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The Outcome of the Oxidations of Unusual Enediamide Motifs Is Governed by the Stabilities of the Intermediate Iminium Ions

  • Muneer Ahamed,

    Affiliation School of Chemistry, The University of Sydney, Sydney, New South Wales, Australia

  • Bun Chan,

    Affiliations School of Chemistry, The University of Sydney, Sydney, New South Wales, Australia, ARC Centre of Excellence for Free Radical Chemistry and Biotechnology, Victoria, Australia

  • Paul Jensen,

    Affiliation School of Chemistry, The University of Sydney, Sydney, New South Wales, Australia

  • Matthew H. Todd

    Affiliation School of Chemistry, The University of Sydney, Sydney, New South Wales, Australia

The Outcome of the Oxidations of Unusual Enediamide Motifs Is Governed by the Stabilities of the Intermediate Iminium Ions

  • Muneer Ahamed, 
  • Bun Chan, 
  • Paul Jensen, 
  • Matthew H. Todd


We compare the results from the oxidation of two unusual “enediamide” motifs (3,4-dihydropyrazin-2(1H)-ones), where a double bond is flanked by two amides. In one case the oxidation led to a ring-opened product arising from the cleavage of the double bond, and in the other a rare cis-dioxygenated compound was obtained. Both products have been characterized by X-ray crystallography. The outcomes of the key reactions are rationalized based on calculated free energies of intermediates.


During the course of previous work on the synthesis of peptidomimetic scaffolds (2, Figure 1) we synthesized an unusual enamide-based heterocycle consisting of a double bond linking two amides (1a). [1] One of the striking features of the chemistry was the degree of stereocontrol of ring closure (to give 2) by the aromatic ring attached to the exocyclic amide, caused by the pseudoaxial orientation of the other benzyl group (derived from the amino acid phenylalanine) blocking one face of the double bond.

During further exploration of this chemistry we obtained an unusual result, now reported here. Attempted epoxidation of 1b gave not the expected epoxide but a derivative 3, which was identified by X-ray crystallography (inset, Figure 1). The benzoic acid derived from the reagent attached itself to the initial oxidation product of the reaction, but the relative stereochemistry of the new substituents was cis. This contrasts with the much more typical trans- ring opening in such reactions. [2][3] but which has been seen in cases where diastereoselectivity in the opening of the epoxide is influenced by adjacent stereocentres [4] (including quaternary stereocentres generated during the epoxidation [5][7]) or chiral auxiliaries.[8][11] In the present case the epoxide presumably opened to give an intermediate acyliminium ion that was attacked from the opposite face of the heterocyclic ring because of the steric effect of the pendant benzyl group.

The motif of interest in 1 may be referred to as an “enediamide” (formally a 3,4-dihydropyrazin-2(1H)-one, or (in non-IUPAC approved nomenclature) a Δ5-2-oxopiperazine); the structure contains two amide nitrogen lone pairs able to act as π-donors to the double bond. Enediamides have been only occasionally reported in the literature.[1], [12][16] Their oxidation [16][18] has not been well explored. Most relevant was a report of enediamide 5 (Figure 2). [19] Oxidation of this structure by mCPBA was reported to give a ring-opened product (6) derived from cleavage of the double bond, rather than formation of an epoxide or dihydroxylated derivative. The identity of this compound was suggested on the basis of NMR studies. This contrasting behaviour of enediamide 5 has recently also become of interest to us. Our laboratory has been leading an open source project on the internet to find an enantioselective synthesis of the important drug praziquantel (PZQ, 4). [20] One of the approaches suggested on the project website [21] was the oxidation of PZQ to give the enediamide 5, which could be subjected to an asymmetric hydrogenation to generate the desired (R)-PZQ. The preparation of 5 is facile, [19], [22] but during the course of screening oxidants, we frequently obtained low yields and multiple byproducts. Given the apparent difference in outcomes of the oxidations of enediamides 1b and 5 (Figure 3) we sought to confirm the identity of the product arising from 5 and address why this reaction outcome was so different to that with enediamide 1b. We presumed (as did Davies et al. in a study of epoxidation of an enamide vs. its ring opening [9]) that the outcome is governed by stability of the intermediate iminium ions, but wished to provide evidence for this presumption.

Results and Discussion

In our hands, treatment of enediamide 5 with one equivalent of mCPBA gave a yield of 40% of the ring-opened product, with the remaining mass balance being starting material. Since the production of 6 requires two equivalents of oxidant, this yield is formally 80%. Use of two equivalents of mCPBA gave the ring-opened product in 78% yield. The use of NaHCO3 as base did not affect these yields. Crystals of 6 suitable for X-ray diffraction were obtained by slow evaporation from a mixed solvent system of Et2O and MeOH, unambiguously confirming the double-imide identity of this molecule (Figure 4).

A plausible mechanism for the formation of this compound involves formation of the epoxide 7 as a first step. This epoxide is unstable with respect to protonation and opening via formation of an acyliminium ion (e.g., 8a, an isomeric compound 8b is considered below) which would be attacked by mCPBA to give 9, triggering ring opening via a Grob fragmentation. [9], [11] The formation of cis-diols from solvolysis of cyclohexene oxides was shown to be promoted by electron-rich aromatic groups at the 1-position, with the reaction occurring via a transition state with significant carbocationic character. [23].

Figure 1. Previous work on the synthesis of peptidomimetic scaffolds, and the unusual stereochemical outcome of the epoxidation of enediamide 1b reported here (Ar = 3-chlorophenyl) proven with X-ray crystallography (inset).

Given that the PZQ-enediamide 5 may itself be formed by an oxidation of PZQ, the same ring opened product 6 can also be obtained directly from PZQ (4). The original report of this reaction gave a reaction time of one week with the use of two equivalents of mCPBA. We treated PZQ with a range of equivalents of the oxidant (Table 1). With three equivalents of mCPBA conversion of starting material was still incomplete after 16 hours. A trace amount (observed in all cases when the reaction was analysed by TLC) of 5 was formed in all cases, but 63% of the ring opened product 6 was generated with the rest of the mass balance being unreacted PZQ. Five equivalents of oxidant were necessary to consume all the starting material and give the ring opened product in high yield. The relative yields suggest enediamide 5 reacts more quickly with mCPBA than the starting material 4.

Figure 2. Synthesis of enediamide 5, an intermediate in the proposed enantioselective synthesis of the drug praziquantel (4), and precursor to a ring-opened oxidation product 6.

In the case of the formation of 3, only one regioisomer was formed, according to the uncomplicated 1H NMR spectrum that gave rise to the crystalline sample used for structure determination. If the attachment of the benzoate is reversible, then the more stable ring opened product has been obtained. The same result would be obtained were the 3-chlorobenzoyl group to migrate between the 2- and 3-oxy substituents of the product. Modeling of the two possible iminium ions (11a and 11b, Figure 5) and the regioisomeric products (12a and 12b) suggests that the iminium ion 11a is preferred to a small extent, and that the product 12a is preferred to a large extent. Assuming the transition state barriers broadly reflect these values, it would appear that thermodynamic arguments explain the outcome (rather than necessitating a Curtin-Hammett calculation of transition state energies). The large difference in product free energies for 12a and 12b are steric in origin. The exocyclic phenethylacyl group forces the adjacent oxo substituent into an axial position. The adjacent (cis) oxo substituent (to which there is a hydrogen bond) is therefore equatorial, and inevitably clashes with the N-methyl group (Figure 6, A and B). There is a “double gauche effect” in the product observed in which the electronegative oxygen and nitrogen substituents both generate this stereoelectronic stabilization (Figure 6, C). [7] The corresponding values for the iminium ion for the ring opening reaction (8a and 8b) show the expected intermediate is heavily favored where the iminium ion double bond is conjugated with the aromatic ring, but the same product would ultimately be formed irrespective of which of 8a or 8b forms. However, the fact that 8a is of considerably lower energy than 8b is significant in that were attack by benzoic acid to occur we would expect products 13a or 13b to form (rather than 13c or 13d). The higher energies of these benzoate-trapped compounds vs. the epoxide 7 imply their formation is not favourable.

What of the different outcomes of the reactions? In the case of enediamide 5, oxidative ring opening is observed, but this is not seen for enediamide 1b. The pathways from starting materials to iminium ions involve a transition state that is slightly lower in energy for 5, but it is illuminating to instead consider the pathways available to the iminium ion. In both cases there is a very large free energy gain in forming the epoxide from the iminium ion, for which the process is essentially barrierless. Alternatively, the trapping of the iminium ion by benzoate yields the stable adducts 13 (from 8) and 12 (from 11) and these trapping reactions are also quite exothermic. In the case of 11a such adduct formation is more favourable than the formation of the epoxide, while for 8a, formation of epoxide is more likely. Presumably the rapid formation of 12 from 11 means the benzoate counterion arising from the oxidation event attaches to the molecule before it can diffuse away – and this may be another reason for the defined stereochemical outcome. In contrast the ready formation of the neutral molecule 7 from 8a allows for the diffusion away of the benzoate and permits the reaction of 8a with mCPBA, triggering the ring opening reaction. Thus 8a (formed preferentially to 8b) coexists with residual oxidant because its trapping with benzoate is less favorable than for 11.

Figure 4. Attempted epoxidation of enediamide 5 gives ring opened product 6, characterized by X-ray crystallography (inset).


The difference in outcome of the epoxidation of two enediamides arises from the relative free energies of epoxides or benzoate-trapped products that can be formed from the intermediate iminium ions. These differences permit one intermediate iminium ion to react with residual oxidant and give a ring-opened product.

The lack of oxidative ring opening of enediamides such as 1b and the defined stereocontrol of the oxidation reaction make these scaffolds attractive for the future stereoselective synthesis of polycyclic peptidomimetic motifs, were intramolecular nucleophiles, such as pendant alcohols, to be employed along with the oxidant.

Materials and Methods

A) Synthesis

A general description of synthetic methods may be found in Text S1.

(2S,3R,6S)-6-Benzyl-3-hydroxy-4-methyl-5-oxo-1-(2-phenylacetyl)piperazin-2-yl 3-chlorobenzoate (3).

To (S)-3-benzyl-1-methyl-4-(2-phenylacetyl)-3,4-dihydropyrazin-2(1H)-one (1b, 30 mg, 0.094 mmol) [1] in DCM (3 mL) at −5°C was added mCPBA (16 mg, 1 eq, pre-washed in aqueous buffer pH 7.5 and dried). The reaction mixture was allowed to warm to rt over 1 h, stirred at rt for 2 h and concentrated in vacuo. The residue was purified by flash column chromatography (EtOAc-petroleum ether, 1∶4, ramping to EtOAc) to give the hemiaminal as white needles (22 mg, 71%). 1H NMR (400 MHz, CDCl3): δ 1.70 (s, 1H, OH), 2.71 (s, 3H, NMe), 3.07 (br d, 1H, J ca. 15, ArCHHCH), 3.22 (br s, 1H, CHO), 3.51 (dd, 1H, J 17.0 & 3.0, ArCHHCH), 3.58 (d, 1H, J 7.6, CHO), 3.79 (d, 1H, 14.8), 3.97 (d, 1H, J 14.4) (ABq, ArCH2CO), 4.80–4.87 (m, 1H, NCHCO), 6.63–6.76 (m, 2H), 6.84 (s, 1H), 7.03 (t, 2H, J 7.2), 7.14 (t, 1H, J 6.8), 7.27–7.48 (m, 5H), 7.55 (d, 1H, J 8.0), 7.80 (d, 1H, J 8.0), 7.89 (s, 1H) (Figure S1). IR (evaporated DCM solution) 3281 br, 1727, 1673, 1639 cm−1. MS (FAB) m/z: 493 (65%, MH+). HRMS (FAB) Calcd. for C27H26ClN2O5 (MH+): 493.15248, found 493.152250.

Figure 5. Regioselectivity in the opening of enediamide epoxides, and a comparison of observed selectivity with calculated M06-2X/6-311+G(3df,2p) free energies (298 K, kJ mol–1) of iminium ions and possible products.

Figure 6. B3-LYP/6-31G(d) minimum energy conformations of A) 12a (found) and B) 12b (not found, showing eclipsed ester and N-Me groups) and C) view along the C2–C3 bond showing gauche arrangements of oxygen and nitrogen substituents.

CCDC 833830 contains the supplementary crystallographic data for this compound. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via The cif file is provided (Cif S1).

2-(Cyclohexanecarbonyl)-6,7-dihydro-2H-pyrazino[2,1-a]isoquinolin-4(3H)-one (5).

2-(Cyclohexanecarbonyl)-3,6,7,11b-tetrahydro-1H-pyrazino[2,1-a]isoquinolin-4-one (rac-4, 0.500 g, 1.602 mmol) was mixed with sulfur (0.102 g, 3.204 mmol, 2 eq), under N2 and the mixture was melted with a hot air gun and kept at ca. 180°C for 15 min. The resultant dark brown oil was purified by flash chromatography (hexane:ethyl acetate, 5∶1) to afford the enediamide as a pale yellow solid (0.315 g, 63%). m. p. 131–134°C (lit. [19] 128–132°C). NMR data complicated by presence of minor rotamer: 1H NMR (300 MHz, CDCl3): δ 1.26–1.88 (m, 10H, cy), 2.63–2.71 (m, 1H, cy), 2.93 (t, 2H, J 5.7, H7), 3.93 (t, 2H, J 5.7, H6), 4.45 (s, 2H, H3), 6.78 (s, 1H, H1), 7.19–7.57 (m, 4H, Ar) (Figure S2). 13C NMR (75 MHz, CDCl3): δ 26.1 (m, 2 major peaks), 29.2, 29.4, 38.8, 41.4, 45.9, 48.7, 106.0, 123.1, 127.7, 127.7, 128.4, 128.8, 134.5, 164.3, 174.5 (C-11b not visible) (Figure S3). IR (evaporated CHCl3 solution): 2952, 2870, 1652, 1463 cm−1. MS (ESI) m/z: 311.1 [(MH)+, 100%], 333.3 [(MNa)+, 55%]. HRMS (ESI) Calcd. for C19H22N2NaO2 (MNa+): 333.15735. Found: 333.15765. Spectroscopic data matched those in the literature. [19].

N-Formyl-N-(2-oxo-2-(1-oxo-3,4-dihydroisoquinoline-2(1yl)ethyl)cyclohexanecarboxamide (6).

2-(Cyclohexanecarbonyl)-6,7-dihydro-2H-pyrazino[2,1-a]isoquinolin-4(3H)-one (5, 0.100 g, 0.322 mmol, 1.0 eq) in DCM (5 mL) was stirred with mCPBA (0.056 g, 0.322 mmol, 1.0 eq). Stirring was continued at rt for 16 h. The reaction mixture was diluted with DCM (15 mL) and washed with H2O (2×5 mL), the organic portion was dried (MgSO4) and concentrated in vacuo. The crude material was purified by flash column chromatography (EtOAc:hexane 1∶4) to afford the ring opened compound as a white solid (44 mg, 40%).

m. p. 117.0–118.5°C (lit. [19] 125°C). 1H NMR (500 MHz, CDCl3): δ 1.25–1.96 (m, 10H, cy), 2.75-2-83 (m, 1H, cy), 3.02 (t, 2H, J 6.0, H4), 4.10 (t, 2H, J 6.0, H3), 5.14 (s, 2H, H9), 7.26 (d, 1H, J obscured by solvent peak, Ar), 7.40 (t, 1H, J 7.6, Ar), 7.53 (d, 1H, J 7.5, Ar), 8.14 (d, 1H, J 7.7, Ar), 9.32 (s, 1H, H10) (Figure S4). 13C NMR (500 MHz, CDCl3): δ 25.6, 25.7, 28.0, 29.5, 42.3, 42.8, 46.6, 127.5, 127.6, 128.7, 129.7, 133.9, 140.2, 162.2, 165.9, 170.4, 177.0 (Figure S5). IR (evaporated CHCl3 solution): 2930, 2857, 1690, 1305, 747 cm−1. MS (ESI) m/z: 365.3 [(MNa)+, 100%]. HRMS (ESI) Calcd. for C19H22N2NaO4 (MNa+): 365.14718 Found: 365.14743. Spectroscopic data matched those in the literature. [19].

CCDC 816518 contains the supplementary crystallographic data for this compound. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via The cif file is provided (Cif S2).

B) Computational Methods

Standard density functional theory calculations were carried out with the GAUSSIAN 09 [24] program. Geometries were obtained at the B3-LYP [25] level of theory with the 6-31G(d) basis set. The vibrational frequencies of stationary points were inspected to ensure that they corresponded to minima on the potential energy surface. Improved relative energies were obtained at the M06-2X [26] level with the 6-311+G(3df,2p) basis set. Zero-point vibrational energies, thermal corrections to enthalpy and entropies were obtained using B3-LYP/6-31G(d) harmonic vibrational frequencies, scaled using appropriate literature scale factors. [27] We account for the effect of solvation using the SMD [28] continuum model with CH2Cl2 parameters. Energies in the text correspond to relative free energies at 298 K. Optimised structure coordinates and electronic energies may be found in Table S1.

Supporting Information

Figure S1.

1H NMR (300 MHz) spectrum of (2S,3R,6S)-6-benzyl-3-hydroxy-4-methyl-5-oxo-1-(2-phenylacetyl)piperazin-2-yl 3-chlorobenzoate (3).


Figure S2.

1H NMR spectrum of 2-(cyclohexanecarbonyl)-6,7-dihydro-2H-pyrazino[2,1-a]isoquinolin-4(3H)-one, (5).


Figure S3.

13C NMR spectrum of 2-(cyclohexanecarbonyl)-6,7-dihydro-2H-pyrazino[2,1-a]isoquinolin-4(3H)-one, (5).


Figure S4.

1H NMR Spectrum of N-formyl-N-(2-oxo-2-(1-oxo-3,4-dihydroisoquinoline-2(1yl)ethyl)cyclohexanecarboxamide, (6).


Figure S5.

13C NMR Spectrum of N-formyl-N-(2-oxo-2-(1-oxo-3,4-dihydroisoquinoline-2(1yl)ethyl)cyclohexanecarboxamide, (6).


Table S1.

B3-LYP/6-31G(d)-optimized structures and M06-2X/6-311+G(3df,2p) electronic energies for various species.


Text S1.

General Experimental Information.


Cif S1.

Crystallographic data file for compound 3.


Cif S2.

Crystallographic data file for compound 6.



We are indebted to Professor Paul A. Bartlett for guidance and resources, Fred Hollander for determining the structure of 3 and Dr Antonio DiPasquale for retrieving the relevant crystallographic data (all at, or formerly at, the University of California, Berkeley) and Peter Turner (The University of Sydney) for assistance with interpreting the data. We thank a referee of a previous version of this paper for bringing references 5 and 7 to our attention.

Author Contributions

Conceived and designed the experiments: MA BC MHT. Performed the experiments: MA BC. Analyzed the data: MA BC MHT. Contributed reagents/materials/analysis tools: PJ. Wrote the paper: MA BC MHT.


  1. 1. Todd MH, Ndubaku C, Bartlett PA (2002) Amino Acid Derived Heterocycles: Lewis Acid Catalyzed and Radical Cyclizations from Peptide Acetals. J Org Chem 67: 3985–3988.
  2. 2. Schreiber SL, Satake K (1984) Total Synthesis of (±)-Asteltoxin. J Am Chem Soc 106: 4186–4188.
  3. 3. Moltke-Leth C, Jørgensen KA (1993) Selective Oxidative Halogenation of Uracils. Acta Chem Scand 47: 1117–1121.
  4. 4. Orsini F, Sello G, Bernasconi S, Fallacara G (2004) Chemoenzymatic Synthesis of Conduritol Analogues. Tetrahedron Lett 45: 9253–9255.
  5. 5. Harayama T, Kotoji K, Yanada R, Yoneda F, Taga T, et al. (1986) Oxidation of Pyrimidine Base Derivatives with m-Chloroperbenzoic Acid. Chem Pharm Bull 34: 2354–2361.
  6. 6. Harayama T, Yanada R, Taga T, Yoneda F (1985) Stereochemistry of Reaction Products of 1,3-Dimethylthymine Epoxide with Amines. Tetrahedron Lett 26: 3587–3590.
  7. 7. Ryang HS, Wang SY (1978) α-Diketone Sensitized Photooxidation of Pyrimidines. J Am Chem Soc 100: 1302–1303.
  8. 8. Adam W, Bosio SG, Turro NJ, Wolff BT (2004) Enecarbamates as Selective Substrates in Oxidations: Chiral-Auxiliary-Controlled Mode Selectivity and Diastereoselectivity in the [2+2] Cycloaddition and Ene Reaction of Singlet Oxygen and in the Epoxidation by DMD and mCPBA. J Org Chem 69: 1704–1715.
  9. 9. Aciro C, Davies SG, Garner AC, Ishii Y, Key MS, et al. (2008) Stereoselective Functionalisation of SuperQuat Enamides: Asymmetric Synthesis of Homochiral 1,2-Diols and α-Benzyloxy Carbonyl Compounds. Tetrahedron 64: 9320–9344.
  10. 10. Frauenrath H, Brethauser D, Reim S, Maurer M, Raabe G (2001) Highly Enantioselective Isomerization of 4,7-Dihydro-1,3-dioxepins Catalyzed by Me-DuPHOS-Modified Dihalogenonickel Complexes and Determination of the Absolute Configuration of the Isomerization Products. Angew Chem Int Ed 40: 177–179.
  11. 11. Xiong H, Hsung RP, Shen L, Hahn JM (2002) Chiral Enamide. Part 1: Epoxidations of Chiral Enamides. A Viable Approach to Chiral Nitrogen Stabilized Oxyallyl Cations in [4+3] Cycloadditions. Tetrahedron Lett 43: 4449–4453.
  12. 12. Cheng JF, Chen M, Arrhenius T, Nadzan A (2002) A Convenient Solution and Solid-phase Synthesis of Δ5–2-Oxopiperazines via N-Acyliminium Ions Cyclization Tetrahedron Lett. 43: 6293–6295.
  13. 13. Lee SC, Park SB (2007) Practical Solid-Phase Parallel Synthesis of Δ5–2-Oxopiperazines via N-Acyliminium Ion Cyclization. J Comb Chem 9: 828–835.
  14. 14. Wai JS, Kim B, Fisher TE, Zhuang L, Embrey MW, et al. (2007) Dihydroxypyridopyrazine-1,6-dione HIV-1 Integrase Inhibitors. Bioorg Med Chem Lett 17: 5595–5599.
  15. 15. Wang W, Ollio S, Herdtweck E, Doemling A (2011) Polycyclic Compounds by Ugi−Pictet−Spengler Sequence. J Org Chem 76: 637–644.
  16. 16. Adam W, Ahrweiler M, Vlcek P (1995) Chemiluminescence of the Labile 1,2-Dioxetanes and Epoxides Produced in the Oxidation of N-Acetylated Dihydro- and Tetrahydropyrazines by Singlet Oxygen, Dimethyldioxirane, and m-Chloroperoxybenzoic Acid. J Am Chem Soc 117: 9690–9692.
  17. 17. Matsumoto K, Tokuyama H, Fukuyama T (2007) Synthetic Studies on Haplophytine: Protective-Group-Controlled Rearrangement. Synlett 2007: 3137–3140.
  18. 18. Girard AL, Enomoto T, Yokouchi S, Tsukano C, Takemoto Y (2011) Control of 6-Exo and 7-Endo Cyclizations of Alkynylamides using Platinum and Bismuth Catalysts. Chem Asian J 6: 1321–1324.
  19. 19. Kiec'-Kononowicz K (1989) Spectral and Chemical Properties of Pyrazino-[2,1-a]-isoquinolin-4-one Derivatives. Arch Pharm 322: 795–799.
  20. 20. Woelfle M, Seerden JP, de Gooijer J, Pouwer K, Olliaro P, et al. (2011) Resolution of Praziquantel. PLoS Negl Trop Dis 5(9): e1260.
  21. 21. Website: Starting from the Racemate | The Synaptic Leap. Available: Accessed 2012 May 19.
  22. 22. Website: Asymmetric Hydrogenation of PZQ Enamide. Available: Accessed 2012 May 19.
  23. 23. Battistini C, Balsamo A, Berti G, Crotti P, Macchia B, et al.. (1974) Effect of Substituents on the Stereoselectivity of the Acid-catalysed Hydrolysis of a Series of Aryloxirans. A New Application of the Hammett Equation. J Chem Soc Chem Commun 712–713.
  24. 24. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, et al.. (2009) Gaussian 09, Revision A.02.
  25. 25. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab-Initio Calculation of Vibrational Absorption and Circular-dichroism Spectra using Density-functional Force-fields. J Phys Chem 98: 11623–11627.
  26. 26. Zhao Y, Truhlar DG (2008) The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 Other Functionals. Theor Chem Acc 120: 215–241.
  27. 27. Merrick JP, Moran D, Radom L (2007) An Evaluation of Harmonic Vibrational Frequency Scale Factors. J Phys Chem A 111: 11683–11700.
  28. 28. Marenich AV, Cramer CJ, Truhlar DG (2009) Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J Phys Chem B 113: 6378–6396.