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Analytical and Bioanalytical Chemistry

, Volume 382, Issue 3, pp 708–717 | Cite as

Chromatography in silico, basic concept in reversed-phase liquid chromatography

  • Toshihiko HanaiEmail author
Original Paper

Abstract

Basic phenomena in reversed-phase liquid chromatography have been quantitatively analyzed using a computational chemical calculation. Pyridine interacted with an ionized silica surface under neutral conditions. Alkyl-chain length affected the contact surface area with an analyte. Steric hindrance was demonstrated using a model graphitic carbon phase and unsaturated alkenes. Quantitative structure–retention relationships in reversed-phase liquid chromatography were demonstrated for phenolic compounds and acidic and basic drugs. The correlations between predicted and measured retention factors were satisfactory. Dissociation constants were derived from the atom partial charge and used to predict retention factors of partially ionized compounds.

Keywords

QSRR Computational chemistry Liquid chromatography Molecular mechanics Atom partial charge pKa 

Introduction

The mechanism of retention in reversed-phase liquid chromatography has been quantitatively analyzed using computational chemical method based on solubility properties. The most important molecular interaction force in reversed-phase liquid chromatography is the hydrophobic interaction, which is a combination of van der Waals volume, repulsion, and London’s dispersion. Hydrogen bonding and electrostatic interaction between an analyte and the alkyl brush of the bonded phase, properties very important in normal-phase and ion-exchange liquid chromatography, respectively [1], were not considered. Organic modifiers compete with an analyte for direct interaction with the bonded phase. Ions, as components of the mobile phase control the dissociation of the analyte. The predominant retention force between an analyte and the alkyl chain bonded phase is the hydrophobic interaction. A system using log P can predict the retention time in reversed-phase liquid chromatography. Log P, however, is the sum of solubility properties and is not the best means of studying quantitative structure–retention relationships (QSRR) in reversed-phase liquid chromatography. The solution can be obtained by controlling the solubility of the analyte under various conditions. Therefore, the basic concept of reversed-phase liquid chromatography was analyzed quantitatively by using a computational chemical method. If the steric effect, which is a very important property in affinity chromatography including enantiomer separations, is neglected, a one-to-one molecular interaction can be used to study the basic molecular interaction.

A basic consideration in reversed-phase liquid chromatography using silica-based packing materials is the inertness of bonded-phase silica gels [2, 3, 4]. The phenomenon of pyridine adsorption was first analyzed using the molecular mechanics calculation of CAChe software, because inertness affects the selectivity of the chromatograms, the order of elution, and quantitative analysis of the chromatograms. The alkyl chain length is a very important factor in reversed-phase liquid chromatography [5]. Selectivity was analyzed using model compounds. An alkane is considered to be an alkyl brush, and the molecular interaction between the alkyl brush and an analyte was quantitatively analyzed using molecular mechanics calculations of the CAChe software. Steric hindrance was studied for adsorption on a model graphitic carbon phase. QSRR in reversed-phase liquid chromatography were studied using chromatographic data for phenolic compounds [6] and acidic [7] and basic drugs [8]. Quantitative analysis was also achieved by using the molecular mechanics calculations of CAChe software.

Experimental

A Dell model Latitude C840 computer equipped with a 2 GHz processor and 1024 MB memory was used. The molecular properties of analytes and model phases and molecular interactions were calculated by use of molecular mechanics (MM2) from Version 5 of the CAChe program (Fujitsu, Tokyo, Japan). The standard properties used were bond stretch, bond angle, dihedral angle, improper torsion, van der Waals forces, hydrogen bonding, and electrostatic forces (MM2/MM3 bond dipoles). The van der Waals cut-off distance was 9 Å . The energy unit was kcal mol−1 (1 kJ mol−1=4.18 kcal mol−1). The Cricket-Graph program from Computer Associates (San Diego, CA, USA) was used for data analysis.

Results and discussion

Adsorption of pyridine

A stable and inert bonded-phase silica gel is required to enable quantitative analysis of retention time in chromatography. One quality-control test used by column manufacturers is the pyridine test [2, 3, 4], which measures the inertness of bonded-phase silica gels from the chromatographic behavior of pyridine. Pyridine is strongly retained on poorly treated bonded-silica gels on which even aniline has a symmetrical peak shape. Phenol is used as the reference compound. The dissociation constants (pKa) of pyridine and phenol are 5.25 and 10.02, respectively, so these compounds are in the molecular form under neutral conditions. For this reason the order of elution depends on the octanol–water partition coefficient (log P). The log P values of pyridine and phenol are 0.70 and 1.54, respectively. Pyridine should be eluted before phenol, but pyridine is occasionally retained longer than phenol. The abnormal chromatographic behavior of pyridine was analyzed by chromatography in silico. The model silica gel surface was constructed with 198 atoms, 189 bonds, and 1406 connectors; 27 silanol groups are present on one side of the surface. The top and side views of the model phase are shown in Fig. 1. Silanol, siloxane, and the ionized forms of silica are shown in Figs. 1A–1C, respectively. The molecular interactions of the silanol form with pyridine and phenol are shown in Figs. 1D and 1E, respectively. The interaction energy values of the final structure (ΔFS) are summarized in Table 1. The interaction energy value (Δ value) was obtained by subtracting the energy value of the complex from the sum of the individual energy values of the analyte and the model phase.
Fig. 1

Retention of pyridine and phenol on silica surface. Black balls oxygen; gray balls silicon; white balls hydrogen. A silanol phase; B siloxane phase; C ionized silicon dioxide phase; D adsorption of pyridine on silanol phase; E adsorption of phenol on silanol phase

Table 1

Molecular interaction energy with model silica gels (unit: kcal mol−1)

Silica surface

ΔFS for pyridine

ΔFS for phenol

SiOH

6.94

20.26

Siloxane

6.01

12.91

SiO

12.68

3.92

The results indicate that when silanol groups are ionized, pyridine is strongly retained on the surface. Generally, silica gel is stable at pH 6.5, and dissolves in higher-pH solution. This means that the silica gel might be partially ionized under neutral conditions and adsorb pyridine. Complete surface coverage is important to avoid unpredictable chromatographic behavior.

Alkyl chain length effect

According to Berendsen and Galan, a dodecyl phase is suitable for practical application in reversed-phase liquid chromatography [5]. The alkyl chain-length effect was studied by computational chemical calculations. Dodecane was used as the brush for the model bonded phase, and the molecular interaction between the dodecane and a variety of analytes was quantitatively analyzed using molecular mechanics calculations. The analytes were alkanes, alkenes, and alkanols. Aromatic compounds were not included in this first analysis because of the requirement of a steric effect. The forms of molecular interaction of dodecane with an analyte are shown in Fig. 2. The van der Waals energy was predominant in the molecular interaction. The calculated energy values for individual compounds and the complexes are summarized in Table 2 with the properties of the compounds. Alkyl chain length affected the retention of a variety of compounds. The retention of larger compounds was constant when a shorter alkyl chain bonded phase was used [5]. A C30 bonded phase was developed for separation of carotenoids because of the requirement of a longer alkyl chain compatible with the size of carotenoid molecules [9, 10]. In in-silico chromatography, the molecular interaction energy was constant for larger analytes. The results were the same for alkanes, alkenes, and alkanols.
Fig. 2

Interactions of alkanes and alkenes on a dodecyl phase (a model alkyl chain of a bonded phase), large balls carbon; small balls hydrogen

Table 2

Molecular properties of alkanes, alkenes, and alkanols

Chemicals

fs

hb

es

vw

FS

HB

ES

VW

Methyl alcohol

0.0605

0

0

−0.077

5.1249

0

0

3.025

Ethyl alcohol

0.8019

0

0

0.583

4.9799

0

0

1.820

Propyl alcohol

1.4662

0

0

1.086

4.7094

0

0

2.234

Butyl alcohol

2.1307

0

0

1.573

4.4579

0

0

1.82

Pentyl alcohol

2.7809

0

0

2.041

4.1053

0

0

1.319

Hexyl alcohol

3.4250

0

0

2.497

3.8288

0

0

0.866

Tetradecane

8.6083

0

0

6.312

4.6461

0

0

0.365

Tridecane

7.9663

0

0

5.850

4.0840

0

0

−0.006

Dodecane

7.3257

0

0

5.383

3.6762

0

0

−0.236

Undecane

6.6823

0

0

4.924

3.3824

0

0

−0.352

Decane

6.0348

0

0

4.462

3.3819

0

0

−0.171

Nonane

5.3978

0

0

3.996

3.5011

0

0

0.129

Octane

4.7556

0

0

3.535

3.6404

0

0

0.426

Heptane

4.1135

0

0

3.069

3.8965

0

0

0.873

Hexane

3.4743

0

0

2.611

4.2497

0

0

1.358

Pentane

2.8290

0

0

2.151

4.6560

0

0

1.950

Butane

2.1765

0

0

1.674

4.9004

0

0

2.405

Propane

1.5011

0

0

1.188

5.1439

0

0

2.857

Ethane

0.8167

0

0

0.682

5.4915

0

0

3.392

Methane

0

0

0

0

5.3661

0

0

3.343

1-Ethene

0.4230

0

0

0.386

5.1134

0

0

3.158

1-Propene

2.1632

0

0

0.525

3.7718

0

0

2.385

1-Butene

2.4863

0

0

1.157

4.4793

0

0

2.543

2-Butene

3.9495

0

0.099

0.609

2.8872

0

0.098

1.957

1,3-Dibutene

−2.9639

0

0

1.132

−0.1779

0

0

1.958

1-Pentene

3.1544

0

0

1.632

4.2291

0

0

2.054

2-Pentene

4.2420

0

0

1.213

3.2818

0

0.098

1.671

1,3-Dipentene

−1.2575

0

0

1.230

−1.3309

0

0

1.385

1-Hexene

3.8062

0

0

2.102

4.1093

0

0

1.600

2-Hexene

4.9020

0

0.099

1.682

3.1446

0

0.098

1.216

3-Hexene

4.5252

0

0.099

1.812

3.5618

0

0.098

1.543

1,3-Dihexene

−0.9595

0

0

1.857

−0.3334

0

0

1.662

1,5-Dihexene

4.2232

0

0.1

1.579

4.3919

0

0.1

1.587

2,4-Dihexene

0.4513

0

0.01

1.304

−2.2327

0

0.01

0.962

1,3,5-Trihexene

−0.6347

0

0

1.872

−5.3345

0

0

0.959

1-Decene

6.3731

0

0

3.956

3.1719

0

0

0.181

2-Decene

7.4747

0

0

3.539

2.7221

0

0.098

−0.039

3-Decene

7.1127

0

0

3.665

2.7233

0

0.098

–0.039

4-Decene

7.1256

0

0

3.671

2.7172

0

0.098

0.009

5-Decene

7.1276

0

0

3.679

2.8538

0

0.098

0.122

fs, hb, es, and vw are final structure, hydrogen bonding, electrostatic, and van der Waals energy values of individual compounds. FS, HB, ES, and VW final structure, hydrogen bonding, electrostatic, and van der Waals energy values of complexes with dodecane; unit: kcal mol−1

Retention depended on the contact surface area of the molecules. The alkenes with multiple double bonds had less contact surface area and the molecular interaction energy was smaller than that expected from the carbon numbers (surface area). The electrons of double bonds and hydroxyl groups did not affect retention. The relationship between molecular interaction energy values of alkyl alcohols, alkanes, and alkenes and their surface area is shown in Fig. 3.
Fig. 3

Alkyl chain length of analytes related to van der Waals energy change

The molecular interaction energy values of alkenes were smaller than for the related alkanes. This result supported the idea that the hydrophobic interaction due to the van der Waals energy is the predominant molecular interaction in reversed-phase liquid chromatography. No dipole–dipole or pi–pi interactions influenced the direct interaction. The effect of lack of dipole–dipole or pi–pi interactions can be studied by investigation of chromatographic behavior on a graphitic carbon phase [11, 12].

Chromatographic behavior on graphitic carbon

Graphitic carbon is a special phase that adsorbs entire compounds. These materials are used mainly for sample collection in several analytical fields. The small porosity material is used as a packing material for gas analysis in gas chromatography and for saccharides and anions in liquid chromatography. Only cations are not adsorbed [11, 12]. Computational chemical analysis for a model graphitic carbon phase was performed using 196 aromatic ring-phase and alkanes and alkenes. The model phase is shown in Fig. 4. The relationship between the molecular interaction energy values and number of decene double bonds is summarized in Fig. 5.
Fig. 4

Adsorption of decane and cis-1,3,5,7,9-pentadecene on a model graphitic carbon phase, large balls carbon; small balls hydrogen

Fig. 5

Conformation effect in molecular interaction

The results indicate that increasing the number of double bonds reduced the molecular interaction energy values, especially for the cis compounds. The predominant interaction force is the van der Waals force. The electrostatic energy did not change after formation of the complex. No pi–pi interactions influenced the direct interaction. The calculated results were in agreement with the chromatographic behavior of fatty acids in reversed-phase liquid chromatography.

The possibility of optimization based on molecular interaction energy values

The reversed-phase liquid chromatographic results for several compounds such as benzoic acid, phenol, 4-chlorophenol, 2,4-dichlorophenol, 2,4,6-trichlorophenol, and 2,3,4,6-tetrachlorophenol, using a pentyl-bonded silica gel were analyzed by means of the molecular interaction energy values calculated by using molecular mechanics [13]. The pentyl-bonded silica gel did not have a silanol effect. Therefore, a model phase was constructed using carbon and hydrogen atoms as shown in Fig. 6. The butyl chains packed together, and there was no empty space between them. These analytes were adsorbed on the top of the phase, where 2,3,4-trimethylphenol was adsorbed (Fig. 6). The correlation between their interaction energy values and logarithmic retention factors was very high, even when these compounds were completely ionized. The regression coefficients for correlation with molecular interaction energy values were 0.986 and 0.976 (n=6), respectively, for molecular and ionized compounds. The regression coefficients for differences in van der Waals energy values were 0.991 and 0.981 (n=6), respectively. The precision of the predicted retention factors of partly ionized compounds using Eq. 1 was very satisfactory.
$$ k = (k_{\text{m}} + k_{\text{i}} {\text{ }}[k{\text{a}}]/[{\text{H}}^ + ])/(1 + [k{\text{a}}]/[{\text{H}}^ + ]) $$
(1)
where km is the maximum retention factor of the unionized form of the analytes, k i is the retention factor of the fully ionized compound, Ka is the dissociation constant; and [H+] is the hydrogen ion concentration of the eluent. The correlation coefficients between predicted and measured retention factors were greater than 0.9 for eluents of pH 3–9 [6].
Fig. 6

Adsorption of 2,3,5-trimethylphenol on butyl-bonded phase, Black balls oxygen; gray balls carbon; white small balls hydrogen. Atomic size of butyl phase is 20%

These results indicated that the new approach for quantitative analysis of retention time was precise. The new approach was examined for chromatographic data of different compounds with new model phases.

Analysis of chromatographic behavior of phenolic compounds measured on an octadecyl-bonded silica gel

The new quantitative analysis system for retention in reversed-phase liquid chromatography was used to analyze the chromatographic behavior of phenolic compounds (listed in Table 3) measured in reversed-phase liquid chromatography using an octadecyl-bonded silica gel and pH-controlled eluent [6]. When the model butyl phase was used to examine this new approach the relationship between the interaction energy and log k revealed several outliers. The correlation coefficient was 0.916 (n=38) excluding dihydroxybenzenes, nitrophenols, and some alkylphenols. Therefore, a silica based pentyl bonded phase was constructed to reduce the steric effect. The correlation coefficient improved to 0.956 (n=42); however, dihydroxybenzenes and some nitrophenols remained as outliers. The adsorption of 2,3,5-trimethylphenol on this pentyl phase is shown in Fig. 7. Further study, based on previous results [6] was performed, and the precision was improved. The nitro and hydroxyl-substituted phenolic compounds were included in the calculation. The calculation for the nitro-substituted phenolic compound recognized the presence of hydrogen bonding in the adsorption, however the hydrogen bonding energy of the complex was identical with the hydrogen bonding energy of the phenolic compounds themselves. That of ortho-substituted compounds was very high, because of intramolecular hydrogen bonding. Hydrogen bonding was not considered to contribute to for the retention. Reduction of the hydrogen bonding energy value of phenolic compounds from the interaction energy values improved the correlation coefficient. The original relation is given as Eq. 2 and the new result is given as Eq. 3.
$$ \Delta {\rm{FS}} = 7.721\left( {\log k_m } \right) + 16.834,\;{\rm{r}} = 0.879,\;{\rm{n}} = 49, $$
(2)
$$ \left( {\Delta {\rm{FS}} - {\rm{hb}}} \right) = 11.606\left( {\log k_m } \right) + 17.967,\;{\rm{r}} = 0.968,\;{\rm{n}} = 49, $$
(3)
Dihydroxybenzenes and nitrophenols were not outliers (Fig.8). The reason for the outliers was mainly intramolecular hydrogen bonding. The hydrogen bonding energy values were very high compared with those for other compounds. The results demonstrated that hydrogen bonding did not contribute to their molecular interaction. A method for prediction of the dissociation constant (pKa) from atom partial charges without Hammett’s equations was proposed [6]. A combination of ΔFS and the predicted pKa values enabled prediction of retention factors in a given pH eluent.
Table 3

Phenolic compounds

1

1,3-Dihydroxybenzene

2

1,4-Dihydroxybenzene

3

1-Hydroxynaphthalene

4

2,3,4,5,6-Pentachlorophenol

5

2,3,4-Trichlorophenol

6

2,3,5-Trichlorophenol

7

2,3,5-Trimethylphenol

8

2,3,6-Trichlorophenol

9

2,3,6-Trimethylphenol

10

2,3-Dichlorophenol

11

2,3-Dimethylphenol

12

2,4,5-Trichlorophenol

13

2,4,6-Trichlorophenol

14

2,4,6-Trimethylphenol

15

2,4-Dibromophenol

16

2,4-Dichlorophenol

17

2,4-Dimethylphenol

18

2,5-Dichlorophenol

19

2,5-Dimethylphenol

20

2,5-Dinitrophenol

21

2,6-Dibromophenol

22

2,6-Dichlorophenol

23

2,6-Dimethylphenol

24

2,6-Dinitrophenol

25

2-Bromophenol

26

2-Chloro-6-methylphenol

27

2-Chlorophenol

28

2-Ethylphenol

29

2-Methylphenol

30

2-Nitrophenol

31

3,4-Dichlorophenol

32

3,4-Dimethylphenol

33

3,5-Dichlorophenol

34

3,5-Dimethylphenol

35

3-Bromophenol

36

3-Chlorophenol

37

3-Ethylphenol

38

3-Methylphenol

39

3-Nitrophenol

40

4-Bromophenol

41

4-Chloro-2-methylphenol

42

4-Chloro-3,5-dimethylphenol

43

4-Chloro-3-methylphenol

44

4-Chlorophenol

45

4-Ethylphenol

46

4-Methylphenol

47

4-Nitrophenol

48

4-tert-Butylphenol

49

Phenol

Fig. 7

Adsorption of 2,3,5-trimethylphenol on a model pentyl bonded silica, Black balls oxygen; dark gray balls carbon; gray balls silicone; white balls hydrogen. Atomic size of pentyl phase is 20%

Fig. 8

Relationship between molecular interaction energy values and log k of the molecular forms of phenolic compounds. Numbers beside symbols, see Table 3

Analysis of the chromatographic behavior of acidic drugs in reversed-phase liquid chromatography

The above approach was used to study the chromatographic behavior of complex compounds such as the acidic drugs listed in Table 4. The chromatographic behavior of acidic drugs measured on a pentyl-bonded phase was previously analyzed using a computational chemical method [7]. The model pentyl-bonded silica gel is shown in Fig. 9, with warfarin adsorbed on the phase.
$$ \Delta {\rm{FS}} = 6.483\left( {\log k_m } \right) + 23.145,\;{\rm{r}} = 0.878,\;{\rm{n}} = 19, $$
(4)
It was not expected that hydrogen bonding would have any direct effect, and the hydrogen bonding energy values were identical after the complex formation. The hydrogen bonding energy values were subtracted from the ΔFS energy values.
Table 4

Acidic and basic drugs

1

p-Aminohippuric acid

2

Barbituric acid

3

Benzoic acid

4

Furosemide

5

p-Hydroxybenzoic acid

6

Ibuprofen

7

Indomethacin

8

Iopanoic acid

9

Mefenamic acid

10

Nalidixic acid

11

Naproxen

12

Nicotinic acid

13

Phenylbutazone

14

Probenocid

15

Salicylic acid

16

Sulfamethoxazole

17

Tolazamide

18

Tolbutamide

19

Warfarin

20

ajmaline

21

Aniline

22

Atropine

23

Carbamazepine

24

Dextromethorphan

25

Homatropine

26

Isopreterenol

27

Lidocaine

28

Prazosin

29

Procaine

30

Pyridine

31

Quinine

32

Theobromine

33

Triamterene

34

Benzylamine

35

Phenylethylamine

36

N,N-Dimethylaniline

Fig. 9

Adsorption of warfarin on a model pentyl-bonded silica, Black balls oxygen; dark gray balls carbon; gray balls silicone; white balls hydrogen. Atomic size of pentyl phase is 20%

The correlation coefficient with log km values, however, did not improve as did the results for phenolic compounds, as shown as Eq. 5.
$$ \left( {\Delta {\rm{FS}} - {\rm{hb}}} \right) = 7.824\left( {\log k_m } \right) + 18.516,\;{\rm{r}} = 0.888,\;{\rm{n}} = 19. $$
(5)
The correlation between ΔFS and log km values is shown in Fig. 10. Hydrogen bonding energy did not affect retention or the correlation coefficient because no intra-molecular hydrogen bonding exists for these acidic drugs.
Fig. 10

Relationship between molecular interaction energy values and log k of molecular-form acidic drugs. Numbers beside symbols, see Table 4

Analysis of the chromatographic behavior of basic drugs in reversed-phase liquid chromatography

The chromatographic behavior of the basic drugs listed in Table 4 measured on a pentyl-bonded silica gel was also analyzed using the computational chemical method [8]. The adsorption of homatropin by the pentyl phase is shown in Fig.11. The correlation between ΔFS and log km is given by the equation:
$$ \Delta {\rm{FS}} = 7.618\left( {\log k_m } \right) + 20.924,\;{\rm{r}} = 0.941,\;{\rm{n}} = 17. $$
(6)
Subtraction of hydrogen bonding energy values did not significantly improve the correlation coefficient as given by the equation:
$$ \left( {\Delta {\rm{FS}} - {\rm{hb}}} \right) = 8.788\left( {\log k_m } \right) + 17.800,\;{\rm{r}} = 0.949,\;{\rm{n}} = 17. $$
(7)
The correlation between ΔFS and log km values is shown in Fig. 12. The effect of hydrogen bonding energy was only important for compounds with intramolecular hydrogen bonding, ortho effect.
Fig. 11

Adsorption of homatropine in a model pentyl-bonded silica, Black balls oxygen; dark gray balls nitrogen; gray balls carbon; light gray balls silicone; white balls hydrogen. Atomic size of pentyl phase is 20%

Fig. 12

Relationship between molecular interaction energy values and log k of molecular-form basic drugs. Numbers beside symbols, see Table 4

Conclusion

The direct calculation of molecular interaction energy values is promising for the development of more precise QSRR, compared with calculation using the octanol–water partition coefficient (log P). Based on solubility parameters, the molecular interaction was considered to be a direct interaction without involvement of the solvent. The correlation coefficient between predicted and measured retention factors was 0.9. The solvent effect might improve the precision but not very much. The design of a model phase suitable for a variety of compounds remains to be achieved. A method for prediction of the dissociation constant (pKa) from atom partial charges without Hammett’s equations is proposed [6, 14]. Further, the improvement of the pKa prediction method based on atom partial charge for a variety of compounds remains to be automated using the above approach.

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Health Research FoundationSakyoKyoto

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