.3970
1.9949
C₁₂-O₆₀; sym CH₃; of (C₃₂-H₃₃; C₃₄-H₃₅) and C₂-C₁-C₃-C₄₀

1071.7177
1039.566169
123.1938
6.7128
1073.0176
1040.827072
197.5919
15.9455
C₆₂-O₆₀; of C₄₆-H₄₇ and asym of CH₃ (C₇₁)

1068.3452
1036.294844
9.8016
1.8104
1067.1028
1035.089716
24.1877
5.7115
C₆₇C₆₄C₆₃C₇₁

1050.9373
1019.409181
13.3402
0.7713
1048.853
1017.38741
37.6705
1.8533
of C₄₆-H₄₇; of C₆₄-H₆₆; C₆₇-C₆₄-C₆₃-C₇₁

1045.5983
1014.230351
69.2901
6.619
1044.7341
1013.392077
62.2356
12.9459
of (C₇₁-H₇₃; C₇₁-H₇₄); of C₂₆-H₂₇; of C₅₃-H₅₄; of C₄₈-H₅₀

1027.1407
996.326479
1.7797
5.289
1027.2885
996.469845
30.2585
3.8663
(C₃₄H₃₅; C₃₂H₃₃)

1022.4549
991.781253
0.9472
2.7037
1020.7406
990.118382
6.3182
4.1772
of C₄₈-C₅₁; asym of CH₃; H₆₆-C₆₄-C₆₃-C₆₂ and H₁₃-C₁₂-C₄-C₅

1017.7638
987.230886
30.0425
3.9798
1015.3161
984.856617
43.5319
8.8798
asym of CH₃; of (C₂₉-H₃₀; C₂₉-H₃₁); C₉-C₂₀-C₁-C₃

1011.5509
981.204373
4.8801
6.6943
1009.814
979.51958
6.3114
13.7312
C₅₁-C₁₄-C₅₃-H₅₄; asym of CH₃ (C₄₂); H₅₈-C₅₇-O₁₅-C₅₅

1002.0581
971.996357
12.1626
2.5574
998.7131
968.751707
27.5923
6.2284
of C₄₆-C₄₈; H₄₇-C₄₆-C₄₈-C₄₉; C₁-C₃-C₄₀-C₂₆

994.6222
964.783534
14.7581
1.7537
993.1115
963.318155
22.8186
4.3633
asym of CH₃ groups; C₃-C₄-C₅-C₄₆; C₄₈-C₅₁-C₆-C₂₆

984.7888
955.245136
9.9824
2.1081
982.8653
953.379341
23.0630
4.4849
C₃₂-C₈-C₂₉-H₃₁; asym of CH₃ groups; H₁₃-C₁₂-C₉-H₁₀

935.5082
907.442954
21.5974
1.5821
933.456
905.45232
35.1689
4.3679
of (C₂₆-H₂₇; C₂₆-H₂₈); asym of CH₃; C₄₀-C₃-C₁-C₂₂

894.4122
867.579834
6.7651
6.1001
892.2404
865.473188
16.1490
13.2213
(C₆₇-H₆₉; C₆₇-H₇₀) and C₆₄-H₆₆

888.7652
862.102244
7.1646
2.8098
886.3304
859.740488
9.5352
6.1863
C₆₄-H₆₆; (C₄₈-H₄₉; C₄₈-H₅₀); (C₆₇-H₆₉; C₆₇-H₇₀)

866.5271
840.531287
1.1709
0.6223
870.9888
844.859136
1.8110
2.3985
of (C₅₃-H₅₄; C₅₅-H₅₆)

863.4892
837.584524
11.2475
6.7108
862.9942
837.104374
10.4041
13.1553
H₅₂-C₅₁-C₄₈-H₄₉; (C₂₆-H₂₇; C₂₆-H₂₈); (C₂₂-H₂₃; C₂₂-H₂₄); H₄₅-C₄₂-C₆-H₅

843.0488
817.757336
17.4461
2.5204
843.0694
817.777318
32.2094
5.1332
(C₃₄-H₃₅; C₃₂-H₃₃) and O₇=C₂-C₁-C₂₂

834.8182
809.773654
8.7574
3.1907
831.3156
806.376132
15.1706
6.936
H₄₇-C₄₆-C₅-C₄; C₄₈-C₅₁-C₆-H₄₂

813.7477
789.335269
1.0138
6.0149
810.0882
785.785554
0.7347
13.0197
C₂₆-C₄₀-C₃-C₄

801.2001
777.164097
32.6376
0.9129
802.8851
778.798547
51.1580
3.2321
Sym CH groups on furan ring

772.7524
749.569828
40.1779
4.4199
769.619
746.53043
62.4072
8.3682
of C₇₁-C₆₃-C₆₂-O₆₀; of H₆₆-C₆₄-C₆₇-H₆₉

765.4691
742.505027
7.1326
7.398
765.0018
742.051746
11.7201
14.1992
Sym CH on furan ring and C₄₂-C₆-C₅₁-C₄₈

751.3513
728.810761
2.6045
2.4905
750.9877
728.458069
5.0319
4.4818
C₅-C₄-C₁₂-C₉ and C₃₄-C₃₂-C₈-C₂₉

738.9121
716.744737
11.6448
0.2055
739.1239
716.950183
16.1963
0.0788
Asym CH on furan ring

722.1832
700.517704
12.3489
2.6117
723.4458
701.742426
18.8683
4.4984
C₁-C₂-C₃₄-C₃₂; C₄-C₁₂-O₆₀-C₆₂

686.9578
666.349066
5.4224
1.4738
685.8912
665.314464
10.7183
2.8493
H₅₈-C₅₇-C₁₄-C₅₃ and C₄₈-C₅₁-C₆-C₄₂

668.865
648.79905
12.8788
0.9188
667.6324
647.603428
18.4726
1.8119
C₉-C₁₂-C₄-C₃₆

646.4378
627.044666
11.8100
0.5746
646.7719
627.368743
21.9688
1.442
C₆₇-C₆₄-C₆₃-C₇₁

619.5628
600.975916
14.5359
2.821
617.9459
599.407523
19.3158
4.5248
C₅₃-C₅₅-O₁₅-C₅₇

616.8961
598.389217
4.4856
1.6795
615.6735
597.203295
10.3745
2.8885
C₅₇-C₁₄-C₅₁-C₄₈

590.7602
573.037394
2.2255
8.0984
590.8644
573.138468
4.8686
15.7435
O₆₀-C₆₂-C₆₃-C₇₁; C₂₆-C₆-C₅-C₄₆

545.9651
529.586147
0.9299
3.7502
549.5733
533.086101
3.8923
7.7962
C₆₂-C₆₃-C₆₄-C₆₇; of CH₃ (C₇₁)

538.3894
522.237718
17.1612
0.4714
536.6383
520.539151
25.1977
1.1212
C₄-C₅-C₆-C₅₁

508.9443
493.675971
1.2889
2.069
507.5983
492.370351
1.4410
4.1594
C₃-C₄-C₅-C₄₆; (C₂₆-H₂₇; C₂₆-H₂₈)

475.643
461.37371
1.2962
4.5398
474.4059
460.173723
2.4947
10.7229
C₁₆-C₈-C₂₉

461.5318
447.685846
2.3465
0.597
461.4543
447.610671
4.0236
0.9512
C₄₈-C₄₆-C₅-C₄

451.0159
437.485423
2.9275
4.0628
448.867
435.40099
4.9702
8.8493
C₃₂-H₃₃; C₂₉-C₈-C₃₂-C₃₄

437.1112
423.997864
1.4877
1.6801
437.3603
424.239491
4.9702
2.869
O₆₀-C₆₂-C₆₃-C₆₄ and (C₂₆-H₂₇; C₂₆-H₂₈)

416.2717
403.783549
7.0349
2.9785
413.098
400.70506
9.3286
5.9324
C₆₂-C₆₃-C₆₄-C₆₇

376.4872
365.192584
0.6057
1.5014
375.9518
364.673246
0.8549
2.7432
C₃₆-C₄-C₁₂

359.436
348.65292
1.0513
0.2212
357.6319
346.902943
0.4099
3.4574
C₂₂-C₁-C₃-C₄₀

347.1844
336.768868
0.2931
1.3363
346.0298
335.648906
0.6318
1.8682
Asym of CH₃ groups

309.437
300.15389
1.4908
0.891
306.2399
297.052703
1.5054
1.1169
C₆₇-C₆₄-C₆₃-C₇₁

231.0043
224.074171
3.5498
0.8619
229.9752
223.075944
7.8008
1.6674
O₆₀-C₆₂-C₆₃-C₆₄

42.7727
41.489519
0.3353
1.5162
39.5275
38.341675
0.5007
4.2131
of (C₁₄-C₅₇; C₁₄-C₅₃)

= bending; τ = out of plane deformation; β = in plane deformation; w = weak; m = medium; s = strong; wagg. = wagging; twist. = twisting; rock. = rocking; scis. = scissoring; ν = stretching; sym = symmetrical and asym = anti-symmetrical.

Figure 8: IR spectra (blue) and Raman spectra (red) of Rubescin E in both gas phase (top) and chloroform solution (bottom) using B3LYP/6-311G(d,p).

The C=O double bond gives rise to a very intense absorption band in IR spectrum. The position and intensity of this band range from 1870 cm⁻¹ to 1540 cm⁻¹ depending on the physical state, electronic, and mass effects of neighboring substituents, intra- and intermolecular interactions, and conjugations [29]. The C=O double bond absorption spectra were observed experimentally at 1720 cm⁻¹ and 1664 cm⁻¹ [1]. In this study, the vibrational mode of C=O was found at 1726.20 cm⁻¹ and 1690.57 cm⁻¹ gas phase and at 1701.01 cm⁻¹ and 1667.59 cm⁻¹ in chloroform. There is good agreement between the vibrational modes with experimental values.

4. Conclusion

In this study, the geometry optimization of Rubescin E has been carried out using ab initio HF and density functional theory DFT (B3LYP and B3PW91) methods in both gas phase and chloroform solution with the 6-311++G(d,p) basis set. The optimized parameters were compared to those of some existing groups of compound present in our molecule, since none of this have been done before for the title molecule and good agreement was found. In order to confirm the geometry of our molecule, the proton-proton coupling constant was evaluated and the results compared to experiment were similar. The calculated results have showed that Rubescin E possesses a HOMO-LUMO energy gap greater than 4, which indicate a hard molecule that can be used as an insulator in many electronic devices. We can also conclude from the HOMO-LUMO analysis that the electron can easily be transferred from the furan to tetrahydrofuran ring. The charge analysis performed using Mulliken population, CHepG, and NBO methods showed positive charge for all hydrogen atoms; it was observed that the most positive (respectively, negative) charge atoms were directly linked to the most negative (respectively, positive) charge atoms and also that all the carbon atoms linked to hydrogen were all negatively charged. The calculated first static hyperpolarizability was found to be more than four times greater than the reported value found in the literature for urea leading us to the conclusion that Rubescin E has very good NLO properties. The calculated optoelectronic properties show large values of refractive index, dielectric constant, and electrical susceptibility, leading us to the conclusion that Rubescin E has strong optical and phonon application. Good agreement was found between the calculated and experimental UV spectrum. The theoretical proton (¹H) and carbon (¹³C) chemical shift values (with respect to TMS) were reported and compared with experimental data, showing a very good agreement for both ¹H and ¹³C NMR. The calculated vibrational frequencies done using the B3LYP/6-311G(d,p) functional in both gas and chloroform solutions were all positive leading us to the conclusion that Rubescin E was stable. Approximate descriptions of the vibrational assignments were done in order to take out the different motions of atoms in the title molecule.

Data Availability

Most of data are already provided in the manuscript. The data [Figures 2 and 4] used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

We are thankful to the Council of Scientific and Industrial Research (CSIR), India, for financial support through Emeritus Professor Scheme (Grant No. 21(0582)/03/EMR-II) to Prof. A.N. Singh of the Physics Department, Bahamas Hindu University, India, which enabled him to purchase the Gaussian Software. We are most grateful to Emeritus Prof. A.N. Singh for donating this software to Dr. Geh Wilson Ejuh, University of Dschang, IUT-FV Bandjoun, Cameroon.

Supplementary Materials

The optimized geometry parameters of the Rubescin E molecule such as bonds length, bonds angles, and dihedral angle, obtained at the three levels RHF, B3PW91, and B3LYP using the 6-311++G(d,p) basis set in gas phase and in a solution of chloroform, are listed in Supplementary Material 1. The vibrational frequencies of the title molecules along with the IR intensity and Raman scattering activity of each vibrational mode obtained at the B3LYP/6-311G(d,p) basis set in both gas phase and a chloroform solution are listed in Supplementary Material 2 associated with this manuscript. (Supplementary Materials)

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