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Chapter 7
Molecular and quantum mechanics
in drug designing
If Quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet
– Neil Bohr
7.1 Introduction
Computer-aided drug designing (CADD) has become an integral part of any drug discov-
ery process [1, 2]. Not only does it reduce the cost and time of the research but it also
provides us valuable insights into the structural, physical, and chemical properties of
potential drug molecules. Molecular mechanics (MM) and quantum mechanics (QM)
play a pivotal role in the drug discovery process, revolutionizing the way new pharma-
ceuticals are designed and developed [3, 4]. MM provides insights into the structural
properties and interactions of molecules, while QM delves into the fundamental behav-
iors of atoms and subatomic particles [5, 6]. In drug designing, MM aids in simulating
the interactions between molecules, enabling researchers to predict how a potential
drug compound interacts with its target protein or receptor [7]. This information guides
the modification of molecular structures to enhance binding affinity and specificity,
thereby increasing the chances of therapeutic success. Additionally, MM simulations
elucidate the stability of drug molecules and their potential side effects, critical for opti-
mizing drug candidates [8, 9]. QM, on the other hand, delves into the electronic struc-
ture of molecules, offering a deep understanding of molecular behavior at the atomic
level [10]. QM calculations provide valuable insights into molecular energetics, reaction
mechanisms, and electronic properties, aiding in the prediction of how a drug molecule
undergoes chemical transformations within the body. This knowledge is indispensable
for designing drugs with desired reactivity and metabolic pathways [11, 12].
The synergy between MM and QM expedites the drug discovery process by guiding
the rational design of compounds with improved pharmacological properties, reduced
toxicity, and enhanced efficacy [13]. By providing a comprehensive understanding of mo-
lecular interactions and reactivity, these computational tools accelerate the identification
of promising drug candidates, offering a more efficient and cost-effective approach to rev-
olutionizing healthcare and advancing the field of pharmaceutical research [14]. Mechan-
ics is a simple terminology of physics that deals with the study of the motion of objects
and their subsequent effect on the environment in which they are present [15]. In the
context of CADD, it is the application of principles of mechanics on potential drug candi-
dates and target receptor molecules to understand their different aspects, which include:
– Different conformations of drug molecules
– Structure and conformations of target receptor molecules
https://doi.org/10.1515/9783111434858-007
– Drug-receptor binding energy calculations
– Calculations of the chemical and physical properties of molecules
– The most energetically stable molecule under different conditions
– Effect of solvents on the drug-receptor interactions
– Other calculations that involve energy terms of the molecules, including drug and
target receptor
Molecular modeling is the combined terminology used in CADD for these types of
studies involving the principles of mechanics (Fig. 7.1). The two most widely used ap-
proaches of molecular modeling for the purpose are MM and QM.
7.2 Molecular mechanics (MM) in drug design
MM is the simpler approach which employs the use of “classical Newtonian mechan-
ics” principles for all the calculations [16]. In this approach, any molecule, whether
drug or receptor, is treated as made up of atoms, which are joined by various bonds
that exhibit spring-like properties [17]. Another major assumption in the MM ap-
Fig. 7.1: Different molecular modeling approaches used in computer-aided drug designing (CADD).
140 Chapter 7 Molecular and quantum mechanics in drug designing
proach is that it considers the additive nature of different parameters employed in
the calculations [18]. This is of concern, particularly, when calculating the potential
energy of any molecule. Total potential energy possessed by any molecule, whether
drug or target receptor, is the summation of different individual energy terms of the
molecule, namely stretching energy, bending energy, torsion energy, an d the non-
bonding energy parameters (Fig. 7.2) [19]. Mathematically this total energy possessed
by the molecule can be expressed by the following equation:
E
total
= Σ E
bend
+ Σ E
str
+ Σ E
torsion
+ Σ E
nonbonding
(7:1)
where E
total
is the total potential energy of the molecule, ΣE
bend
, ΣE
str
, ΣE
torsion
,and
ΣE
nonbonding
are individual energy terms due to stretching, bending, torsion, and non-
bonding interactions, respectively, of the molecule.
7.2.1 Stretching and bending energy
The change in stretching energy in the molecule is repr esented by ΣE
str
of equation
(7.1) and denotes the changes occurring due to the changes in the bond length of the
molecules, whereas, ΣE
bend
of equation (7.1) represents the bending energy changes
due to changes in the bond angles inside the molecule. Both of these parameters fol-
low the simple Hooke’s law and are considered to follow the simple harmonic motion.
Mathematically, these are calculated by using the following two equations:
Fig. 7.2: Different types of interactions occurring inside a molecule that constitute its potential energy.
7.2 Molecular mechanics (MM) in drug design 141
Σ E
str
= Σ k
b
ðr − r
0
Þ
2
(7:2)
Σ E
bend
= Σ k
θ
ðθ − θ
0
Þ
2
(7:3)
where k
b
and k
θ
are the force constants of Hook’s law, r is the current bond length, r
0
is the initial bond length, θ is the current bond angle, and θ
0
is the initial bond angle.
Both of the above equations employed are quadratic in nature and a parabola is ob-
tained when the energy is plotted against the bond angles or bond lengths (Fig. 7.3). It is
important to note that the energy changes due to bond stretching are quite large and can-
not be calculated accurately using simple Hooke’s law assumptions. A more accurate way
ofcalculatingthisenergyisthroughMorsepotential by using the following equation:
Σ E
str
= Σ D
e
ð1 − e
− α r− r
0
ðÞ
Þ
2
(7:4)
where D
e
and α are constants defining the depth and width of the potential well, re-
spectively, when a plot is plotted between potential and bond length (Fig. 7.4).
7.2.2 Torsion energy
Torsion energy is represented by ΣE
torsion
in equation (7.1) and it comes into play
when the molecule contains more than three atoms. These energies play a role due to
the rotation of bonds. To understand this, consider an example of n-butane; when we
rotate the molecule along the carbon–carbon bond we obtain different conformations,
which differ in the energy (Fig. 7.5). The most stable conformation in terms of energy
is the anti-form having a dihedral angle between the CH
3
–CH
3
groups of 180°. Simi-
larly fully eclipsed conformation will have a dihedral angle of 0° between the CH
3
–
Fig. 7.3: The energy plot diagram between the energy of the molecule and the bond angle inside the
molecule.
142 Chapter 7 Molecular and quantum mechanics in drug designing
CH
3
groups and is the least stable in energy terms due to high repulsion between the
bulky methyl groups. Likewise, other conformations having different energies exist
between these two extreme conformations.
Mathematically, this energy term is calculated by using the following equation:
Σ E
torsion
= Σ A½1 + cos nτ + ϕðÞ (7:5)
where A is the constant term, τ is the current dihedral angle, and ϕ is the initial dihe-
dral angle of the molecule.
7.2.3 Nonbonding energy terms
Nonbonding energy terms is represented by ΣE
nonbonding
in equation (7.1). It depicts
the changes in the energy due to electrostatic, Van der Waals, and hydrogen-bonding
type of interactions inside the molecule. Mathematically, it can be denoted by the fol-
lowing equation:
Σ E
nonbonding
= Σ E
electrostatic
+ Σ E
Van der Waals
+ Σ E
H‐bond
(7:6)
To calculate total nonbonding energy changes in a molecule, electrostatic, Van der
Waals, and H-bonding type energy changes are calculated separately and then added.
The electrostatic energy changes in the molecule can be calculated through Coulomb’s
law and can be calculated using the following equation:
Fig. 7.4: The plot between the potential energy of the molecule and the interatomic distance inside the
molecule.
7.2 Molecular mechanics (MM) in drug design 143
Fig. 7.5: The energy plot for the energy of the different conformations of the n-butane.
144 Chapter 7 Molecular and quantum mechanics in drug designing
ΣE
electrostatic
= Σðq
1
q
2
=ϵ r
12
Þ (7:7)
where q
1
and q
2
are individual charges on atom 1 and atom 2, r
12
is the distance between
these two atoms, and ϵ represents the dielectric constant. Similarly, the Van der Waals
interactions can be calculated from the following equation of Lennard-Jones potential:
Σ E
Van der Waals
= Σ −A
12
=r
6
12
+ B
12
=r
12
12
(7:8)
where A and B aretheconstantsknownasthedegreeofstickinessanddegreeof
hardness, respectively, and r
12
represents the distance between atoms 1 and atom 2.
H-bonding type of interaction also plays an important role in the nonbonding interac-
tions and can be calculated by using the following equation:
Σ E
H‐bond
= Σ A
12
=r
12
12
− B
12
=r
10
12
(7:9)
where r
12
and constants A and B represent the same meaning as discussed above in
the Lennard-Jones potential equation (7.8).
7.2.4 Cross-bonding energy terms
A single molecule consists of many atoms connected through several bonds. In these
atoms stretching, bending, and rotation of the bonds occurs simultaneously inside the
molecule (Fig. 7.6). Therefore, for calculating the energy of the whole molecule, it is
indispensable to consider these cross interactions separately and energy related to
them should be calculated separately. Mathematically they can be calculated by using
the following equations:
Σ E
str−str
= Σ k
12
r
1
− r
10
ðÞðr
2
− r
20
Þ (7:10)
Σ E
str−bend
= Σ k
12
r
1
− r
10
ðÞðθ
2
− θ
20
Þ (7:11)
Σ E
bend−bend
= Σ k
12
θ
1
− θ
10
ðÞθ
2
− θ
20
ðÞ (7:12)
where r
1
and r
2
represent the current bond length and r
10
and r
20
represent the initial
bond length between atoms, respectively. θ
1
and θ
2
are current bond angles and θ
10
and θ
20
are their initial bond angles, respectively.
7.2.5 Concept of force field in molecular mechanics (MM)
The concept of a force field within MM is a fundamental tool that enables the simula-
tion and prediction of molecular interactions and behaviors. A force field is a set of
mathematical functions and parameters that describes the energy and forces acting
between atoms and molecules in a system. It guides the computation of potential energy
7.2 Molecular mechanics (MM) in drug design 145
surfaces and molecular dynamics trajectories, offering insights into how molecules in-
teract and change over time. Force fields account for various types of interactions, in-
cluding bond stretching, angle bending, dihedral rotation, Van der Waals forces, and
electrostatic interactions. These interactions collectively shape the overall energy land-
scape of a molecule, influencing its stability, conformational changes, and binding affin-
ities. In drug discovery, force fields are employed to model the interactions between
drug candidates and their target proteins or receptors. By calculating the potential en-
ergy of different conformations and configurations, researchers can predict the most
stable and energetically favorable binding modes. This information guides structural
modifications of drug candidates to enhance their binding affinity and selectivity. How-
ever, it is important to note that force fields have limitations, such as their empirical
nature and potential inaccuracies in capturing specific interactions. Therefore, they are
often parameterized and validated against experimental data to improve their accu-
racy. In essence, the concept of a force field in MM serves as a bridge between theoreti-
cal calculations and real-world molecular behaviors, facilitating the rational design of
drug molecules with the desired properties for effective and targeted therapies.
While studying CADD approaches, especially structure-based drug designing, the
force field is one of the most common terms we come across. For making any sort of
calculation in the MM we must be familiar with the meaning of force field. The sim-
plest definition of the force field is that it is a certain set of defined formulae or func-
tions that are used for the calculations in MM. At present, there are numerous force
fields available for computational scientists and each of them has its own algorithm
for the energy calculation of the molecules. The choice of force fields to be employed
depends upon the type of computational study being conducted, that is, for the energy
minimization of a drug molecule; the choice of force field will be different from that
for the force field employed for the molecular dynamics simulations. Force fields like
Fig. 7.6: Different types of the cross-bonding energy terms inside the molecule, that is,
stretching–stretching, stretching–bending, and stretching–bending interactions.
146 Chapter 7 Molecular and quantum mechanics in drug designing
CHARMM, AMBER, OPLS, MMFF, Dreiding, and UFF are a few of the most commonly
employed force fields in MM.
Classification of the force fields is done based on their development. The first gen-
eration of the force fields, also known as class I force fields, are the initial force fields
that were developed and they use the basic equation (7.1) mentioned above for the
calculations of energy. The second generation of the force fields, also known as class
II force fields, are the ones that are more advanced than class I and also incorporate
the cross-binding energy terms for the energy calculations of the molecule. The latest
in this class is the class III force fields, which were developed in the 1990s. These force
fields also take into account the electronic polarization factors while calculating the
energy of the molecules. Examples of each class of the force field are given in Tab. 7.1.
With time, continuous evolution is seen in the development of various force fields;
some of the class I and II force fields like OPLS, CHARMM, MM, and AMBER have also
introduced their versions that take into account the phenomenon of polarization.
7.3 Quantum mechanics (QM) in drug designing
QM has emerged as a transformative force in the realm of drug designing, enabling a
deeper understanding of molecular interactions and behaviors at the atomic and sub-
atomic levels [20]. QM, a fundamental theory in physics, describes the behavior of matter
and energy at the smallest scales, providing insights into the electronic structure and
properties of molecules [21]. In drug designing, QM calculations offer unparalleled preci-
sion in predicting molecular properties, reaction mechanisms, and energetics [22]. By sim-
ulating the quantum behavior of electrons and nuclei within molecules, QM allows
researchers to explore intricate details of chemical reactions, such as bond formation and
breaking, which are crucial in drug metabolism and interactions with target proteins. QM
approaches enable the accurate computation of electronic energies, helping the determi-
nation of molecular stability and reactivity. Additionally, QM studies shed light on the
electronic properties of drug candidates, aiding in the identification of electron-rich or
Tab. 7.1: Classification of various force fields applied in molecular mechanics.
Classification of force fields
S. no. Types of force field Examples
Class I force fields AMBER, CHARMM, COSMIC, DREIDING, ECEPP, ENCAD, ESFF, GROMOS,
MM, OPLS, PFF, TRIPOS, YETI
Class II force fields CFF, CVFF, EFF, MM,MM,MM, MMFF, QMFF, SDFF, UFF
Class III force fields Allinger’sMM, Accelrys CFF, AMOEBA, DRUDE FF
7.3 Quantum mechanics (QM) in drug designing 147
electron-deficient regions crucial for binding to protein-active sites [23, 24]. Furthermore,
QM computations facilitate the analysis of molecular spectroscopy, offering insights into
vibrational frequencies, electronic transitions, and NMR spectra. These spectroscopic data
aid in characterizing drug structures and interactions. While computationally intensive,
QM provides invaluable insights into the behavior of molecules that cannot be fully cap-
tured by classical methods. By integrating QM calculations with other techniques, such as
MM and molecular dynamics simulations, drug designers can make more informed deci-
sions in optimizing drug candidates for enhanced efficacy and reduced toxicity [25]. In
the QM methodology, electrons and nuclei are considered as separate entities for all the
calculations, which is contrary to the principle of MM. There is no consideration made
for the inclusion of “ch emical bonds” in the QM-based calculations [26]. Basically in the
QM approach, a solution of the time-independent Schrodinger wave equation is sought
for making all the calculations. Solutions of the Schrodinger wave equation provide us
with information regarding the position and energy of the electron in space. Based on the
methodology, QM approaches used in CADD can be divided into ab initio methods, den-
sity functional theory (DFT) calculations, and semiempirical approaches.
7.3.1 Ab initio methods in the CADD
The meaning of the Latin term ab initio is “from the beginning.” Hence, all the calcu-
lations involved in this methodology are derived mathematically from the first princi-
ple and there is no inclusion of any experimental data for the approximation purpose
[27]. All calculations in the ab initio approaches are dependent on the solutions of the
time-independent Schrodinger wave equation:
d
2
dx
2
!
+
d
2
dy
2
!
+
d
2
dz
2
!"#
Ψ + 8π
2
m
E − VðÞ
Ψ
h
2
= 0(7:13)
The above is the simplest depiction of the complex time-independent Schrodinger
wave equation where the [(d
2
/dx
2
)+(d
2
/dy
2
)+(d
2
/dz
2
)] term represents the partial de-
rivative of the particle with respect to all three direction coordinates in the space, Ψ
is the wave function, m is the mass of the particle, E is the total energy of the particle,
V represents its potential energy, and h is the Planck’s constant [28].
Ab initio methods in CADD play a pivotal role in unraveling the intricate molecu-
lar interactions that drive drug discovery. These methods are rooted in QM and offer
an atomistic perspective on molecular behavior, sidestepping empirical parameters.
By solving the Schrödinger equation, ab initio methods provide accurate insights into
electronic structure, energy landscapes, and reaction pathways. They are used to pre-
dict properties critical for drug design, such as binding affinities, reaction energies,
and molecular geometries. Additionally, a b initio methods excel in exploring non-
covalent interactions and transition states, enhancingourunderstandingofdrug-
148 Chapter 7 Molecular and quantum mechanics in drug designing
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