Pertemuan Ke-2 Molekuler Mekanik

Mekanika

Molekuler

Pertemuan ke-2

Pendahuluan

Mekanika molekuler (Molecular Mechanics) adalah pendekatan modeling berdasarkan mekanika klasik
Terminologi yang sama dengan pendekatan ini adalah Force

Field Method

Satuan penyusun (building blocks) dalam metode mekanika molekuler adalah atom, elektron tidak dianggap sebagai partikel individual
Konsekuensinya ikatan antar atom tidak dilihat sebagai hasil penyelesaian persamaan Schrödinger untuk elektron
Informasi tentang ikatan dinyatakan secara eksplisit yang berarti diillustrasikan secara fisik bukan sebagai hasil interaksi elektron valensi
Mekanika molekuler telah terbukti bermanfaat untuk menjelaskan sistem dengan molekul besar atau padatan

Menguraikan Sistem

Deskripsi sistem: apa unit dasar (partikel) yang dipilih, ada berapa banyak?
• Kondisi awal: Dimana posisi partikel
dan bagaimana kecepatannya
Interaksi: Apa bentuk persamaan matematika untuk gaya yang bekerja antar partikel tersebut
Persamaan dinamik: Apa bentuk

Hierarki Satuan Penyusun untuk Mengurai Sistem Kimia

Elektron Atoms Molekul

Nuklei Protons

Makromolekul Neutrons

Pemilihan Satuan Penyusun (Building

Blocks)

Jika memilih inti atom dan elektron sebagai partikel penyusun, kita bisa mengurai atom dan

molekul namun tidak bisa mengurai struktur

internal inti atom

Jika memilih atom sebagai partikel penyusun, kita bisa mengurai struktur molekul namun tidak bisa mengurai distribusi elektron
Jika memilih molekul (asam amino) sebagai partikel penyusun, kita bisa mengurai struktur

overall makromolekul (protein) namun tidak

bisa mengurai pergerakan atom-atom dalam molekul.

Pemilihan Kondisi Awal

Posisi ruang yang lengkap (complete phase space) dari suatu sistem adalah sesuatu yang sangat besar:
Mencakup semua nilai yang mungkin dari posisi dan
kecepatan satu partikel
Kita hanya bisa mengurai sebagian kecil saja dari kondisi ini
Misalnya suatu isomer (struktural atau konformasional) dan reaksi kimia ingin coba diuraikan
Senyawa C

_{6 H}

_{6 memiliki banyak kemungkinan}

spesifik

pada senyawa benzene, maka kondisi awal sistem

Interaksi Partikel dan Persamaan Dinamik

Pada level atomik, interaksi dasar yang bekerja hanya interaksi elektromagnetik
Pada pendekatan Mekanika Molekuler, interaksi antar partikel disusun dalam bentuk parameter yaitu interaksi stretching, bending, torsional, van der Waals dll.
• Persamaan dinamik menjelaskan bagaimana
suatu sistem berubah dengan perubahan waktu, Misal: dengan menggunakan GLBB
kita bisa menjelaskan posisi sistem setelah

₁

₂

�=� � � � � waktu tertentu

Interaksi Fundamental

Name Particles Rang

e (m)

Relative

Strengt

Strong Interaction

Quarks  10 ^- ₁₅

100 Weak Interaction

Quarks, leptons  10 ^- ₁₅ 0.001

Electromagneti c Charged particles



1 Gravitational Mass 

10 ^-40

Keterangan

• Strong interaction adalah gaya yang menahan inti atom

agar tetap utuh walaupun ada tolak menolak antar proton
didalam
Weak interaction gaya yang bertanggung jawab pada
peluruhan inti atom dengan mengkoversi neutron menjadi
proton (-decay)
• Keduanya adalah gaya yang bekerja short range dan hanya
signifikan within the atomic nucleus
Interaksi elektromagnetik dan gravitasional berbanding terbalik dengan jarak partikel
Interaksi elektromagnetik terjadi antara partikel bermuatan
Interaksi gravitasional terjadi antara partikel yang

Pendekatan didalam

Force Field a.k.a

Mekanika Molekuler

Force field menggunakan pendekatan mekanika klasik seperti persamaan Newton untuk mendeskripsikan sistem
Aspek kuantum dan energi elektron ditiadakan/tidak diperhitungkan
Dengan pendekatan klasik, permasalahan direduksi menjadi menentukan energi sistem pada struktur geometri tertentu
Seringkali juga digunakan untuk menentukan geometri
untuk molekul yang paling stabil atau konformasi terbaik
yang melibatkan interkonversi antar konformasi
Untuk keperluan ini perhitungkan diarahkan pada
penentuan energi minima pada potential energy surface

Potential Energy

(Flash info)

Surface

(Flash info)

Definisi

Atom-atom dalam molekul disatukan bersama oleh ikatan kimia
• Saat atom terdistorsi, ikatan akan meregang atau menekuk/
mengkerut yang menyebabkan energi potensial sistem meningkat
• Setelah susunan geometri atom-atom yang baru terbentuk,
molekul berada dalam kondisi stasioner. Pada posisi ini energi sistem tidak dipengaruhi oleh energi kinetik tetapi oleh posisi atom-atom (potensial)
Energi dari molekul merupakan fungsi dari posisi inti, saat inti bergerak, elektron secara cepat akan menyesuaikan
• Hubungan antara energi molekuler dan geometri molekuler
dapat dipetakan menjadi sebuah potential energy surface

Terminologi dalam Mekanika Molekuler

Molekul dalam MM diilustrasikan sebagai ball and

spring dimana atom digambarkan memiliki ukuran

kelembutan

ikatan

panjang

kekakuan

Dasar dari pendekatan FF/MM ini adalah bahwa molekul tersusun atas unit dengan struktur yang serupa hanya berada dalam molekul yang berbeda
• Misalnya semua ikatan ini sama pada molekul apa pun

CH memiliki panjang 1,06 sd 1,10 Å Vibrasi regang CH 2900 sd 3300 cm ^-1 CH dapat dikembangkan lagi menjadi CH yang terikat pada ikatan tunggal, ganda atau rangkap 3

Tipe Atom dalam MM

Penggambaran molekul yang tersusun atas unit struktural (gugus fungsi) serupa dengan bentuk molekul yang berbeda pada Kimia Organik • Kimiawan organik biasanya menggunakan ball n stick atau huruf nama atom dan garis ikatan untuk menggambarkan molekul
• FF method mirip dengan pendekatan ini

dengan penambahan atom dan ikatan

tidak memiliki satu ukuran dan panjang
yang fixed
Unit struktural yang serupa pada molekul yang berbeda ini diimplementasikan dalam FF dengan istilah tipe atom
• Tipe atom tergantung pada nomor atom
dan jenis ikatan kimia yang terlibat

Energi dalam Force

Field Method

• Energi dalam Force Field ditulis sebagai jumlah dari
semua suku
Masing-masing suku menguraikan energi yang
dibutuhkan untuk mendistorsi molekul dalam arah
tertentu

E FF = E str + E bend + E tors + E vdw + E el + E cross

Dimana E str adalah energi stretching ikatan antara 2 atom, E bend energi yang dibutuhkan untuk membengkokkan sudut ikatan, E tors energi untuk
proses rotasi memutar disekitar ikatan, E vdw dan E el

menguraikan interaksi atom-atom non-ikatan dan

Energi dalam Force Field

The Stretch Energy

E _str

adalah fungsi energi untuk meregangkan ikatan antara 2 tipe atom A dan B

Dalam bentuknya yang paling sederhana, E _str dituliskan sebagai deret Taylor disekitar Panjang ikatan “natural” atau “kesetimbangan” R .
Parameter R bukan Panjang ikatan kesetimbangan sembarang molekul,
Ia adalah parameter yang saat digunakan untuk menghitung struktur energi minimum suatu molekul akan menghasilkan geometri dengan Panjang ikatan kesetimbangan berdasarkan eksperiment

₂

1 �� 

�� 

The Bending Energy

E adalan energi yang dibutuhkan untuk _bend membengkokan sudut yang dibentuk oleh 3 atom ABC, dimana ada ikatan yang terbentuk antara A dan B dan antara B dan C • Bentuk persamaannya juga merupakan deret

Taylor disekitar sudut ikatan “natural” yang berakhir pada orde kedua dan memberikan pendekatan harmonik _{�� } ₂

� = � − � = � � − � _��

( ) ( )

The Out-of-Plane Bending Energy ₂

If the central B atom in the angle ABC is sp -hybridized, there is a significant energy penalty associated with making the centre pyramidal, since the four atoms prefer to be located in a plane. If the four atoms are exactly in a plane, the sum of the three angles with B as the central atom should be exactly 360°, however, a quite large pyramidalization may be achieved without seriously distorting any of these three angles.
Taking the bond distances to 1.5Å, and moving the central atom 0.2 Å out of the plane, only reduces the angle sum to  (i.e. only a 1.7° decrease per angle).

354.8 • The corresponding out-of-plane angle, , is 7.7  for this case.

Very large force constants must be used if the ABC, ABD and

CBD angle distortions are to reflect the energy cost associated with the pyramidalization.

This would have the consequence that the in-plane angle deformations for a planar structure would become unrealistically stiff.
Thus a special out-of-plane energy bend term (E _oop

) is usually added, while the in-plane angles (ABC, ABD and CBD) are treated as in the general case above

E _oop

may be written as a harmonic term in the angle  (the equilibrium angle for a planar structure is zero) or as a quadratic function in the distance d, as given in equation below

atau

The Out-of-Plane Bending Energy

The Torsional Energy

E describes part of _tors the energy change associated with rotation around a B—C bond in a four-atom sequence A—B—C—D, where A—B, B—C and C—D are bonded
Looking down the B— C bond, the torsional angle is defined as the angle formed by the A —B and C—D bonds as shown in Figure.

The torsional energy is fundamentally different from E _str and E in three aspects: _bend

1. A rotational barrier has contributions from both the non- bonded (van der Waals and electrostatic) terms, as well as the torsional energy, and the torsional parameters are therefore intimately coupled to the non-bonded parameters.

2. The torsional energy function must be periodic in the angle 

: if the bond is rotated 360° the energy should return to the same value.

3. The cost in energy for distorting a molecule by rotation around a bond is often low, i.e. large deviations from the minimum energy structure may occur, and a Taylor expansion in  is therefore not a good idea.

To encompass the periodicity, E _{tors is written as a} Fourier series.



( ) = ( ) � � �� 

��  ∑

The n = 1 term describes a rotation that is periodic by 360°, the n = 2 term is periodic by 180°, the n = 3 term is
periodic by 120°, and so on. The V constants determine
_n
the size of the barrier for rotation around the B—C bond.
Depending on the situation, some of these V constants _n may be zero. In ethane, for example, the most stable
conformation is one where the hydrogens are staggered
relative to each other, while the eclipsed conformation represents an energy maximum.
As the three hydrogens at each end are identical, it is clear that there are three energetically equivalent
staggered, and three equivalent eclipsed, conformations.
The rotational energy profile must therefore have three minima and three maxima.

Energi Torsional Etana

The Van der Waals Energy

E _vdw

is the van der Waals energy describing the repulsion or attraction between atoms that are not directly bonded.

, it describes the non-bonded energy.

Together with the electrostatic term E el
E _vdw

may be interpreted as the non-polar part of the interaction not related to electrostatic energy due to (atomic) charges.

This may for example be the interaction between two methane molecules, or two methyl groups at different ends of the same molecule.

E is zero at large interatomic distances and _vdw becomes very repulsive for short distances.
• In quantum mechanical terms, the latter is due to the
overlap of the electron clouds of the two atoms, as the negatively charged electrons repel each other.
At intermediate distances, however, there is a slight attraction between two such electron clouds from
induced dipole–dipole interactions, physically due to
electron correlation
Even if the molecule (or part of a molecule) has no permanent dipole moment, the motion of the
electrons will create a slightly uneven distribution at

This dipole moment will induce a charge polarization in the neighbor molecule (or another part of the same molecule), creating an attraction, and it can be derived theoretically that this attraction varies as the inverse sixth power of the distance between the two fragments.
E vdw is very positive at small distances, has a minimum that is slightly negative at a distance corresponding to the two atoms just “touching” each other, and approaches zero as the distance becomes large.
A general functional form that fits these conditions is given in eq. (2.11). _��

_{�� }

�

( ) = ( )

� � � � −

_{�� }

_��

₆

�

The Electrostatic Energy: Charges and Dipoles

• The other part of the non-bonded interaction is due to
internal (re)distribution of the electrons, creating positive and negative parts of the molecule.
A carbonyl group, for example, has a negatively charged oxygen and a positively charged carbon.
At the lowest approximation, this can be modelled by assigning (partial) charges to each atom.
• Alternatively, the bond may be assigned a bond dipole

moment. These two descriptions give similar (but not
identical) results.
Only in the long distance limit of interaction between
such molecules do the two descriptions give identical
results.

The interaction between point charges is given by the Coulomb potential, with  being a dielectric constant.
The atomic charges can be assigned by empirical rules, but are more commonly assigned by fitting to the electrostatic potential _{� �} calculated by electronic structure methods

_��

� �

( )

� � _�� = _��



� _{� �} _��  

( ) = cos  − 3 � �

��  _�� _�� ₃ ( _{� �} )



( � )

Cross Terms

The first five terms in the general energy expression, eq. (2.1), are common to all force fields. The last term, E , covers _cross coupling between these fundamental, or diagonal, terms. Consider for example a molecule such as H ^{2 O.}
It has an equilibrium angle of 104.5° and an O—H distance of
0.958 Å. If the angle is compressed to say 90 , and the optimal
bond length is determined by electronic structure calculations, the equilibrium distance becomes 0.968Å, i.e. slightly longer.
Similarly, if the angle is widened, the lowest energy bond length becomes shorter than 0.958Å. This may qualitatively be
understood by noting that the hydrogens come closer together if
the angle is reduced.
This leads to an increased repulsion between the hydrogens, which can be partly alleviated by making the bonds longer. If only the first five terms in the force field energy are included, this

It may be taken into account by including a term that depends on both bond length and angle.

E may in general include a whole series of _cross

terms that couple two (or more) of the bonded terms.

The components in E are usually written as _cross products of first-order Taylor expansions in the individual coordinates.
The most important of these is the stretch/bend term, which for an A—B—C sequence may be _{�� } written as in eq. (2.31)

� = � � − � � − � − � − � ( ) ( ) ( ) _{�� /�� [}

]

Aplikasi MM: Padatan Ionik

Aplikasi mekanika molekuler pada padatan ionik serupa dengan kalkulasi energi kisi
Bahkan metode MM memang bisa digunakan untuk menghitung energi kisi, juga efek adanya cacat pada senyawa ionik dan sifat kristal
Pertanyaan awal untuk mengurai energi kisi:
Apa gaya yang menahan ion-ion berkumpul membentuk kristal pada lattice site –nya
Jawabannya adalah gaya tarik elektrostatik

Aspek Energi dalam Ikatan Ionik: Energi Kisi

Misalkan ada suatu reaksi antara unsur logam yang reaktif (Li) dan mudah melepas elektron dengan gas halogen (F) yang cenderung menarik elektron:

Li(g)  Li (g) + e

IE = 520 kJ

F(g) + e  F (g) EA = -328 kJ

Reaksi total:

Li(g) + F(g)  Li (g) + F (g) IE + EA = 192

1 kJ

• Energi total yang dibutuhkan reaksi ini bahkan

lebih besar karena kita harus mengkonversi Li
dan F kedalam bentuk gas
• Akan tetapi eksperimen menunjukkan enthalpi
pembentukan padatan LiF (∆H

f ) = -617 kJ

Jika kedua unsur dalam bentuk gas:
Li

(g) + F

(g)  LiF(g) ∆H = -755 kJ

Energi kisi adalah perubahan enthalpi yang menyertai ion-ion gas yang bergabung membentuk padatan ionik:
Li

(g) + F

(g)  LiF(s) ∆H

kisi LiF = energi kisi = -1050 kJ

Daur Born-Haber

Nilai Energi Born-Haber

H Li = 161 kJ

oatom

BE F = 159 kJ

IE 1 (Li) = 520 kJ
EA (F) = -328 kJ
H (LiF) = -1050 kJ

oLattice

H LiF = -617 kJ

Total Energi :

 H LiF = H Li + ½ BE F + IE (Li) + EA (F) + of oatom ² ¹

Pendekatan Mekanika Molekuler

• Ion-ion diasumsikan berada pada situs kisi masing-masing
sesuai dengan muatan formalnya, sehingga NaCl misalnya _{- +} membentuk array of Na and Cl ions.
The net interaction can be obtained by summing the interactions over all the pairs of ions, including not only _{- +}
the attraction between Na and Cl but also the repulsion
between ions of the same sign.
The net interaction decreases with distance but slowly so that it is difficult to obtain an accurate value.
To calculate lattice energies, this summation be achieved
for simple lattice structures by introducing the Madelung
constant.
However, for layer structures with low symmetry this

Madelung Constants

There are many factors to be considered such as covalent character and electron-electron interactions in ionic solids.
But for simplicity, let us consider the ionic solids as a
collection of positive and negative ions. In this simple

view, appropriate number of cations and anions come
together to form a solid.
The positive ions experience both attraction and
repulsion from ions of opposite charge and ions of the
same charge.
The Madelung constant is a property of the crystal structure and depends on the lattice parameters, anion- cation distances, and molecular volume of the crystal

Before considering a three-dimensional crystal lattice, we shall discuss the calculation of the energetics of a linear chain of ions of alternate signs
• Let us select the positive sodium ion in the middle
(at x = 0) as a reference and let r be the shortest
distance between adjacent ions (the sum of ionic
radii).
The Coulomb energy of the other ions in this 1D lattice on this sodium atom can be decomposed

Nearest Neighbors (first shell): This reference sodium ion has two negative chloride ions as its neighbors on either side at r so the Coulombic energy of these interactions is

Next Nearest Neighbors (second shell): Similarly the repulsive energy due to the next two positive sodium ions at a distance of 2r is

• Next Next Nearest Neighbors (third

shell): The attractive Coulomb energy

• and so on. Thus the total energy due to
all the ions in the linear array is

1 �

2 1− − … + + �=

4 � � � ( )

[ ]

We can use the following Maclaurin expan>&n
to simplify the sum in the parenthesis of

Equation before as to obtain

The first factor of Equation is the Coulomb energy for a single pair of sodium and chloride ions, while (2 ln2) the factor is the Madelung constant (M1.38 ) per molecule.
The Madelung constant is named after Erwin Medelung and is a geometrical factor that depends on the arrangement of ions in the solid. If the lattice were different (when

MM Approach …

Since the computer programs in use are set up to be of
general application, they employ methods that give a good
approximation to the sum over an infinite lattice for any unit cell.
However, electrostatic interaction is not that has to be considered. We know, for example, that ions are not just
point charges but have a size; the shell of electrons around

each nucleus prevents too close an approach by other ions.
We therefore include a term to allow for the interaction
between shells on the different ions. It would be possible to

give each ion a fixed size and insist that the ions cannot be
closer than their combined radii.
However, most programs use a different approach by including terms representing intermolecular forces.

The intermolecular forces act between cations, and between cations and anions, as well as between anions.
• For oxides in particular, however, the cation-
cation term is often ignored.
Salts such as magnesium oxide can be
thought of as close-packed arrays of anions
with cations occupying the octahedral holes.
Because the cations are held apart by the anions, the cation-cation interaction is un-

Octahedral Hole

The final thing we need to take into account is the polarizability of the ions. This is a measure of how easily the ions are deformed from their normal spherical shape.
In a perfect crystal, the ions are in very symmetrical environments and can be thought of as spherical. If one ion moves to an interstitial site, leaving its original position vacant, then the environment may not be so symmetrical and it may be deformed by the surrounding ions.
A very simple way to model this is to divide the ionic charge between a core that stays fixed at the position of the ion and a surrounding shell

The shell behaves as though it were attached to the core by springs. Take a chloride ion, for example. If the surrounding ions move so that there is a greater positive charge in one direction, then the shell will move so that the total charge on the ion is distributed over two centers producing a dipole.
Opposing this will be the pull of the springs that attach it to the core.

For ionic solids, the most important term for lattice energies is the electrostatic term; for sodium chloride, for example, the total lattice

₁

^-
energy in a typical calculation is -762.073 kJ mol
_-1 , of which -861.135 kJ mol is due to the
electrostatic interaction while the intermolecular
_-1 force and shell terms contribute +99.062 kJ mol .

• Thus the contributions of the intermolecular force

• These other terms may have a greater relevance
in the study of defects.

Crystal Defects in Silver Chloride

Silver halides are used in photography to capture light and form an image.
The action of light on the halide produces silver which forms the black areas of the negative (Figure 2.2).
The formation of silver depends on the presence of Frenkel defects in the crystal

Two most common point defects in crystals are Frenkel defects and Schottky defects. What are these?
In Schottky defects, equal numbers of cations and anions are missing (for 1 : 1 structures such as AgCl).
In Frenkel defects, an ion is displaced from its lattice site to an interstitial site; for example, a small cation in a crystal with the NaCl structure can move to a tetrahedral hole from the octahedral hole normally occupied.
We can use molecular mechanics to estimate the energies of these defects in silver halides.
The dominant defect in silver halides is a Frenkel defect, in which a silver ion moves to an interstitial site. To calculate the energy required to form this defect we simply remove a silver ion from one position, put it in its new position and compare

In a Frenkel defect, there is a vacancy where an ion should
be and an ion in a more crowded interstitial position. Would
you expect the ions in the vicinity of the defect to stay on their lattice positions?
• It would be reasonable to suppose that the ions would adjust

their positions to allow the interstitial atom more room, and
to take up the space left by the vacancy.
When calculating the energy of formation of the defect the
nearest atoms are allowed to adjust their position to obtain
the lowest energy for the crystal including the defect.
• Figure 2.3 (overleaf) shows how the chloride ions move when

a Frenkel defect forms in AgCl; in the perfect crystal (Figure
2.3a) there is just one Ag-Cl bond length, whereas in the defect crystal (Figure 2.3b) the Ag-C1 bond lengths are

(a) Perfect AgCl. (b) A Frenkel defect in

AgCl

• For an estimate of the actual numbers of defects we need

) ) to know the Gibbs energy of formation, but the major contribution comes from the internal energy.

Calculated values for the energy of formation of cation

Zeolite

Zeolites* have frameworks of silicon, aluminium and oxygen atoms which form channels and cages, e.g. Figure 2.4.
They form a wide variety of structures but all are based on silicon tetrahedrally bound to oxygen.
Differing numbers of silicon atoms are replaced by aluminium. Other cations, notably those of Groups I, II and the lanthanides, are present in the structures to balance the charge.
Surprisingly such structures can be very successfully modelled by considering them as a collection of ions and using

Silicon is not normally thought of as forming Si
ions; indeed silica, SO , and silicates do contain

₂

• The most successful way of doing this is to add a
term that represents the resistance of OSiO and OAlO bond angles to deviation from the tetrahedral angle.
• The covalency of zeolites and related compounds
is also reflected in the relative size of the

For one form of silica, SO , for example, a calculated

₂

_-1

_-1
16029.976 kJ mol from electrostatic interactions, _-1

+3553.796 kJ mol from intermolecular force terms and
_-1
the core-shell spring term, and 1.913 kJ mol from those
OSiO bond angles that were not tetrahedral.

The energy due to the term keeping the angles tetrahedral is small, but without this term the zeolite structure is lost.
With this addition, the structures of a wide variety of
zeolites, both naturally occurring minerals and synthetic
zeolites tailored to act as catalysts, can be modelled and then used to answer questions such as which position
will the non-framework ions and molecules occupy and
how do ions travel through the structure?

Modelling Organic Molecules

The power of this method for organic molecules lies in the
adoption of a relatively small set of parameters that can be
transferred to any molecule you want.
But what sort of parameters might be needed? Can we
simply use electrostatic and intermolecular forces? How do
we allow for bonds and different conformations • Let us start by looking at a very simple molecule - ethane.

Ethane is H ₃ C-CH ₃ .

As for solids, we do need to include an electrostatic interaction, but what charge are we going to give carbon and hydrogen atoms?
• Obviously +4 or -4 on C and +I or -1 on H are unrealistic and
would not even give a neutral molecule.
Think for a moment about the process of bond formation

When two atoms form a covalent bond, they share electrons. If the atoms are unalike then one atom has a larger share than the other, resulting in a
positive charge on one atom and a negative charge
on the other.
But the charge transferred is less than one electron.

For diatomic molecules, the charge on each atom can be obtained experimentally.

• In the molecule HCI, for example, the hydrogen atom
has a charge of +O. 18 and the chlorine atom a charge of -0.18.
The fractional charges are known as partial

A convenient way of setting up a set of transferable partial charges is to give each atom a contribution to the
partial charge from each type of bond that it is involved
in.
For example, in chloroethane, CH

₃

₂

consider contributions for the carbon atoms for carbon

bound to carbon, carbon bound to hydrogen and carbon

For elements such as oxygen, which can be singly or doubly bonded (C-O or C=O), we need different partial charge contributions for each type of bond
In one available computer program carbon bonded to hydrogen gives a contribution of +0.053
As well as the electrostatic interaction arising from the partial charges, we also need intermolecular forces.
• These can be important for large atoms such as bromine

Cocaine analogue - Ecgonine

List all the bond terms you would need to describe the compound on the left