Ab initio conformational analysis of flavone and related compounds

Ab initio conformational analysis of flavone andrelated compounds

A. Mantasa, E. Dereteya, F.H. Ferrettib, M. Estradab, I.G. Csizmadiaa,*aDepartment of Chemistry University of Toronto, Toronto, Ont., Canada M5S 3H6

bArea de Quı´mica-Fısica, Facultad de Quı´mica, Bioquı´mica y Farmacia, Universidad Nacional de San Luis,Chacabuco y Pedernera, 5700 San Luis, Argentina

Abstract

Conformational analysis is performed on flavone (2-phenyl-4-H-benzopyran-4-one) and three other related compounds2-phenyl pyranone, beta-phenyl naphthalene and biphenyl using quantum chemical calculations. For each compound, therotation of the phenyl group with respect to the rest of the molecule is studied, and conclusions are drawn concerningthe relationship of flavone and the other three molecules.q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Flavone; 2-Phenyl pyranone; Beta-phenyl naphthalene; Biphenyl; Ab initio conformational analysis; Antioxidant; Free radical

1. Introduction

Flavonoids belong to the family of polyphenoliccompounds, which occur as yellow pigments in plants[1,2]. The possibility of an essential biological role offlavonoids in mammalian physiology was firstsuggested in 1936 by Szent-Gyo¨rgyi [2]. Szent-Gyorgyi found that flavonoids strengthenedcapillary walls in ways Vitamin C could not. Sinceit was thought to enhance permeability of bloodvessels, they were referred to as Vitamin P (P forpermeability) [2]. Nowadays, more than any othertime since the first discovery by Szent-Gyo¨rgyi,flavonoids have been the main focus of manyresearchers.

Flavonoids are glycosides of flavones as illustratedin Scheme 1. Note that –OH and –OCH3 functionalitymay be focused all around the three rings of flavones.This scheme also illustrates that the pyranone ringmay also occur in its hydrogenated or reduced form.Scheme 2 also indicates that, in addition, the reduc-tion [RED] of the pyranone ring may also be oxidized[OX] via hydrogenation at position 3. All of theseclearly indicate that one may anticipate a largenumber of structural variants for these polyphenolicaglycones.

Numerous studies have been underway for theisolation of flavonoid related compounds such asflavones, isoflavones and flavanones (cf. Scheme 3).Various flavones and flavanones have been isolated bybio-activity fractionation from plants such asFeijoasellowiana (the fruit of pineapple guava), andEriodictyon californicum (a sticky shrub whosedried leaves are used medicinally) [3]. Acacetin andkaempferide are two flavones isolated from theseplants and have demonstrated high activity at

Journal of Molecular Structure (Theochem) 504 (2000) 77–103

0166-1280/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0166-1280(00)00357-2

www.elsevier.nl/locate/theochem

* Corresponding author. Tel./fax:11-416-978-3598.E-mail addresses:[email protected]

(A. Mantas), [email protected] (E. Deretey),[email protected] (F.H. Ferretti), [email protected] (M. Estrada),[email protected] (I.G. Csizmadia).

nontoxic doses in inhibiting Benzo[a]pyrene carcino-genesis [4]. Same studies have shown that flavones aremore active inhibitors than their corresponding iso-flavones and flavanones [4]. These findings renderflavones as the best possible chemopreventive agentson tumor formation. In the same context of anti-cancer activity of flavones, warfarin, a flavone relatedcompound has been used as a drug for its antimeta-static effect in lung cancer [5]. In addition, recentstudy has been focusing on the anti-HIV activity of

flavonoid compounds [6]. Flavonoids are also thoughtto help reduce heart disease. Experiments done indogs with stenosed coronary arteries have shownthat Provex Plusw, a commercial mixture of flavo-noids, inhibits platelet activity significantly [7]. Thisinfers that flavonoids may protect against coronaryartery disease, acute occlusive thrombosis and deathfrom myocardial infarction [7].

Many of the beneficial effects of flavonoids are adirect result of their antioxidant properties [1]. The

A. Mantas et al. / Journal of Molecular Structure (Theochem) 504 (2000) 77–10378

Scheme 1.

antioxidant activity of a-tocopherol (Vitamin E),considered as a flavone related compound and presentin plasma and erythrocyte membranes [8], acts againstlipid peroxidation [9], a process which causes agingand various other degenerative diseases [10]. It is notsurprising, therefore, that many cosmetic creams haveVitamin E as an essential ingredient. Structuralaspects of the antioxidant activity of flavonoids havebeen the main interest of many researchers [11–13]. Itis also believed that flavonoids can work directly asanti-aging factors by scavenging free radicals—thebyproducts of normal metabolism.

It seems that flavonoids have beneficial effects invarious aspects of human health, and further study onthese compounds will not end up being futile. Thefocus of this paper is to attempt a conformational

analysis of flavone, the parent molecule of theflavonoid compounds. Having analyzed the parentmolecule further suggestions and conclusions can bedrawn for the reactivity of flavonoids.

2. Computational methods

gaussian 94 is used to perform Hartree–Fock (HF)calculations on the compounds of interest. Due to thesize of the molecules investigated, the HF calculationsemployed two basis sets of modest size STO-3G and3-21G. Potential energy curves are plotted usingAXUM 5.0. The compounds studied are shown inScheme 4.

The compounds of interest were first modeled by

A. Mantas et al. / Journal of Molecular Structure (Theochem) 504 (2000) 77–103 79

Scheme 2.

the semi-empirical AM1 method. After the structureswere determined at HF/STO-3G level of theory, arelaxed scan for every 158 of rotation of the phenylgroup were again carried out. The minima obtained bythe scan for each compound were optimized at HF/STO-3G and HF/3-21G levels of theory. Frequencycalculations performed at the HF/3-21G level ensuredthat the critical points given as minima by the optimi-zations are indeed minima on the potential energysurface.

3. Results and discussion

The phenyl torsional energies computed as a one-dimensional (1D)-scan at the HF/STO-3G levels forflavone [1], 2-phenyl pyranone [2], b-phenyl naphtha-lene [3] and biphenyl [4] are summarized in Tables1–4, respectively. Graphical representations of thephenyl torsional potential for [1], [2], [3] and [4] areshown in Figs. 1–4, respectively. It is interesting tonote that the potentials for the oxygen containingheterocyclic compounds [1] and [2] are almost iden-tical. The torsional potentials for the hydrocarbons [3]and [4] are again almost identical but the relative

barrier heights and, therefore, the shape of the poten-tial energy curves (PEC) are completely differentfrom those of [1] and [2].

An educated guess [14] suggested that the barrier at0 and 1808 would be higher as steric destabilizationmight exceed conjugative stabilization. By the sameargument, the 90 and 2708 conformers would be lowersince steric hindrance, which assumed to be dominantis reduced but conjugative stabilization completelydisappeared. Our computed PECs have shown directlythe opposite to be true.

The four minima occurring at the torsional angles

�0 1 a�; �1802 a�; �1801 a�; �3602 a�

are identical because the phenyl group has no sub-stituent at either theortho (o) or meta(m) positions.For this reason, it was satisfactory to optimize onlyone of the four equivalent minima. This was carriedout at two levels of theory: HF/STO-3G and HF/3-21G using the standard thresholds of optimization.Tight optimizations have also been carried out atHF/3-21G level of theory. The optimized geometriesare summarized in Tables 5–8 for compounds [1–4],respectively. The angle (a ) values which measure


Scheme 3.

deviation from coplanarity are summarized in Table 9for the compounds involved. The graphical represen-tation of the non-planarity of the four compounds isshown in Fig. 5.

In order to determine barriers to rotation, twoconformations need to be considered. For all fourcompounds, planar structure corresponds to thelower barrier and the perpendicular structure corre-sponds to the higher barrier. Due to the symmetryof these molecules, the transition state (TS)structures can be determined by constrainedoptimization. The total and relative energies of

the transition state structures are summarized inTable 10.

Excluding the C–H, C4–C5, C3–C4, C2–C11,C2–C3 and C4–O18 bonds, the rest of the bondlengths in flavone [1] range from 1.37 to 1.39 A˚ .This may suggest that we are dealing with ap electrondelocalized system, therefore, with a highly conju-gated molecule, and hence its small deviation fromcoplanarity, i.e. 8.848 as shown in Table 9. It seemsthat the oxygen (O1) contributes to the delocalizationof the p electrons in the system allowing thecompound to behave aromatically. However, judging


Scheme 4.

from the C4–C5 and C3–C4 bond lengths of 1.47 and1.46 A, respectively, the pyrane ring must be slightlyconjugated compared to the rest of the molecule.Furthermore, the C2–C11 bond length of 1.48 A˚ iscloser to that of a single bond than of a delocalizedone, which suggests that conjugation across thephenyl ring and the rest of the molecule is not ashigh as expected. Another important thing to notice,concerning the flavone molecule, is that C2–C3 andC4–O18 bond lengths of 1.33 and 1.22 A˚ , respec-tively, are smaller compared to the other bonds-excluding the C–H bonds. This would suggest thatthe p electrons tend to be mostly localized in thevicinity of the C2–C3 and C4–O18 bonds. From theabove observations, one may conclude that eventhough the flavone molecule may be highly

conjugated,p electron delocalization is not distribu-ted evenly.

In general, the results show that flavone and 2-phenyl pyranone behave almost the same. The devia-tion from coplanarity angle (a), as shown in Table 9,is 8.84 and 5.098 for flavone [1] and 2-phenyl pyra-none [2], respectively. However, forb-phenylnaphthalene [3] and biphenyl [4], the angle of thephenyl ring with respect to the rest of the moleculeis 51.06 and 50.868, respectively. The calculatedvalues of the torsional angles obtained by both opti-mizations, tight and regular at HF/3-21G, are compar-able, whereas, the torsional angle values as computedby HF/STO-3G are considerably different than theones computed at the larger basis set (cf. Table 9).

Looking at Table 10, the energy barrier of phenyl


Table 1Energies and relative energies as functions of theD(C12–C11–C2–O1) torsional angle in flavone [1]

Torsional angle (8) Energy (hartree) DE (kcal/mol)

0 2 714.5489182 0.1415 2 714.5490954 0.0320.82 2 714.5491401 0.0030 2 714.5489733 0.1045 2 714.5478525 0.8160 2 714.5459744 1.9975 2 714.5442425 3.0790 2 714.5435639 3.50105 2 714.5442686 3.06120 2 714.5459878 1.98135 2 714.5478514 0.81150 2 714.5489719 0.11159.18 2 714.5491401 0.00165 2 714.5490954 0.03180 2 714.5489182 0.14195 2 714.5490954 0.03200.82 2 714.5491401 0.00210 2 714.5489719 0.11225 2 714.5478514 0.81240 2 714.5459878 1.98255 2 714.5442686 3.06270 2 714.5435639 3.50285 2 714.5442425 3.07300 2 714.5459744 1.99315 2 714.5478523 0.81330 2 714.5489733 0.10339.18 2 714.5491401 0.00345 2 714.5490954 0.03360 2 714.5489180 0.14

Table 2Energies and relative energies as functions of theD(C9–C8–C2–O1) torsional angle in 2-phenyl pyranone [2]


0 2 563.7347153 0.1115 2 563.7348621 0.0219.55 2 563.7348886 0.0030 2 563.7346886 0.1345 2 563.7335362 0.8560 2 563.7316537 2.0375 2 563.7299313 3.1190 2 563.7292571 3.53105 2 563.7299541 3.10120 2 563.7316632 2.02135 2 563.7335323 0.85150 2 563.7346862 0.13160.45 2 563.7348886 0.00165 2 563.7348624 0.02180 2 563.7347152 0.11195 2 563.7348624 0.02199.55 2 563.7348886 0.00210 2 563.7346861 0.13225 2 563.7335324 0.85240 2 563.7316632 2.02255 2 563.7299542 3.10270 2 563.7292573 3.53285 2 563.7299313 3.11300 2 563.7316537 2.03315 2 563.7335361 0.85330 2 563.7346887 0.13340.45 2 563.7348886 0.00345 2 563.7348622 0.02360 2 563.7347153 0.11

rotation as computed at HF/3-21G level of theory forflavone [1] and 2-phenyl pyranone [2], is basicallyzero, which suggests that more likely there is noobservable transition state at zero degrees torsionalangle. The energy barrier for phenyl rotationcomputed at the HF/STO-3G corresponds to a low-transition state at 08 and a high-transition state at 908.However, the energy barrier for phenyl rotationcomputed at the HF/3-21G corresponds to a high-transition state at 908 and a low-transition state at08, i.e. the low-transition state became a high oneusing a larger basis set. The numerical resultssummarized in Tables 9 and 10 are presentedgraphically in Fig. 6.

The vibrational frequencies for the minima of thefour molecules, as shown in Table 11, are all positive

which suggests that the critical points obtained by thetight optimizations are actual minima on the potentialenergy surface.

Information about the reactivity of the four mole-cules is given by the Mulliken charges, which areshown in Scheme 5. Flavone [1] and 2-phenyl pyra-none [2] have three atoms with positive charge, and allthree of them are part of the pyran ring. The positivecharged atoms for flavone and 2-phenyl pyranone areC2, C4, and C6. This would suggest that a nucleophi-lic or a free radical would more likely attack at thesethree sites of either flavone or 2-phenyl pyranone. Onthe other hand,b-phenyl naphthalene [3] and biphenyl[4] have no atoms with positive charge, which meansthat these two molecules are not candidates fornucleophilic or radical attack.


Table 3Energies and relative energies as functions of theD(C12–C11–C2–C1) torsional angle inb-phenyl naphthalene [3]


0 2 605.4407188 2.1015 2 605.4420654 1.2530 2 605.4437623 0.1938.60 2 605.4440623 0.0045 2 605.4439041 0.1060 2 605.4425800 0.9375 2 605.4409262 1.9790 2 605.4401848 2.43105 2 605.4409182 1.97120 2 605.4426043 0.91135 2 605.4439194 0.09141.40 2 605.4440623 0.00150 2 605.4437447 0.20165 2 605.4420408 1.27180 2 605.4407188 2.10195 2 605.4420408 1.27210 2 605.4437446 0.20218.60 2 605.4440623 0.00225 2 605.4439192 0.09240 2 605.4426044 0.91255 2 605.4409182 1.97270 2 605.4401848 2.43285 2 605.4409263 1.97300 2 605.4425800 0.93315 2 605.4439038 0.10321.40 2 605.4440623 0.00330 2 605.4437623 0.19345 2 605.4420656 1.25360 2 605.4407189 2.10

Table 4Energies and relative energies as functions of theD(C8–C7–C1–C2) torsional angle in biphenyl [4]


0 2 454.6451766 2.0815 2 454.6464924 1.2530 2 454.6481793 0.1938.71 2 454.6484852 0.0045 2 454.6483318 0.1060 2 454.6470116 0.9275 2 454.6453602 1.9690 2 454.6446322 2.42105 2 454.6453649 1.96120 2 454.6470259 0.92135 2 454.6483344 0.09141.29 2 454.6484852 0.00150 2 454.6481838 0.19165 2 454.6465001 1.25180 2 454.6451767 2.08195 2 454.6465003 1.25210 2 454.6481840 0.19218.71 2 454.6484852 0.00225 2 454.6483346 0.09240 2 454.6470260 0.92255 2 454.6453651 1.96270 2 454.6446323 2.42285 2 454.6453603 1.96300 2 454.6470116 0.92315 2 454.6483318 0.10321.29 2 454.6484852 0.00330 2 454.6481792 0.19345 2 454.6464925 1.25360 2 454.6451767 2.08


Fig. 1. Phenyl rotational potential,D(C12–C11–C2–O1) of flavone [1] computed at the HF/STO-3G level of theory.

Fig. 2. Phenyl rotational potential,D(C9–C8–C2–O1) of 2-phenyl pyranone [2] computed at the HF/STO-3G level of theory.


Fig. 3. Phenyl rotational potential,D(C12–C11–C2–C1) ofb-phenyl naphthalene [3] computed at the HF/STO-3G level of theory.

Fig. 4. Phenyl rotational potential,D(C8–C7–C1–C2) of biphenyl [4] computed at the HF/STO-3G level of theory.


Table 5Optimized geometrical parameters of flavone [1] as computed at the HF/STO-3G and HF/3-21G levels of theory

Minimum Transition state

Regular optimization Tightoptimization

Regular optimization

HF/3-21G

HF/STO-3G HF/3-21G HF/3-21G At 908 At 1808

Bond length(A)C2–O1 1.3917 1.3713 1.3714 1.3723 1.3713C3–C2 1.3293 1.3311 1.3311 1.3248 1.3312C4–C3 1.4940 1.4583 1.4584 1.4621 1.4582C5–C4 1.5067 1.4740 1.4740 1.4751 1.4738C6–O1 1.3943 1.3756 1.3756 1.3764 1.3755C6–C5 1.3912 1.3778 1.3778 1.3791 1.3776C7–C6 1.4015 1.3848 1.3848 1.3855 1.3849C8–C7 1.3765 1.3758 1.3758 1.3752 1.3758C9–C8 1.3968 1.3944 1.3944 1.3950 1.3945C10–C5 1.3974 1.3898 1.3898 1.3907 1.3898C10–C9 1.3769 1.3740 1.3740 1.3733 1.3739C11–C2 1.5078 1.4757 1.4758 1.4832 1.4762C12–C11 1.3940 1.3911 1.3911 1.3857 1.3913C13–C12 1.3848 1.3803 1.3803 1.3834 1.3801C14–C13 1.3870 1.3852 1.3852 1.3841 1.3853C15–C14 1.3869 1.3827 1.3827 1.3841 1.3824C16–C11 1.3945 1.3892 1.3892 1.3858 1.3893C16–C15 1.3847 1.3823 1.3823 1.3833 1.3824H17–C3 1.0781 1.0660 1.0660 1.0677 1.0658O18–C4 1.2271 1.2205 1.2205 1.2197 1.2206H19–C10 1.0839 1.0706 1.0706 1.0706 1.0706H20–C9 1.0817 1.0708 1.0708 1.0708 1.0708H21–C8 1.0834 1.0715 1.0715 1.0716 1.0715H22–C7 1.0816 1.0692 1.0692 1.0692 1.0692H23–C12 1.0816 1.0702 1.0702 1.0717 1.0700H24–C13 1.0825 1.0714 1.0714 1.0715 1.0714H25–C14 1.0828 1.0717 1.0717 1.0717 1.0717H26–C15 1.0825 1.0715 1.0715 1.0715 1.0715H27–C16 1.0821 1.0678 1.0678 1.0716 1.0676

Bond angle(8)C3–C2–O1 124.3346 120.9778 120.9699 122.2557 120.8943C4–C3–C2 122.3499 122.5628 122.5665 122.1014 122.6024C5–C4–C3 112.8546 114.2717 114.2724 113.9856 114.2883C6–O1–C2 117.0099 121.3208 121.3253 120.2928 121.3786C6–C5–C4 119.5691 120.2807 120.2792 120.5537 120.2554C5–C6–O1 123.8792 120.5838 120.5841 120.8097 120.5833C7–C6–O1 115.6879 118.0325 118.0332 117.8737 118.0332C7–C6–C5 120.4330 121.3839 121.3827 121.3155 121.3856C8–C7–C6 119.5997 118.7817 118.7824 118.8485 118.7766C9–C8–C7 120.4947 120.7278 120.7279 120.7263 120.7307C10–C5–C4 121.5316 120.5578 120.5586 120.3249 120.5790C10–C5–C6 118.8993 119.1616 119.1622 119.0892 119.1354C10–C9–C8 119.6495 119.6110 119.6106 119.6072 119.6112C9–C10–C5 120.9240 120.3342 120.3343 120.4113 120.3608C11–C2–O1 110.6644 112.0667 112.0656 112.9895 112.0466C11–C2–C3 124.9958 126.9535 126.9624 124.7549 127.0592C12–C11–C2 121.4989 121.4465 121.4511 119.9958 121.5214C13–C12–C11 120.4115 120.3145 120.3174 119.9367 120.3450C14–C13–C12 120.2279 120.2044 120.2051 120.0567 120.2178


Table 5 (continued)




HF/3-21G


C15–C14–C13 119.7721 119.7489 119.7473 120.0064 119.7253C16–C11–C2 119.5470 119.3551 119.3562 119.9960 119.3411C16–C11–C12 118.9541 119.1985 119.1927 120.0064 119.1373C16–C15–C14 120.1070 120.2120 120.2126 120.0544 120.2193C15–C16–C11 120.5264 120.3197 120.3227 119.9390 120.3546H17–C3–C2 120.2427 120.7548 120.7589 119.7565 120.8384H17–C3–C4 117.4053 116.6796 116.6717 118.1422 116.5594O18–C4–C3 123.8753 123.4675 123.4662 123.6682 123.4420O18–C4–C5 123.2700 122.2607 122.2611 122.3188 122.2417H19–C10–C5 118.1331 117.8606 117.8598 117.8078 117.8243H19–C10–C9 120.9429 121.8055 121.8059 121.7800 121.8148H20–C9–C8 119.9554 119.9672 119.9666 119.9586 119.9603H20–C9–C10 120.3951 120.4219 120.4228 120.4358 120.4305H21–C8–C7 119.6794 119.4411 119.4420 119.4632 119.4443H21–C8–C9 119.8261 119.8312 119.8302 119.8105 119.8251H22–C7–C6 118.9459 119.0967 119.0956 118.9089 119.1050H22–C7–C8 121.4544 122.1217 122.1219 122.2427 122.1186H23–C12–C11 120.1150 120.4323 120.4336 119.7424 120.5031C13–C12–H23 119.4702 119.2500 119.2456 120.3208 119.1520C12–C13–H24 119.7078 119.6633 119.6640 119.8071 119.6503C14–C13–H24 120.0644 120.1320 120.1305 120.1363 120.1320C13–C14–H25 120.0906 120.0517 120.0518 119.9978 120.0601C15–C14–H25 120.1372 120.1993 120.2006 119.9959 120.2148C14–C15–H26 120.0827 120.1531 120.1528 120.1354 120.1578C16–C15–H26 119.8106 119.6351 119.6345 119.8102 119.6228C11–C16–H27 119.2595 119.2880 119.2870 119.7440 119.2783C15–C16–H27 120.2142 120.3926 120.3902 120.3167 120.3666

Dihedral angle(8)C4–C3–C2–O1 20.6307 20.6396 20.6457 0.0105 20.0008C5–C4–C3–C2 0.5500 0.3852 0.3856 20.0184 0.0001C6–C5–C4–C3 20.1497 20.0056 20.0030 0.0157 0.0002C7–C6–C5–C4 179.9237 179.9310 179.9309 179.9950 180C8–C7–C6–C5 20.0234 20.0155 20.0150 0.0013 0C9–C8–C7–C6 0.0045 20.0037 20.0039 20.0012 0C10–C9–C8–C7 0.0035 0.0124 0.0124 0.0001 0C11–C2–O1–C6 179.4513 180.0042 180.0088 180.0198 180.0011C12–C11–C2–O1 159.1805 171.1603 171.1620 90.0000 179.9999C13–C12–C11–C2 179.6384 179.4601 179.4593 2179.7486 2180.0002C14–C13–C12–C11 0.0393 0.1007 0.1010 0.1240 0.0005C15–C14–C13–C12 0.1895 0.1889 0.1885 0.0037 20.0007C16–C15–C14–C13 20.1110 20.1132 20.1128 20.0036 0.0005H17–C3–C2–O1 178.8112 178.7213 178.7151 2180.0038 179.9996O18–C4–C3–C2 2179.6011 2179.7757 2179.7734 2179.9726 179.9983H19–C10–C9–C8 179.9931 2179.9911 180.0088 180.0019 2179.9999H20–C9–C8–C7 179.9979 180.0013 180.0014 180.0005 2180H21–C8–C7–C6 179.9962 179.9795 179.9792 2180.0013 2180H22–C7–C6–C5 179.9461 179.9134 179.9137 179.9995 180H23–C12–C11–C2 21.0345 21.2146 21.2148 0.4531 20.0001H24–C13–C12–C11 179.8226 179.8551 179.8541 2179.7993 2179.9998H25–C14–C13–C12 179.9963 2180.0108 179.9885 2179.9188 179.9995H26–C15–C14–C13 179.9079 179.8485 179.8488 2179.9205 2179.9996


Table 5 (continued)




HF/3-21G


H27–C16–C15–C14 179.9064 179.8087 179.8110 2179.9124 179.9999C6–O1–C2–C3 0.2476 0.5001 0.5092 0 0C11–C2–C3–C4 2179.7212 179.9357 179.9347 179.9901 180C11–C2–C3–H17 20.2793 20.7035 20.7045 20.0245 0H17–C3–C4–C5 2178.9069 2179.0003 2178.9997 180 180H17–C3–C4–O18 0.9420 0.8389 0.8412 0.0416 0O18–C4–C5–C6 179.9997 2179.8472 2179.8461 179.9707 180C3–C4–C5–C10 179.7375 179.8985 179.9016 2179.9892 180O18–C4–C5–C10 20.1127 0.0570 0.0585 20.0341 0C2–O1–C6–C5 0.1768 20.1163 20.1223 0 0C2–O1–C6–C7 2179.9386 179.8367 179.8306 180 180C4–C5–C6–O1 20.1969 20.1177 20.1177 0 0C10–C5–C6–O1 179.9131 179.9769 179.9763 180 180C10–C5–C6–C7 0.0337 0.0255 0.0250 0 0O1–C6–C7–C8 2179.9123 2179.9681 180.0325 180 180O1–C6–C7–H22 0.0572 20.0390 20.0388 0 0H22–C7–C8–C9 179.9642 2179.9306 2179.9303 180 180H22–C7–C8–H21 0.0275 0.0528 0.0528 0 0H21–C8–C9–C10 179.9881 2179.9710 180.0294 180 180H21–C8–C9–H20 0.0063 0.0181 0.0183 0 0C4–C5–C10–C9 2179.9135 2179.9218 2179.9218 180 180C6–C5–C10–C9 20.0257 20.0165 20.0161 0 0C4–C5–C10–H19 0.0868 0.0678 0.0675 0 0C6–C5–C10–H19 179.9746 179.9731 179.9732 180 180C8–C9–C10–C5 0.0072 0 20.0022 0 0H20–C9–C10–C5 179.9871 2179.9911 180.0089 180 180H20–C9–C10–H19 0.0125 0.0201 0.0199 0 0C3–C2–C11–C12 221.6222 29.3717 29.3750 289.9812 0O1–C2–C11–C16 220.8399 28.9187 28.9176 289.4969 0C3–C2–C11–C16 158.3575 170.5494 170.5453 90.5222 180C16–C11–C12–C13 20.3414 20.4609 20.4611 20.2518 0C16–C11–C12–H23 178.9857 178.8645 178.8647 179.9500 180H23–C12–C13–C14 2179.2922 2179.2327 2179.2328 179.9213 0H23–C12–C13–H24 0.4912 0.5218 0.5202 0 0H24–C13–C14–C15 2179.5930 2179.5645 2179.5634 179.9269 180H24–C13–C14–H25 0.2138 0.2359 0.2366 0 0H25–C14–C15–C16 2179.9177 2179.9133 2179.9126 179.9190 180H25–C14–C15–H26 0.1012 0.0485 2179.9126 0 0C2–C11–C16–C15 2179.5598 2179.3863 2179.3853 179.7488 180C12–C11–C16–C15 0.4203 0.5366 0.5368 0.2519 0C2–C11–C16–H27 0.3379 0.5533 0.5515 20.4619 0C12–C11–C16–H27 2179.6819 2179.5241 2179.5264 2179.9588 180C14–C15–C16–C11 20.1968 20.2526 20.2529 20.1242 0H26–C15–C16–C11 179.9064 179.7857 179.7854 179.7931 180H26–C15–C16–H27 20.1125 20.1531 20.1507 0 0C7–C6–O1–C2 2179.9387 178.2416 179.8306 180 180

Etotal (hartree) 2714.5491401 2719.5533998 2719.5533998 2719.5453950 2719.5533929


Table 6Optimized geometrical parameters of 2-phenyl pyranone [2] as computed at the HF/STO-3G and 3-21G levels of theory




HF/3-21G


Bond length(A)O1–C2 1.3940 1.3735 1.3735 1.3755 1.3735C3–C2 1.3300 1.3303 1.3303 1.3241 1.3303C4–C3 1.4968 1.4635 1.4635 1.4672 1.4635C5–C4 1.4989 1.4685 1.4685 1.4686 1.4684C6–C5 1.3203 1.3194 1.3194 1.3210 1.3194O7–C4 1.2272 1.2196 1.2196 1.2190 1.2196C8–C2 1.5068 1.4752 1.4752 1.4821 1.4753C9–C8 1.3941 1.3911 1.3911 1.3859 1.3911C10–C9 1.3847 1.3803 1.3803 1.3833 1.3802C11–C10 1.3870 1.3852 1.3852 1.3841 1.3852C12–C11 1.3869 1.3825 1.3825 1.3841 1.3824C13–C12 1.3847 1.3824 1.3824 1.3833 1.3824C14–C9 1.0186 1.0701 1.0701 1.0717 1.0701H15–C10 1.0825 1.0714 1.0714 1.0715 1.0714H16–C11 1.0828 1.0717 1.0717 1.0717 1.0717H17–C12 1.0825 1.0715 1.0715 1.0715 1.0715H18–C13 1.0821 1.0679 1.0679 1.0717 1.0679H19–C6 1.0887 1.0665 1.0665 1.0667 1.0665H20–C5 1.0800 1.0678 1.0678 1.0680 1.0678H21–C3 1.0785 1.0661 1.0661 1.0679 1.0660C6–O1 1.3847 1.3709 1.3708 1.3704 1.3708C13–C8 1.3945 1.3892 1.3892 1.3859 1.3892

Bond angle(8)C3–C2–O1 123.5147 120.2745 120.2744 121.4835 120.2499C4–C3–C2 122.1895 122.5621 122.5622 122.1330 122.5755C5–C4–C3 111.8695 113.5545 113.5547 113.2423 113.5604C6–C5–C4 120.5028 120.7160 120.7159 121.0466 120.7041O7–C4–C3 123.9530 123.1875 123.1884 123.3918 123.1778C8–C2–O1 110.9817 112.3080 112.3086 113.3097 112.2958C9–C8–C2 121.4630 121.4594 121.4604 120.0241 121.4851C10–C9–C8 120.4076 120.3423 120.3427 119.9723 120.3509C11–C10–C9 120.2326 120.2218 120.2221 120.0501 120.2270C12–C11–C10 119.7672 119.7145 119.7150 120.0045 119.7073C13–C12–C11 120.1125 120.2247 120.2248 120.0477 120.2271H14–C9–C8 120.1294 120.4676 120.4687 119.7289 120.4920H15–C10–C9 119.7010 119.6490 119.6485 119.8118 119.6416H16–C11–C10 120.0924 120.0649 120.0652 119.9989 120.0699H17–C12–C11 120.0874 120.1565 120.1563 120.1368 120.1567H18–C13–C12 120.1758 120.3105 120.3104 120.2956 120.3034H19–C6–C5 123.4029 126.0186 126.0199 125.7735 126.0208H20–C5–C4 119.1304 118.6819 118.6812 118.5143 118.6913H21–C3–C2 120.2143 120.7167 120.7168 119.6697 120.7476C6–O1–C2 115.9783 120.2564 120.2584 119.2500 120.2710C5–C6–O1 125.9429 122.6356 122.6354 122.8449 122.6392O7–C4–C5 124.1774 123.2579 123.2569 123.3661 123.2618


Table 6 (continued)




HF/3-21G


C8–C2–C3 125.4988 127.4167 127.4159 125.2069 127.4544C13–C8–C2 119.5803 119.3944 119.3943 120.0239 119.3867C13–C8–C9 118.9567 119.1462 119.1451 119.9504 119.1284C12–C13–C8 120.5223 120.3488 120.3490 119.9748 120.3596H14–C9–C10 119.4599 119.1890 119.1876 120.2985 119.1572H15–C10–C11 120.0661 120.1290 120.1294 120.1381 120.1315H16–C11–C12 120.1402 120.2197 120.2198 119.9966 120.2229H17–C12–C13 119.8002 119.6188 119.6188 119.8156 119.6163H18–C13–C8 119.3019 119.3407 119.3402 119.7293 119.3373H19–C6–O1 110.6541 111.3458 111.3328 111.3818 111.3402H20–C5–C6 120.3667 120.6021 120.6177 120.4393 120.6046H21–C3–C4 117.5943 116.7203 116.7203 118.1974 116.6771

Dihedral angle(8)C4–C3–C2–O1 20.5891 20.3829 20.3799 0.0028 20.0002C5–C4–C3–C2 0.4757 0.2526 0.2503 20.0055 0.0007C6–C5–C4–C3 20.1119 20.0065 20.0059 0.0059 20.0006O7–C4–C3–C2 2179.6509 2179.8535 2179.8546 2179.9938 180.0009C8–C2–O1–C6 179.5288 179.9638 179.9637 180.0172 179.9996C9–C8–C2–O1 160.4477 174.8721 174.9145 90 180C10–C9–C8–C2 179.6296 179.6876 179.6911 2179.7481 179.9999C11–C10–C9–C8 0.0505 0.0732 0.0727 0.1218 0.0001C12–C11–C10–C9 0.1716 0.1049 0.1044 20.0032 0C13–C12–C11–C10 20.1174 20.0727 20.0723 0.0041 0H14–C9–C8–C2 21.0093 20.7073 0.7006 0.4907 20.0001H15–C10–C9–C8 179.8410 179.9226 179.9232 2179.7930 2180H16–C11–C10–C9 179.9881 179.9870 179.9867 2179.9167 180H17–C12–C11–C10 179.9125 179.9077 179.9079 180.0953 2180H18–C13–C12–C11 179.9387 179.8979 179.8988 2179.8734 2180H19–C6–C5–C4 179.9551 179.9381 179.9388 179.9985 180.0001H20–C5–C4–C3 179.7812 179.9234 179.9245 180.0052 2180.0005H21–C3–C2–O1 178.8923 179.2690 179.2741 179.9944 2179.9999C6–O1–C2–C3 0.2857 0.2599 0.2583 0 0C8–C2–C3–C4 2179.7211 2180.0380 179.9634 179.9837 180H21–C3–C2–C8 20.2396 20.3861 20.3827 20.0248 0H21–C3–C4–C5 2179.0186 2179.4123 2179.4169 180 180H21–C3–C4–O7 0.8547 0.4816 0.4783 0.0144 0O7–C4–C5–C6 180.0150 180.0997 2179.9011 179.9943 180O7–C4–C5–H20 20.0918 0.0296 0.0296 20.0065 0C2–O1–C6–C5 0.1039 20.0127 20.0128 0 0C2–O1–C6–H19 179.9961 179.9488 179.9488 180 180C4–C5–C6–O1 20.1657 20.1062 20.1055 0 0H20–C5–C6–O1 179.9424 179.9653 179.9655 180 180H20–C5–C6–H19 0.0633 0.0096 0.0097 0 0C3–C2–C8–C9 220.3275 25.4498 25.4059 289.9822 0O1–C2–C8–C13 219.6012 25.1600 25.1156 289.5069 0C3–C2–C8–C13 159.6237 174.5180 174.5642 90.5111 180C13–C8–C9–C10 20.3219 20.2803 20.2789 20.2409 0


Table 6 (continued)




HF/3-21G


C13–C8–C9–H14 179.0393 179.3248 179.3295 180 180H14–C9–C10–C11 2179.3149 2179.5369 2179.5407 179.8817 180H14–C9–C10–H15 0.4756 0.3125 0.3099 20.0332 0H15–C10–C11–C12 2179.6181 2179.7438 2179.7454 179.9114 180H15–C10–C11–H16 0.1984 0.1383 0.1370 0 0H16–C11–C12–C13 180.0661 2179.9546 2179.9545 179.9177 180H16–C11–C12–H17 0.0960 0.0257 0.0258 0.0088 0C2–C8–C13–C12 2179.5760 2179.6560 2179.6597 179.7491 180C9–C8–C13–C12 0.3763 0.3125 0.3110 0.2418 0C2–C8–C13–H18 0.3271 0.3085 0.3047 20.4997 0C9–C8–C13–H18 2179.7206 2179.7229 2179.7248 179.9933 180H17–C12–C13–C8 179.8111 179.8817 179.8825 179.7858 180H17–C12–C13–H18 20.0911 20.0825 20.0816 0.0356 0H18–C13–C8–C2 0.3271 0.3085 0.3047 20.4997 0H16–C11–C12–H17 0.0960 0.0257 0.0258 0.0088 0H20–C5–C4–O7 20.0918 0.0296 0.0296 20.0065 0

Etotal (hartree) 2563.7348886 2567.7332640 2567.7332642 2567.7253492 2567.7332634

Table 7Optimized geometrical parameters ofb-phenyl naphthalene [3] as computed at the HF/STO-3G and HF/3-21G levels of theory




HF/3-21G


Bond length(A)C2–C1 1.3609 1.3616 1.3616 1.3588 1.3658C3–C2 1.4340 1.4209 1.4209 1.4191 1.4261C4–C3 1.3516 1.3556 1.3556 1.6561 1.3544C6–C5 1.3534 1.3572 1.3572 1.3569 1.3574C7–C6 1.4256 1.4144 1.4144 1.4145 1.4146C8–C7 1.3531 1.3570 1.3570 1.3570 1.3569C9–C1 1.4293 1.4173 1.4173 1.4185 1.4158C9–C8 1.4321 1.4189 1.4189 1.4188 1.4196C10–C4 1.4308 1.4180 1.4180 1.4182 1.4158C10–C5 1.4307 1.4178 1.4178 1.4183 1.4170C10–C9 1.4041 1.4077 1.4078 1.4075 1.4051C11–C2 1.5072 1.4893 1.4893 1.4948 1.5009C12–C11 1.3948 1.3904 1.3904 1.3876 1.3937C13–C12 1.3851 1.3829 1.3829 1.3841 1.3831


Table 7 (continued)




HF/3-21G


C14–C13 1.3863 1.3843 1.3844 1.3841 1.3812C15–C14 1.3864 1.3837 1.3837 1.3841 1.3832C16–C11 1.3950 1.3896 1.3896 1.3876 1.3955C16–C15 1.3849 1.3839 1.3836 1.3841 1.3808H17–C1 1.0820 1.0728 1.0728 1.0729 1.0695H18–C3 1.0819 1.0717 1.0717 1.0718 1.0679H19–C4 1.0828 1.0729 1.0729 1.0729 1.0729H20–C5 1.0827 1.0729 1.0729 1.0729 1.0729H21–C6 1.0826 1.0718 1.0718 1.0719 1.0718H22–C7 1.0826 1.0719 1.0719 1.0719 1.0718H23–C8 1.0827 1.0728 1.0728 1.0729 1.0729H24–C12 1.0819 1.0721 1.0721 1.0720 1.0682H25–C16 1.0819 1.0719 1.0719 1.0721 1.0687H26–C13 1.0827 1.0721 1.0721 1.0721 1.0721H27–C15 1.0827 1.0721 1.0721 1.0721 1.0721H28–C14 1.0824 1.0718 1.0718 1.0720 1.0716

Bond angle(8)C3–C2–C1 118.6004 119.1199 119.1204 119.5294 117.3883C4–C3–C2 121.1135 120.8228 120.8230 120.6429 121.6631C5–C6–C7 120.2840 120.2584 120.2586 120.2723 120.2476C6–C7–C8 120.3320 120.3329 120.3332 120.3238 120.3547C2–C1–C9 121.6455 121.3342 121.3336 121.1199 122.2918C7–C8–C9 120.7266 120.7065 120.7057 120.6958 120.6595C1–C9–C8 121.9580 121.9232 121.9224 121.7479 121.7197C3–C4–C10 120.9406 120.9145 120.9142 121.1782 121.2037C6–C5–C10 120.6838 120.6784 120.6777 120.6723 120.5635C4–C10–C5 122.3692 122.2441 122.2438 122.1446 122.6525C1–C9–C10 119.1622 119.1629 119.1633 119.1080 119.4178C8–C9–C10 118.8796 118.9130 118.9135 118.9495 118.8628C4–C10–C9 118.5369 118.6456 118.6454 118.7690 118.0354C5–C10–C9 119.0939 119.1103 119.1107 119.0865 119.3123C11–C2–C1 121.4329 121.1513 121.1502 121.0859 121.9069C3–C2–C11 119.9665 119.7287 119.7293 119.3847 120.7049C12–C11–C2 120.8208 120.4693 120.4681 120.3524 121.4952C11–C12–C13 120.8447 120.5319 120.5317 120.3401 121.4277C12–C13–C14 120.2055 120.2022 120.2024 120.1282 120.4938C13–C14–C15 119.5602 119.6394 119.6391 119.7595 118.9800C2–C11–C16 120.8390 120.6399 120.6407 120.3436 121.3399C16–C11–C12 118.3395 118.8907 118.8911 119.3033 117.1653C14–C15–C16 120.2191 120.2057 120.2058 120.1351 120.4725C11–C16–C15 120.8304 120.5297 120.5297 120.3343 121.4614C2–C1–H17 120.3498 119.9888 119.9900 120.0045 121.0033C9–C1–H17 118.0003 118.6676 118.6669 118.8575 116.7049C2–C3–H18 118.8063 118.7891 118.7869 118.7074 119.9916C4–C3–H18 120.0742 120.3810 120.3800 120.6497 118.3365C3–C4–H19 120.5002 120.3402 120.3402 120.4441 119.9986C10–C4–H19 118.5588 118.7434 118.7437 118.7251 118.7979


Table 7 (continued)




HF/3-21G


C6–C5–H20 120.7644 120.5967 120.5967 120.6340 120.6525C10–C5–H20 118.5518 118.7250 118.7256 118.6940 118.7843C5–C6–H21 120.6006 120.3419 120.3414 120.3438 120.3602C7–C6–H21 119.1154 118.7249 119.4000 119.3840 119.3923C6–C7–H22 119.0960 119.3751 119.3754 119.3655 119.3629C8–C7–H22 120.5720 120.2920 120.2913 120.3107 120.2826C7–C8–H23 120.7418 120.5793 120.5792 120.6033 120.5484C9–C8–H23 118.5316 118.7142 118.7151 118.7010 118.7923C11–C12–H24 119.6241 119.4801 119.4803 119.3964 120.6641C13–C12–H24 119.5268 119.9786 119.9787 120.2635 117.9083C11–C16–H25 119.7075 119.3844 119.3862 119.4021 120.4874C15–C16–H25 119.4572 120.0759 120.0741 120.2639 118.0516C12–C13–H26 119.7548 119.7574 119.7577 119.8134 119.3723C14–C13–H26 120.0394 120.0392 120.0387 120.0584 120.1340C14–C15–H27 120.0302 120.0491 120.0503 120.0557 120.1009C16–C15–H27 119.7506 119.7434 119.7421 119.8093 119.4267C13–C14–H28 120.2231 120.1713 120.1706 120.1199 120.5290C15–C14–H28 120.2166 120.1892 120.1902 120.1207 120.4911

Dihedral angle(8)C3–C2–C1–C9 20.1364 20.0784 20.0770 0.0175 –0.0032C3–C2–C1–H17 2179.3604 178.7899 178.7908 180.0150 179.9995C11–C2–C1–C9 179.7486 2180.0038 179.9960 179.9995 179.9962C11–C2–C1–H17 0.5247 21.1354 21.1362 0 0C4–C3–C2–C1 20.0920 0.0499 0.0493 20.0153 20.0100C4–C3–C2–C11 179.9789 179.9764 179.9773 180 179.9907H18–C3–C2–C1 2179.2040 178.9001 178.8974 179.9953 2180.0019H18–C3–C2–C11 0.9092 21.1734 21.1745 0.0130 0C10–C4–C3–C2 0.2680 20.0471 20.0477 0 0.0167C10–C4–C3–H18 179.3688 2178.8790 2178.8775 179.9933 2179.9914H19–C4–C3–C2 2179.5371 179.4413 179.4414 180.0103 180.0085H19–C4–C3–H18 20.4363 0.6095 0.6116 0 0C7–C6–C5–C10 0.0010 20.0224 20.0219 0 0C7–C6–C5–H20 179.9702 179.9470 179.9466 180 2179.9917H21–C6–C5–C10 179.9795 180.0203 180.0212 180 180H21–C6–C5–H20 0.0083 20.0103 20.0103 0 0C8–C7–C6–C5 20.0295 0.0543 0.0540 20.0005 20.0005C8–C7–C6–H21 179.9917 180.0119 180.0113 180 180H22–C7–C6–C5 179.9784 180.0708 2179.9307 2180.0016 179.9989H22–C7–C6–H21 20.0004 0.0285 0.0266 0 0C9–C8–C7–C6 20.0254 0.0740 0.0742 0 0C9–C8–C7–H22 179.9666 180.0573 2179.9412 180 180H23–C8–C7–C6 179.9945 180.0512 180.0492 2180.0006 2179.9996H23–C8–C7–H22 20.0026 0.0346 0.0338 0 0C8–C9–C1–C2 2179.7145 179.7753 179.7753 179.9908 2179.9900C8–C9–C1–H17 20.4730 0.8924 0.8929 20.0068 0.0076C10–C9–C1–C2 0.1853 0.1039 0.1030 20.0086 0.0095C10–C9–C1–H17 179.4269 2178.7790 2178.7794 179.9940 2179.9932


Table 7 (continued)




HF/3-21G


C1–C9–C8–C7 179.9925 180.0977 2179.9036 180 180C1–C9–C8–H23 20.0227 0.1200 0.1209 0 0C10–C9–C8–C7 0.1074 20.2302 20.2306 0 0C10–C9–C8–H23 2179.9228 179.7922 179.7940 180 180C5–C10–C4–C3 179.8131 2179.9660 180.0332 180 179.9823C5–C10–C4–H19 20.3781 0.5375 0.5361 0 20.0097C9–C10–C4–C3 20.2131 0.0716 0.0726 0 0.0726C9–C10–C4–H19 179.5958 2179.4249 2179.4245 180 180C4–C10–C5–C6 179.9447 179.9024 179.9035 180 180C4–C10–C5–H20 0.0271 20.0676 20.0656 0 0C9–C10–C5–C6 0.0815 20.1354 0.1360 0 0C9–C10–C5–H20 179.9466 179.8946 179.8948 180 179.9899C4–C10–C9–C1 20.0110 20.0975 20.0978 0 0C4–C10–C9–C8 179.8919 2179.7789 2179.7800 180 180C5–C10–C9–C1 179.9637 179.9389 179.9404 180 180C5–C10–C9–C8 20.1333 0.2576 0.2581 0 0C12–C11–C2–C1 38.5967 128.9274 128.9388 90 179.9999C12–C11–C2–C3 2141.5198 250.9975 250.9877 290.0181 0C16–C11–C2–C1 2141.0875 250.9677 250.9507 290.3672 0C16–C11–C2–C3 38.7960 129.1074 129.1228 89.6150 180C13–C12–C11–C2 2179.7570 2179.7207 2179.7188 179.7063 179.9990C13–C12–C11–C16 20.0651 0.1762 0.1726 0.0726 0C24–C12–C11–C2 1.0105 20.8342 20.8320 20.3735 20.0007H24–C12–C11–C16 2179.2976 179.0627 179.0594 179.9899 180C14–C13–C12–C11 0.1840 20.0573 20.0574 20.0457 0.0005C14–C13–C12–H24 179.4173 2178.9383 2178.9387 2179.9623 180H26–C13–C12–C11 2179.6473 179.5392 179.5421 179.9179 179.9999H26–C13–C12–H24 20.4141 0.6583 0.6608 0 0.0005C15–C14–C13–C12 20.0912 20.0324 20.0300 0.0183 0.0012C15–C14–C13–H26 179.7396 2179.6278 2179.6284 2179.9453 180H28–C14–C13–C12 179.9367 2179.9534 180.0468 2180.0052 2179.9998H28–C14–C13–H26 20.2324 0.4512 0.4484 0.0313 0C16–C15–C14–C13 20.1184 0.0005 20.0004 20.0186 20.0018C16–C15–C14–H28 179.8536 2180.0785 179.9228 180 180H27–C15–C14–C13 179.7473 2179.5114 2179.5141 2180.0600 2180.0010H27–C15–C14–H28 20.2807 0.4095 0.4091 20.0365 0C15–C16–C11–C2 179.5460 179.6885 179.6881 2179.7096 180C15–C16–C11–C12 20.1459 20.2082 20.2031 20.0729 0H25–C16–C11–C2 0.3604 21.4581 21.4620 0.3757 0H25–C16–C11–C12 2179.3315 178.6452 178.6468 2179.9876 180C11–C16–C15–C14 0.2391 0.1216 0.1187 0.0463 0C11–C16–C15–H27 2179.6270 179.6350 179.6339 2179.9124 180H25–C16–C15–C14 179.4267 2178.7239 2178.7233 2180.0397 180.0010H25–C16–C15–H27 20.4394 0.7895 0.7918 0 0

Etotal (hartree) 2605.4440623 2609.4851177 2609.4851177 2609.4837481 2609.4788252


Table 8Optimized geometrical parameters of biphenyl [4] as computed at the HF/STO-3G and HF/3-21G levels of theory




HF/3-21G


Bond length(A)C2–C1 1.3948 1.3899 1.3899 1.3876 1.3944C3–C2 1.3850 1.3833 1.3833 1.3842 1.3820C4–C3 1.3863 1.3840 1.3840 1.3841 1.3821C5–C4 1.3863 1.3840 1.3840 1.3841 1.3821C6–C1 1.3948 1.3899 1.3899 1.3876 1.3944C6–C5 1.3850 1.3833 1.3833 1.3842 1.3820C7–C1 1.5075 1.4897 1.4897 1.4952 1.5020C8–C7 1.3948 1.3899 1.3899 1.3876 1.3944C9–C8 1.3850 1.3833 1.3833 1.3842 1.3820C10–C9 1.3863 1.3840 1.3840 1.3841 1.3821C11–C10 1.3863 1.3840 1.3840 1.3841 1.3821C12–C7 1.3948 1.3899 1.3899 1.3876 1.3944C12–C11 1.3850 1.3833 1.3833 1.3842 1.3820C13–C2 1.0819 1.0720 1.0720 1.0720 1.0685H14–C3 1.0827 1.0721 1.0721 1.0721 1.0721H15–C4 1.0824 1.0719 1.0719 1.0720 1.0716H16–C5 1.0827 1.0721 1.0721 1.0721 1.0721H17–C6 1.0819 1.0720 1.0720 1.0720 1.0685H18–C8 1.0819 1.0720 1.0720 1.0720 1.0685H19–C9 1.0827 1.0721 1.0721 1.0721 1.0721H20–C10 1.0824 1.0719 1.0719 1.0720 1.0716H21–C11 1.0827 1.0721 1.0721 1.0721 1.0721H22–C12 1.0719 1.0720 1.0720 1.0720 1.0685

Bond angle(8)C1–C2–C3 120.8359 120.5455 120.5458 120.3618 121.4406C2–C3–C4 120.2103 120.2043 120.2046 120.1353 120.2103C3–C4–C5 119.5614 119.6307 119.6301 119.7417 118.9831C2–C1–C6 118.3459 118.8696 118.8691 119.2638 117.1791C4–C5–C6 120.2104 120.2042 120.2046 120.1366 120.4776C1–C6–C5 120.8359 120.5455 120.5458 120.3609 121.4413C2–C1–C7 120.8272 120.5659 120.5654 120.3696 121.4097C6–C1–C7 120.8270 120.5645 120.5655 120.3668 121.4114C1–C7–C8 120.8272 120.5658 120.5654 120.3698 121.4102C7–C8–C9 120.8358 120.5455 120.5458 120.3618 121.4406C8–C9–C10 120.2103 120.2043 120.2046 120.1353 120.4784C9–C10–C11 119.5614 119.6308 119.6301 119.7417 118.9831C1–C7–C12 120.8271 120.5645 120.5655 120.3666 121.4109C8–C7–C12 118.3459 118.8696 118.8691 119.2638 117.1792C10–C11–C12 120.2104 120.2042 120.2046 120.1366 120.4776C7–C12–C11 120.8359 120.5456 120.5458 120.3609 121.4413C1–C2–H13 119.6631 119.4203 119.4232 119.3883 120.5495C3–C2–H13 119.4966 120.0249 120.0216 120.2500 118.0100C2–C3–H14 119.7553 119.7505 119.7519 119.8140 119.4074


Table 8 (continued)




HF/3-21G


C4–C3–H14 120.0343 120.0438 120.0421 120.0508 120.1143C3–C4–H15 120.2191 120.1842 120.1849 120.1292 120.5085C5–C4–H15 120.2196 120.1850 120.1850 120.1291 120.5085C4–C5–H16 120.0344 120.0443 120.0421 120.0498 120.1143C6–C5–H16 119.7551 119.7501 119.7519 119.8137 119.4082C1–C6–H17 119.6634 119.4203 119.4232 119.3886 120.5491C5–C6–H17 119.4964 120.0248 120.0216 120.2507 118.0097C7–C8–H18 119.6631 119.4203 119.4232 118.3883 120.5497C9–C8–H18 119.4966 120.0250 120.0216 120.2500 118.0098C8–C9–H19 119.7554 119.7505 119.7519 119.8141 119.4074C10–C9–H19 120.0343 120.0438 120.0421 120.0508 120.1144C9–C10–H20 120.2191 120.1842 120.1849 120.1292 120.5086C11–C10–H20 120.2196 120.1850 120.1850 120.1292 120.5084C10–C11–H21 120.0344 120.0443 120.0421 120.0498 120.1142C12–C11–H21 119.7551 119.7501 119.7519 119.8137 119.4083C7–C12–H22 119.6634 119.4203 119.4232 119.3886 120.5489C11–C12–H22 119.4964 120.0248 120.0216 120.2508 118.0099

Dihedral angle(8)C3–C2–C1–C6 20.0984 0.0258 0.0192 0 0C3–C2–C1–C7 179.9026 180.0165 180.0193 179.9993 180H13–C2–C1–C6 180.6808 2178.8690 2178.8723 2179.9999 2180.0001H13–C2–C1–C7 0.6816 1.1217 1.1277 0 0C4–C3–C2–C1 0.1972 20.0380 20.0386 0.0001 20.0001C4–C3–C2–H13 179.4195 178.8501 178.8463 180 180H14–C3–C2–C1 180.3546 2179.6014 2179.6016 2179.9999 180H14–C3–C2–H13 20.4233 20.7132 20.7167 0 0C5–C4–C3–C2 20.0970 0.0142 0.0192 20.0002 0.0001C5–C4–C3–H14 179.7453 179.5762 179.5810 180 180H15–C4–C3–C2 2180.0976 180.0189 180.0192 179.9999 2179.9999H15–C4–C3–H14 20.2555 20.4191 20.4191 0 0C6–C5–C4–C3 20.0991 0.0214 0.0192 0.0001 20.0001C6–C5–C4–H15 179.9017 180.0167 180.0192 180 180H16–C5–C4–C3 179.7433 179.5818 179.5810 180.0001 179.9999H16–C5–C4–H15 20.2561 20.4229 20.4190 0 0C5–C6–C1–C2 20.0990 0.0099 0.0193 0 0C5–C6–C1–C7 179.9003 2179.9808 180.0193 180 180H17–C6–C1–C2 2179.3203 2178.8767 2178.8723 180 180H17–C6–C1–C7 0.6790 1.1326 1.1277 0 0C1–C6–C5–C4 0.1986 20.0336 20.0386 0 0C1–C6–C5–C16 2179.6444 2179.5953 2179.6017 180 180H17–C6–C5–C4 179.4210 178.8463 178.8463 2180 2180H17–C6–C5–H16 20.4218 20.7154 20.7167 0 0C8–C7–C1–C2 38.7051 50.8649 50.8540 90.0001 180C8–C7–C1–C6 2141.2942 2129.1446 2129.1460 290.0009 0C12–C7–C1–C2 2141.2939 2129.1446 2129.1460 290.0008 0


Table 8 (continued)




HF/3-21G


C12–C7–C1–C6 38.7071 50.8459 50.8541 89.9984 180C9–C8–C7–C1 179.9029 180.0165 180.0193 2180.0003 180C9–C8–C7–C12 20.0982 0.0258 0.0192 0 0H18–C8–C7–C1 0.6819 1.1217 1.1277 20.0005 20.0001H18–C8–C7–C12 2179.3194 2178.8690 2178.8723 180 180C10–C9–C8–C7 0.1970 20.0380 20.0386 20.0005 0C10–C9–C8–H18 179.4194 178.8501 178.8463 180 180H19–C9–C8–C7 2179.6456 2179.6014 2179.6016 2180.0003 2180H19–C9–C8–H18 20.4233 20.7132 20.7167 0 0C11–C10–C9–C8 20.0968 0.0142 0.0192 0.0003 0C11–C10–C9–H19 179.7455 179.5762 179.5810 180 180H20–C10–C9–C8 2180.0975 180.0189 180.0192 2179.9997 180H20–C10–C9–H19 20.2553 20.4190 20.4191 0 0C12–C11–C10–C9 20.0992 0.0214 0.0192 20.0003 0C12–C11–C10–H20 179.9016 180.0167 180.0192 180 180H21–C11–C10–C9 2180.2568 179.5818 179.5810 179.9997 180H21–C11–C10–H20 20.2561 20.4229 20.4190 0 0C11–C12–C7–C1 179.9000 2179.9808 180.0193 180 180C11–C12–C7–C8 20.0990 0.0099 0.0193 0 0H22–C12–C7–C1 0.6787 1.1326 1.1277 0 0H22–C12–C7–C8 2179.3204 2178.8767 2178.8723 180 180C7–C12–C11–C10 0.1986 20.0336 20.0386 0 0C7–C12–C11–C21 2179.6444 2179.5953 2179.6017 180 180H22–C12–C11–C10 179.4210 178.8463 178.8463 2180.0016 180H22–C12–C11–H21 20.4218 20.7154 20.7167 0 0

Etotal (hartree) 2454.6484852 2457.6886723 2457.6886723 2457.6872832 2457.6824505

Table 9Deviation from coplanarity angle (a) values computed for compounds [1], [2], [3] and [4] at various levels of theory

Compound Torsional anglea a (8)a

Regular optimization Tight optimization

HF/STO-3G HF/3-21G HF/3-21G

[1] C12–C11–C2–O1 20.82 8.84 8.84[2] C9–C8–C2–O1 19.55 5.13 5.09[3] C1–C2–C11–C12 38.60 51.07 51.06[4] C8–C7–C1–C2 38.71 50.86 50.85

a Four equivalent torsional angles govern minimum energy conformations: (01 a), (1802 a ), (1801 a ) and (3602 a).


Fig. 5. HF/3-21G optimized molecular structures and corresponding dihedral angles of compounds [1–4].

4. Conclusions

Hydrocarbons (biphenyl andb-phenyl naphthalene)are noticeably different from oxygen containing hetero-cyclic analogs, such as 2-phenyl pyranone and flavone,as far as phenyl rotation is concerned. By looking at the

Mulliken charges, it was concluded that the oxygencontaining compounds are expected to have differentreactivity than the hydrocarbons. While there arenoticeable differences, the topology at the potentialenergy curves (number of minima and the transitionstructures) are the same for all four compounds.


Table 10Low and high energy barriers of phenyl rotation computed at various levels of theory for compounds [1]–[4]

Molecules E (hartree) DE (kcal/mol)a

Minimum energy conformation Transition state (TS) Transition state (TS)

Low (08) High (908) Low (08) High (908)

HF/STO-3G (Normal optimization)[1] 2714.5491401 2714.5489182 2714.5435639 0.14 3.50[2] 2563.7348886 2563.7347153 2563.7292571 0.11 3.53[3] 2605.4440623 2605.4407188 2605.4401848 2.10 2.43[4] 2454.6484852 2454.6451766 2454.6446322 2.08 2.42

HF/3-21G (Normal optimization)[1] 2719.5533998 2719.5533929 2719.5453950 0.004 5.02[2] 2567.7332640 2567.7332634 2567.7253492 0.000 4.97[3] 2609.4851177 2609.4788252 2609.4837481 3.95 0.86[4] 2457.6886723 2457.6824505 2457.6872832 3.90 0.87

a DE �kcal=mol� � 627:51 {E�TS� 2 E�min�} :

Fig. 6. Torsional angles and relative energies of the low and high transition states (TS) in comparison with the minimum energy structure of [1–4].


Table 11Vibrational frequencies (cm21) of flavone [1], 2-phenyl pyranone [2], b-phenyl naphthalene [3] and biphenyl [4] computed at the HF/3-21Glevel of theory after tight optimization

Compound [1] [2] [3] [4]Number of modes (3N-6) 75 57 78 60

1 15.1859 9.6532 49.3362 59.99902 64.6436 99.2635 66.9096 103.47033 122.5688 158.0096 92.9850 125.93214 146.0023 186.6297 190.6626 309.56525 181.5123 255.0715 208.7334 333.35426 235.3390 333.0002 279.6060 389.65657 288.7392 413.9175 300.5178 466.72808 320.0361 462.2647 380.9728 473.70979 328.6724 471.2751 443.9030 576.0596

10 383.9759 526.8492 469.5156 617.946011 465.7323 546.9243 473.6695 703.228612 503.0353 559.1656 549.6476 705.736913 536.2407 708.8787 576.6352 717.377214 550.5216 712.3369 587.2024 809.179315 566.4534 757.1750 618.1270 811.741116 621.6428 798.3511 633.8696 824.248417 651.3184 799.3164 707.4116 868.382718 673.0474 831.9694 715.0980 902.274419 711.5692 908.6044 754.1612 991.577020 759.5250 919.7677 778.5132 993.664921 767.7801 972.1401 810.1029 1079.274122 789.3827 990.2620 838.6650 1080.229423 804.2939 997.7038 864.2011 1096.206324 816.1083 1075.8732 886.6670 1107.407425 901.2987 1102.0987 897.9383 1139.675726 911.6202 1109.4695 946.3612 1141.286427 942.4865 1133.5932 960.5045 1157.382428 947.0597 1138.4770 992.7870 1159.117529 987.9681 1141.3483 1011.0681 1160.013730 989.8662 1164.9351 1057.8310 1180.882231 1044.4967 1178.5469 1075.3700 1187.252632 1090.8169 1196.2609 1079.6828 1190.917133 1093.1470 1199.8258 1092.3767 1193.771734 1108.8666 1254.0326 1100.4278 1236.153435 1115.8216 1335.9093 1137.0680 1248.562336 1138.9276 1343.0797 1141.2619 1328.279137 1142.3388 1354.0332 1142.1309 1330.550038 1163.6984 1374.0340 1158.3205 1344.105339 1165.1803 1398.3892 1163.3030 1350.904040 1196.1397 1482.4784 1181.1969 1395.193141 1199.5898 1513.2723 1187.7385 1488.201442 1205.6393 1548.8708 1191.6325 1509.583643 1213.0438 1621.7255 1210.2690 1605.272644 1244.5396 1672.9626 1241.7694 1628.144145 1252.1631 1748.2417 1267.3485 1661.4349


Table 11 (continued)

Compound [1] [2] [3] [4]Number of modes (3N-6) 75 57 78 60

46 1263.7095 1775.6216 1305.2959 1675.736947 1337.9993 1788.8780 1325.3228 1738.690948 1341.9642 1832.1812 1329.6386 1751.344849 1353.6004 1910.7667 1346.7301 1771.026750 1358.8910 3358.2845 1356.4009 1776.423251 1378.7367 3369.7809 1408.8232 3348.865352 1401.7239 3382.5300 1415.6657 3349.518853 1455.3391 3394.9088 1468.4646 3355.035954 1490.4252 3418.9379 1480.0948 3357.034155 1515.3134 3425.5105 1500.0828 3365.778456 1621.3861 3445.0135 1523.6823 3368.419757 1633.6121 3447.4624 1595.7899 3373.192258 1648.4815 1620.1153 3374.987259 1672.4167 1638.1448 3384.818460 1746.0518 1657.9674 3385.971561 1748.5145 1670.373962 1775.6386 1740.399163 1786.5670 1747.387964 1812.2130 1773.125465 1900.8133 1786.376566 3358.2462 1810.474567 3366.7858 3345.365068 3369.8991 3348.196169 3382.4930 3349.401570 3383.1146 3351.391271 3394.8919 3355.526572 3400.3887 3357.342073 3407.5768 3366.771474 3427.1672 3367.188975 3445.7519 3374.159976 3376.256977 3382.431378 3385.6430

Acknowledgements

The authors would like to thank the NCI for the useof services of the Frederick Biomedical Supercomput-ing Center. The continuous financial support of theNatural Science and Engineering Research Council(NSERC) of Canada is gratefully acknowledged.

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Documents

Ab initio conformational analysis of flavone and related compounds