163
6 Electronic Circular dichroism Spectroscopy in Structural Analysis …
the developement of time-dependent density functional theory [22–27] (the timedependent hartree-Fock approach, developed earlier, is generally not suitable for
handling excited states and the wave function methods including electron correlation are too costly in terms of computational resources), and soon afterwards they
have been carried out for molecules of biological significance, including amino
acids [28, 29], and for small peptides [30–32].
Nowadays, the majority of ab initio quantum chemical calculations of the Cd
spectra are carried out by means of dFt. there are two main factors influencing
the quality of the results of such calculations: a selection of a basis set and of an
exchange-correlation functional. While there is a general consensus that the basis
set suitable for calculations of the Cd spectra should be similarly built as for other
optical properties (a balanced valenced set and diffuse functions are necessary),
the choice of an exchange-correlation functional is more problematic, especially
for transitions to diffuse Rydberg states. Some authors advocate the use of rangeseparated functionals for the purpose [33], but the issue is still debated. Assuring
gauge invariance, a major problem in calculations of the optical rotation, is a not a
critical issue in the case of Cd, since the results obtained using the velocity gauge
and the length gauge with and without gauge-including orbital are very similar [34].
A lot of effort is devoted to extending the range of systems tractable by means
of ab initio methods (for example through developement of linear scaling methods,
and adaptation of gPu computing for the purpose). Still, most of the chiral molecules of biochemical and biological interest are far too large to be handled by means
of ab initio quantum chemical calculations. thus, at the present, the only feasible
method to utilize quantum chemistry in calculations of ECd spectra for sizable
peptides is to carry out the calculations for one chromophore unit and to simulate
the final spectrum by treating the biopolymer as an assemble of chromophores and
transfering the optical properties calculated for individual chromophores to this
assemble [35, 36]. this can be done by means of several different methods. the
most approximate is the dipole interaction model [37], which considers individual
atoms and the amide chromophore to be point dipole oscillators. In the presence of
an electric field, they interact through mutually induced dipole moments. Another
approach to calculating protein Cd is the matrix method [38, 39], where a hamiltonian matrix is constructed assuming the protein consists of non-interacting chromophoric groups. this matrix is then diagonalized by a unitary transformation, which
describes the transition from a non-interacting regime to an interacting regime.
using this transformation, the properties calculated for individual chromophores
(for example amide groups) are transformed and the Cd of the protein is computed.
In some cases, meaningful information can even be obtained from a simplified
exciton coupling approach [40–42], in which the rotatory strength of the coupled
system is calculated from the electric dipole transition moments and the position
vector between them.
most of the simulations of the Cd spectra of proteins are focused on modelling
of interacting amide chromphores. An isolated amide chromphore is usually approximated by N-methylacetamide (see for example Refs. 43–45), and a number
of succesful simulations of the Cd spectra of peptides have been carried out by
6 Electronic Circular dichroism Spectroscopy in Structural Analysis …
the developement of time-dependent density functional theory [22–27] (the timedependent hartree-Fock approach, developed earlier, is generally not suitable for
handling excited states and the wave function methods including electron correlation are too costly in terms of computational resources), and soon afterwards they
have been carried out for molecules of biological significance, including amino
acids [28, 29], and for small peptides [30–32].
Nowadays, the majority of ab initio quantum chemical calculations of the Cd
spectra are carried out by means of dFt. there are two main factors influencing
the quality of the results of such calculations: a selection of a basis set and of an
exchange-correlation functional. While there is a general consensus that the basis
set suitable for calculations of the Cd spectra should be similarly built as for other
optical properties (a balanced valenced set and diffuse functions are necessary),
the choice of an exchange-correlation functional is more problematic, especially
for transitions to diffuse Rydberg states. Some authors advocate the use of rangeseparated functionals for the purpose [33], but the issue is still debated. Assuring
gauge invariance, a major problem in calculations of the optical rotation, is a not a
critical issue in the case of Cd, since the results obtained using the velocity gauge
and the length gauge with and without gauge-including orbital are very similar [34].
A lot of effort is devoted to extending the range of systems tractable by means
of ab initio methods (for example through developement of linear scaling methods,
and adaptation of gPu computing for the purpose). Still, most of the chiral molecules of biochemical and biological interest are far too large to be handled by means
of ab initio quantum chemical calculations. thus, at the present, the only feasible
method to utilize quantum chemistry in calculations of ECd spectra for sizable
peptides is to carry out the calculations for one chromophore unit and to simulate
the final spectrum by treating the biopolymer as an assemble of chromophores and
transfering the optical properties calculated for individual chromophores to this
assemble [35, 36]. this can be done by means of several different methods. the
most approximate is the dipole interaction model [37], which considers individual
atoms and the amide chromophore to be point dipole oscillators. In the presence of
an electric field, they interact through mutually induced dipole moments. Another
approach to calculating protein Cd is the matrix method [38, 39], where a hamiltonian matrix is constructed assuming the protein consists of non-interacting chromophoric groups. this matrix is then diagonalized by a unitary transformation, which
describes the transition from a non-interacting regime to an interacting regime.
using this transformation, the properties calculated for individual chromophores
(for example amide groups) are transformed and the Cd of the protein is computed.
In some cases, meaningful information can even be obtained from a simplified
exciton coupling approach [40–42], in which the rotatory strength of the coupled
system is calculated from the electric dipole transition moments and the position
vector between them.
most of the simulations of the Cd spectra of proteins are focused on modelling
of interacting amide chromphores. An isolated amide chromphore is usually approximated by N-methylacetamide (see for example Refs. 43–45), and a number
of succesful simulations of the Cd spectra of peptides have been carried out by