# Specific rotation: (Now Stale) Work in progress

Recording optical rotation with a polarimeter: The plane of polarisation of plane polarised light (4) rotates (6) as it passes through an optically active sample (5). This angle is determined with a rotatable polarizing filter (7).

In stereochemistry, the specific rotation [α] of a chemical compound is defined as the observed angle of optical rotation when plane-polarized light is passed through a sample with a path length of 1 dm and a sample concentration of 1 g/ml.[1] It is the main property used to quantify the chirality of a molecular species or a mineral. The specific rotation of a pure material is an intrinsic property of that material at a given wavelength and temperature. The formal unit for specific rotation values is deg dm−1cm3 g−1 but values are reported in scientific literature as degrees.[2] A positive value means dextrorotatory (clockwise) rotation and a negative value means levorotatory rotation.

## Measurement

Compound name [α]D20
(S)-2-Bromobutane +23.1°
(R)-2-Bromobutane −23.1°
D-Fructose −92.4°
D-Glucose +52.5°
D-Sucrose +66.47°[3]
D-Lactose +52.3°
Camphor +44.26°[3]
Cavicularin +168.2°[4]
Cholesterol −31.5°[3]
Cocaine −16°[3]
Paclitaxel (Taxol) −49°[5]
Penicillin V +233°[3]
Morphine −132°[3]
Hexol bromocamphorsulphonate +2640°[6]

Optical rotation is measured with an instrument called a polarimeter. For a given wavelength there is a linear relationship between the observed rotation and the concentration of optically active compound in the sample. Values should be accompanied by the temperature at which the measurement was performed, assumed to be room temperature unless otherwise stated.

$[\alpha]_\lambda^T = \frac{ \alpha}{l \times c}$

In this equation, l is the path length in decimeters and c is the concentration in g/mL, for a sample at a temperature T (given in degrees Celsius) and wavelength λ (in nanometers).[2]

For pure liquids, the density ρ (Greek letter "rho") in g/mL is equivalent to concentration, and the equation is expressed with ρ in place of c:

$[\alpha]_\lambda^T = \frac{\alpha}{l \times \rho}$

If the wavelength of the light used is 589 nm (the sodium D line), the symbol “D” is used for the wavelength, as in the expression [α]D. The rotation is reported using degrees, and the sign of the rotation (+ or −) is always given.

When using this equation, the concentration and the solvent may be provided in parentheses after the rotation. No units of concentration are given (it is assumed to be g/100mL).[clarification needed]

If a 1% w/v solution of a rotating substance in ethanol gave a clockwise rotation of 6.2° dm-1 cm3 g-1 when measured at 20 °C with light from a sodium lamp, this would be expressed as follows:

$[\alpha]_D^{20} = +6.2$° (c 1.0, EtOH)

### Dealing with large and small rotations

If the specific rotation is very or the sample is very concentrated, the actual rotation of the sample may be greater than 180°. A single polarimeter measurement cannot detect when this has happened (for example, the values +270° and −90° are indistinguishable, nor are the values 361° and 1°). In these cases, varying the concentration or path length allows one to determine the true value.

In cases of very small or very large angles, one can also use the variation of specific rotation with wavelength to facilitate measurement. Switching wavelength is particularly useful when the angle is small.[citation needed] Many polarimeters are equipped with a mercury lamp (in addition to the sodium lamp) for this purpose.

### Mixtures

A Saccharometer, a type of polarimeter with a "sugar scale" for direct reading of sucrose concentration in the Berlin Sugar Museum. Produced by Schmidt & Haensch GmbH, Berlin.

In theory, the optical purity of a sample containing a mixture of enantiomers can be determined from the measured optical rotation. For example, if a sample of 2-bromobutane measured under standard conditions has an observed rotation of −9.2°, this indicates that the net effect is due to 9.2°/23.1°=40% of the R enantiomer. This value (40%) is called the enantiomeric excess. The remainder of the sample is a racemic mixture of the enantiomers (30% R and 30% S), which has no net contribution to the observed rotation. The total concentration of the R enantiomer is 70%. The utility of this method is limited as the presence of small amounts of highly rotating impurities can greatly affect the rotation of a given sample. Moreover, the optical rotation of a compound may not be linearly dependent on its enantiomeric excess because of aggregation in solution. Other methods of determining the enantiomeric ratio such as gas chromatography or HPLC with a chiral column are generally preferred.[citation needed]

## Absolute configuration

The variation of specific rotation with wavelength is the basis of optical rotatory dispersion (ORD), an analytical technique that can be used to elucidate the absolute configuration of certain compounds.[citation needed]

## References

1. ^ "Specific Rotation.". Merriam-Webster.com. Retrieved 12 August 2013.
2. ^ a b Mohrig, J. R.; Hammond, C. N.; Schatz, P. F. (2010). Techniques in Organic Chemistry (Third ed.). W. H. Freeman and Company. pp. 209–210.
3. McMurry, John (2011). Fundamentals of Organic Chemistry. Cengage Learning. p. 196. ISBN 9781439049716.
4. ^ M. Toyota, T. Yoshida, Y. Kan, S. Takaoka, Y. Asakawa (1996). "(+)-Cavicularin: A Novel Optically Active Cyclic Bibenzyl-Dihydrophenanthrene Derivative from the Liverwort Cavicularia densa Steph". Tetrahedron Letters 37 (27): 4745–4748. doi:10.1016/0040-4039(96)00956-2.
5. ^ O'Neil, M.J., ed. (2006). "Taxol". The Merck Index - An Encyclopedia of Chemicals, Drugs, and Biologicals. Whitehouse Station, NJ: Merck and Co., Inc. p. 1204.
6. ^ Werner, A. (1907). "Über mehrkernige Metallammoniake" [Poly-​nucleated Metal-​amines]. Ber. Dtsch. Chem. Ges. (in German) 40: 2103–2125. doi:10.1002/cber.190704002126. ISSN 0365-9496.

{{DEFAULTSORT:Specific Rotation}} Category:Chemical properties

# Specific rotation#Measurement: The measurement section

Examples
Compound name [α]D20
(S)-2-Bromobutane +23.1°
(R)-2-Bromobutane −23.1°
D-Fructose −92°[1]
D-Glucose +52.7°[1]
D-Sucrose +66.37°[1]
D-Lactose +52.3°[1]
Camphor +44.26°[1]
Cholesterol −31.5°[1]
Taxol A −49°[2]
Penicillin V +223°[3]
(+)-Cavicularin +168.2°[4]
Hexol bromocamphorsulphonate 2640°[5]
All values are given in units of deg dm−1cm3 g−1

Optical rotation is measured with an instrument called a polarimeter. There is a linear relationship between the observed rotation and the concentration of optically active compound in the sample for any wavelength. The relationship between the observed rotation and the wavelength of light used is not linear. The form of the equation used to calculate specific rotation varies slightly depending on the nature of the sample.

### Solutions and mixtures

$[\alpha]_\lambda^T = \frac{ \alpha}{l \times c}$

In this equation, α (Greek letter "alpha") is the measured rotation in degrees, l is the path length in decimeters, c is the concentration in g/mL, T is the temperature at which the measurement was taken (in degrees Celsius), and λ is the wavelength in nanometers.[6]

For practical and historical reasons, concentrations are often reported in units of g/100mL. In this case, a correction factor in the numerator is necessary:[7]:248[8]:123

$[\alpha]_\lambda^T = \frac{ 100 \times \alpha}{l \times c}$

When using this equation, the concentration and the solvent may be provided in parentheses after the rotation. The rotation is reported using degrees, and no units of concentration are given (it is assumed to be g/100mL). The sign of the rotation (+ or −) is always given. If the wavelength of the light used is 589 nanometer (the sodium D line), the symbol “D” is used. If the temperature is omitted, it is assumed to be at standard room temperature (20 °C).

For example, the specific rotation of a compound would be reported in the scientific literature as:[9]

$[\alpha]_D^{20} +6.2$° (c 1.00, EtOH)

### Pure liquids

For a pure liquid, the mass concentration of that liquid is equivalent to the mass density. Therefore d or ρ (Greek letter "rho"), the density of the liquid in g/mL, is presented in this form of the equation instead of c.

$[\alpha]_\lambda^T = \frac{\alpha}{l \times \rho}$

The term neat may be used to indicate a pure liquid, and the density of the liquid reported. For example, the specific rotation of trans-(−)-(2S,3S)-2,3-dimethyloxirane would be reported as follows:[10]

$[\alpha]_D^{25} -58.8$° (neat), $d_4^{25} = 0.7998$

### Solids

Variation in specific rotation of quartz with wavelength[11]
Wavelength (nm) [α]D20
407.9 48.112
435.8 41.546
480.0 33.674
546.1 25.535
589.3 21.726
633.0 18.690
730.7 13.830
1084.8 6.063
1141.2 5.450
1152.6 5.338
1177.0 5.108

As specific rotation experiments are often performed in quartz cells, knowing the specific rotation of quartz itself is important to obtain accurate measurements for the sample in question. (This is true, but only amounts to WP:Synthesis unless a WP:RS is given.)

#### Normal quartz plate

In the field of saccharimetry, a normal quartz plate has replaced the normal sugar solution as a reference standard. The normal sugar solution contains 26 g sucrose in 100 ml water and has a specific rotation ([α]D20) of 66.529°, or 100 °S on the International Sugar Scale. The thickness of the normal quartz plate is between 1.5934−1.5940 mm.[12]

#### Thin films

The specific rotation of a thin film may be measured by treating the film as a thin plate. The film is first cast on an optically transparent and non-rotating material such as glass, and the thickness (path length) of the film measured using a tool such as a micrometer.[13]

#### Powders and suspensions

Suspensions of crystalline solids and polymers are stirred constantly during measurement in a specially designed quartz cell. Powders are sieved to a suitable grain size,[14] and suspended in a liquid with a refractive index equal to that of the powder.[13] The differences in specific rotation between dissolved and suspended samples may demonstrate additional rotation due to the assembly of molecules in the solid phase,[13] or due to the secondary structure of molecules such as RNA.[14]

### Gases

The specific rotations of gaseous samples are used to illustrate and quantify solvent effects by comparison to the measurement obtained in solution.[15]

Specific rotation [α]25 for pinene and its derivatives[15]
Compound Gas phase Cyclohexane solution
633 nm 355 nm 633 nm 355 nm
(1R,5R)-(+)-pinene 48 192 46 165
(1S,5S)-(−)-pinene −12 71 −17 22
(1S)-(−)-cis-pinane 5 −63 19 −88

### References to be incorporated:

Some of them refer to the specific rotation explicitly, some refer simply to "optical rotation" but then present [α]D or [α]T values.

• [13] Vogl. The specific rotation of polymers is measured in solution, suspension and as thin films. Suspensions are stirred during measurements in a quartz cell, the suspending medium is chosen to match the refractive index of the suspended solid. Solutions measured with a path length of 10 cm. Thickness of polymer films measured using a micrometer.
• [10] The phrase neat is used in place of the concentration remark for pure liquids. $[\alpha]_\lambda^T = \frac{\alpha}{l \times d}$ for neat liquids and solids. Solutions are described as in the article, the correction factor, for practical reasons. "Rather than stating the correct CGS units it is now agreed that any reference to a dimension is avoided." Includes recommendations for optical purity calculations and information on ORD. Gases mentioned.
• [11] Crystalline quartz. Secondary source on specific rotation at various wavelengths (ORD). $[\alpha] = \frac{10^4 \times \alpha}{d \times C}$ d in mm, C in g/ 100 cm3. Rest of info is on Faraday effect.
• [12] Very detailed and extremely long. Focuses on saccharimetry. Describes the normal sugar solution, and the normal quartz plate. Also reccommends using the mercury line instead of the sodium D line for measurements, for various reasons.
• [14] Vogl. Includes diagram of apparatus for the measurement of the specific rotations of suspensions. Describes the sieving procedure. Differences between solid state and dissolved RNA, for example.
• personal essay? Otto Vogl is quite prolific in this area, or so it seems. A review by him could be ideal.
• [16] The International Pharmacopoeia tends to muddy the waters with the introduction of several variables that appear to cancel down to concentration, albeit with correction factors and unit changes thrown in to the bargain. "[C]alculated with reference to a layer 100 mm [1 dm] thick, and divided by the relative density (specific gravity)..." $[\alpha]^t_\lambda = \frac{10000 a}{l c} = \frac{10000 a}{l d p}$ l in mm, c in g/ 100ml, d is relative density, p in g/ 100g (That makes dp g/100ml). Also mentions molar rotation and SI units.
• [17] Dispenses with much of the bittiness of the Pharmacopoeia, while also swapping wavelength and temperature, i.e. $[\alpha]^\lambda_t$ . Detailed recommended procedure and error reduction included.
• [18] And then, a phycics book comes along and dispenses with the standards used in chemistry and pharmacy (and it is likely other physics books do the same). Introduces in a form similar to the Beer-Lambert-Bouger Law, and explains that additivity may apply, but secondary effects cause issues with mixtures. $\theta = \alpha_\lambda C l$ for solutions, $\theta = \alpha_\lambda l$ for solids and "homogeneous liquids".
• [15] Gas phase measurements, and comparison with solution- used to demonstrate solvent effects on specific rotation. Temperature dependance of various terpene derivatives.

### Dealing with large and small rotations

If a compound has a very large specific rotation or a sample is very concentrated, the actual rotation of the sample may be larger than 180°, and so a single polarimeter measurement cannot detect when this has happened (for example, the values +270° and −90° are not distinguishable, nor are the values 361° and 1°). In these cases, measuring the rotation at several different concentrations allows one to determine the true value. Another method would be to use shorter path-lengths to perform the measurements.

In cases of very small or very large angles, one can also use the variation of specific rotation with wavelength to facilitate measurement. Switching wavelength is particularly useful when the angle is small. Many polarimeters are equipped with a mercury lamp (in addition to the sodium lamp) for this purpose.

# Specific rotation: Current article

In chemistry, specific rotation ([α]) is a property of a chiral chemical compound.[7]:244 It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sample of a compound in solution.[19]:2-65 Compounds which rotate light clockwise are said to be dextrorotary, and correspond with positive specific rotation values, while compounds which rotate light counterclockwise are said to be levorotary, and correspond with negative values.[7]:245 If a compound is able to rotate plane-polarized light, it is said to be “optically active”.

Specific rotation is an intensive property, distinguishing it from the more general phenomenon of optical rotation. As such, the observed rotation (α) of a sample of a compound can be used to quantify the enantiomeric excess of that compound, provided that the specific rotation ([α]) for the enantiopure compound is known. The variance of specific rotation with wavelength—a phenomenon known as optical rotatory dispersion—can be used to find the absolute configuration of a molecule.[8]:124 The concentration of bulk sugar solutions is sometimes determined by comparison of the observed optical rotation with the known specific rotation.

## Definition

The CRC Handbook of Chemistry and Physics defines specific rotation as:

For an optically active substance, defined by [α]θλ = α/γl, where α is the angle through which plane polarized light is rotated by a solution of mass concentration γ and path length l. Here θ is the Celsius temperature and λ the wavelength of the light at which the measurement is carried out.[19]

Although the formal unit for specific rotation values is deg mL g−1 dm−1, values for specific rotation are typically reported in units of degrees.[20] These values should always be accompanied by information about the temperature, solvent, concentration, and wavelength of light used, as all of these variables can affect the observed rotation. As noted above, temperature and wavelength are frequently reported as a superscript and subscript, respectively, while the solvent and concentration are reported parenthetically, or omitted entirely. Unless stated otherwise, path length is assumed to be one decimeter,[21] and concentration is assumed to be one gram per milliliter.[citation needed]

## Measurement

Examples
Compound name [α]D20
(S)-2-Bromobutane +23.1°
(R)-2-Bromobutane −23.1°
D-Fructose −92°[1]
D-Glucose +52.7°[1]
D-Sucrose +66.37°[1]
D-Lactose +52.3°[1]
Camphor +44.26°[1]
Cholesterol −31.5°[1]
Taxol A −49°[22]
Penicillin V +223°[23]
(+)-Cavicularin +168.2°[24]
Hexol bromocamphorsulphonate 2640°[25]
All values are given in units of deg dm−1cm3 g−1

Optical rotation is measured with an instrument called a polarimeter. There is a linear relationship between the observed rotation and the concentration of optically active compound in the sample. There is a nonlinear relationship between the observed rotation and the wavelength of light used. Specific rotation is calculated using either of two equations, depending on whether the sample is a pure chemical to be tested or that chemical dissolved in solution.

### For pure liquids

This equation is used:

$[\alpha]_\lambda^T = \frac{\alpha}{l \times \rho}$

In this equation, α (Greek letter "alpha") is the measured rotation in degrees, l is the path length in decimeters, and ρ (Greek letter "rho") is the density of the liquid in g/mL, for a sample at a temperature T (given in degrees Celsius) and wavelength λ (in nanometers). If the wavelength of the light used is 589 nanometers (the sodium D line), the symbol “D” is used. The sign of the rotation (+ or −) is always given.

$[\alpha]_D^{20} +6.2$°

### For solutions

For solutions, a slightly different equation is used:

$[\alpha]_\lambda^T = \frac{ \alpha}{l \times c}$

In this equation, α (Greek letter "alpha") is the measured rotation in degrees, l is the path length in decimeters, c is the concentration in g/mL, T is the temperature at which the measurement was taken (in degrees Celsius), and λ is the wavelength in nanometers.[6]

For practical and historical reasons, concentrations are often reported in units of g/100mL. In this case, a correction factor in the numerator is necessary:[7]:248[8]:123

$[\alpha]_\lambda^T = \frac{ 100 \times \alpha}{l \times c}$

When using this equation, the concentration and the solvent may be provided in parentheses after the rotation. The rotation is reported using degrees, and no units of concentration are given (it is assumed to be g/100mL). The sign of the rotation (+ or −) is always given. If the wavelength of the light used is 589 nanometer (the sodium D line), the symbol “D” is used. If the temperature is omitted, it is assumed to be at standard room temperature (20 °C).

For example, the specific rotation of a compound would be reported in the scientific literature as:[26]

$[\alpha]_D^{20} +6.2$° (c 1.00, EtOH)

### Dealing with large and small rotations

If a compound has a very large specific rotation or a sample is very concentrated, the actual rotation of the sample may be larger than 180°, and so a single polarimeter measurement cannot detect when this has happened (for example, the values +270° and −90° are not distinguishable, nor are the values 361° and 1°). In these cases, measuring the rotation at several different concentrations allows one to determine the true value. Another method would be to use shorter path-lengths to perform the measurements.

In cases of very small or very large angles, one can also use the variation of specific rotation with wavelength to facilitate measurement. Switching wavelength is particularly useful when the angle is small. Many polarimeters are equipped with a mercury lamp (in addition to the sodium lamp) for this purpose.

## Applications

### Enantiomeric excess

If the specific rotation of a pure chiral compound is known, it is possible to use the observed rotation to determine the enantiomeric excess (ee), or "optical purity", of a sample of the compound, by using the formula:[8]:124

$ee(\%) = \frac{\alpha_\text{obs} \times 100}{[\alpha]_\lambda}$

For example, if a sample of bromobutane measured under standard conditions has an observed rotation of −9.2°, this indicates that the net effect is due to (9.2°/23.1°)(100%) = 40% of the R enantiomer. The remainder of the sample is a racemic mixture of the enantiomers (30% R and 30% S), which has no net contribution to the observed rotation. The enantiomeric excess is 40%; the total concentration of R is 70%.

However, in practice the utility of this method is limited, as the presence of small amounts of highly rotating impurities can greatly affect the rotation of a given sample. Moreover, the optical rotation of a compound may be non-linearly dependent on its enantiomeric excess because of aggregation in solution. For these reasons other methods of determining the enantiomeric ratio, such as gas chromatography or HPLC with a chiral column, are generally preferred.

### Absolute configuration

The variation of specific rotation with wavelength is called optical rotatory dispersion (ORD). ORD can be used in conjunction with computational methods to determine the absolute configuration of certain compounds.[27]

## References

1. R. C. Weast (1974). Handbook of Chemistry and Physics (55th ed.). CRC Press.
2. ^ "The Merck Index Online: Paclitaxel". Royal Society of Chemistry. Retrieved 30 June 2014.
3. ^ "The Merck Index Online: Penicillin V". Royal Society of Chemistry. Retrieved 30 June 2014.
4. ^ M. Toyota et. al. (1 July 1996). "(+)-Cavicularin: A novel optically active cyclic bibenzyl-dihydrophenanthrene derivative from the liverwort Cavicularia densa Steph". Tetrahedron Letters (Elsevier) 37 (27): 4745–4748. doi:10.1016/0040-4039(96)00956-2. Retrieved 26 June 2014.
5. ^ A. Werner "Über mehrkernige Metallammoniake" Chem. Ber. 1907, volume 40, pp. 2103–2125. doi:10.1002/cber.190704002126
6. ^ a b P. Y. Bruice (2011). Organic Chemistry (Sixth ed.). Prentice Hall. pp. 209–210.
7. ^ a b c d Vogel, Arthur I. (1996). Vogel's textbook of practical organic chemistry (5th ed. ed.). Harlow: Longman. ISBN 0582462363.
8. ^ a b c d F. A. Carey; R. J. Sundberg (2007). Advanced Organic Chemistry, Part A: Structure and Mechanisms (Fifth ed.). Springer. doi:10.1007/978-0-387-44899-2.
9. ^ Coghill, Anne M.; Garson, Lorrin R. (2006). The ACS style guide (3rd ed.). Washington, D.C.: American Chemical Society. p. 274. doi:10.1021/bk-2006-STYG.ch013. ISBN 978-0-8412-3999-9.
10. ^ a b Houben-Weyl Methods of Organic Chemistry. E21a Stereoselective Synthesis (Additional and supplementary volumes to the 4th ed.). Georg Thieme Verlag. 14 May 2014. ISBN 9783132195042. Retrieved 30 September 2014. "Rather than stating the correct CGS units it is now agreed that any reference to a dimension is avoided."
11. ^ a b King, R. J.; Raine, K. W. (1995). "2.5.10 Optical rotation". Kaye & Laby (16th ed.). Retrieved 30 September 2014.
12. ^ a b Bates, Frederick; Jackson, Richard F. (June 1916). "Constants of the Quartz-Wedge Saccharimeter and the Specific Rotation of Sucrose". Bulletin of the Bureau of Standards 13: 67–128. doi:10.6028/bulletin.294. Retrieved 30 September 2014. "It has been shown [Bates, Bull. Bur. Standards 2, p. 239, Reprint No. 34 (1906).] by one of us that the so-called yellow-green line, λ = 5461 Å of the mercury spectrum possesses marked advantages over λ = 5892.5 Å as the standard light source for polarimetric work. It is more stable, has a greater intensity, and is far easier to obtain pure at the high intensity required."
13. ^ a b c d Bartuš, Ján; Vogl, Otto (January 1994). "Optical Activity Measurements in Solids 5. Optical Rotation of Natural Polymers". Polymer International 33 (1): 25–36. doi:10.1002/pi.1994.210330104. Retrieved 30 September 2014. "The optical activity of suspensions was measured in a rectangular quartz cell with a path length of 10mm with stirring. The speed of the rotation of the magnetic stirring bar was 700 & 50rpm. The results were recorded using a Linear 1200 recorder. The procedure for accurate measurements was described in detail earlier. [Bartus, J., & Vogl, O., Polymer Bull., 28 (1992) 203.] The optical activity of polymer solutions was measured in a glass cell with a path length of 10cm. The polymer solutions in the appropriate solvents were prepared in 10 ml volumetric flasks. Polymer films were cast on a glass plate from concentrated solutions. The thickness of the films was measured with a micrometer and the optical activity was recorded after mounting of films in a cell compartment of the polarimeter."
14. ^ a b c Vogl, Otto; Bartus, Jan; Murdoch, Joseph R. (April 1990). "Solid-state, optical-rotation measurements on macromolecules using powder-suspensions". Monatshefte für Chemie 121 (4): 311–316. doi:10.1007/BF00808933. Retrieved 30 September 2014.
15. ^ a b c Wiberg, Kenneth B.; Wang, Yi-gui; Murphy, Michael J.; Vaccaro, Patrick H. (2004). "Temperature Dependence of Optical Rotation: α-Pinene, β-Pinene, Pinane, Camphene, Camphor and Fenchone". J. Phys. Chem. A 108 (26): 5559. doi:10.1021/jp040085g.
16. ^ The International Pharmacopoeia 1 (4th ed.). World Health Organization. 2006. pp. 1151–1154. ISBN 924156301X. Retrieved 30 September 2014.
17. ^ "Application Note: Determination of Optical Rotation and Specific Rotation". Anton Paar. 21 July 2011. Retrieved 30 September 2014.
18. ^ Wagh, Sanjay Moreshwar; Deshpande, Dilip Abasaheb (19 November 2012). "5.12 Phenomenon of Optical Rotation". Essentials of Physics 2. PHI Learning. pp. 187–189. ISBN 9788120346437. Retrieved 30 September 2014.
19. ^ a b Haynes, William M. (2014). CRC Handbook of Chemistry and Physics. (95th ed.). CRC Press. ISBN 9781482208672.
20. ^ Mohrig, J. R.; Hammond, C. N.; Schatz, P. F. (2010). Techniques in Organic Chemistry (Third ed.). W. H. Freeman and Company. pp. 209–210.
21. ^ Carroll, Felix A. (2010). Perspectives on structure and mechanism in organic chemistry (2nd ed.). Hoboken, N.J.: John Wiley. p. 87. ISBN 978-0-470-27610-5.
22. ^ "The Merck Index Online: Paclitaxel". Royal Society of Chemistry. Retrieved 30 June 2014.
23. ^ "The Merck Index Online: Penicillin V". Royal Society of Chemistry. Retrieved 30 June 2014.
24. ^ M. Toyota et. al. (1 July 1996). "(+)-Cavicularin: A novel optically active cyclic bibenzyl-dihydrophenanthrene derivative from the liverwort Cavicularia densa Steph". Tetrahedron Letters (Elsevier) 37 (27): 4745–4748. doi:10.1016/0040-4039(96)00956-2. Retrieved 26 June 2014.
25. ^ A. Werner "Über mehrkernige Metallammoniake" Chem. Ber. 1907, volume 40, pp. 2103–2125. doi:10.1002/cber.190704002126
26. ^ Coghill, Anne M.; Garson, Lorrin R. (2006). The ACS style guide (3rd ed.). Washington, D.C.: American Chemical Society. p. 274. doi:10.1021/bk-2006-STYG.ch013. ISBN 978-0-8412-3999-9.
27. ^ Polavarapu, Prasad L. "Optical rotation: Recent advances in determining the absolute configuration". Chirality 14 (10): 768–781. doi:10.1002/chir.10145.