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Atomic and molecular orbitals

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Atomic orbitals represent the probability of finding electrons around an atom's nucleus. Molecular orbitals are formed from the overlap of atomic orbitals during bond formation. There are two types of molecular orbitals - sigma bonds form from head-on overlaps and result in electron density between the nuclei, while pi bonds form from sideways overlaps and have electron density above and below the bond. The in-phase combination of atomic orbitals is bonding and lowers energy, while out-of-phase combinations are antibonding and increase energy. Molecular orbital theory explains how bonds form through constructive and destructive interference of atomic orbitals.

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ORGANIC CHEMISTRY ATOMIC ORBITALS and MOLECULAR ORBITALS by: J. B. Andres-Catipon
OBJECTIVE Be able to know about atomic orbitals and molecular orbitals and understand them through bond formation.
TERMS AND DEFINITIONS  Orbitals - They represent the probability of finding an electron in any one place. They correspond to different energies. So an electron in an orbital has definite energy. Orbitals are best described with quantum mechanics.  Atomic Orbitals – the region in space just outside the nucleus of the atom where the probability of finding the electrons is at the highest (95%).  Molecular Orbitals – formed as a result from the overlap of two atomic orbitals, wherein a pair of electrons occupying.  Electron Density – a measure of the probability of finding an electron in an orbital.  Wave Function – mathematical description of the volume of space occupied by an electron having a certain amount of energy.  A node in an orbital – is the place where a crest and a trough meet.  Quantum Mechanics is based on the wave properties of matter. Quantization of energy is the consequence of these properties.
FOREWORD As it has been studied previously, electrons in atoms treated as waves effectively than as compact particles in circular or elliptical orbits. Such particles like electrons, atoms or molecules do not obey Isaac Newton’s Law but rather obeys a different kind of mechanics called quantum mechanics. One of the underlying principles of quantum mechanics is that we cannot determine precisely the paths that electrons follow as they move about atomic nuclei (HEISENBERG UNCERTAINTY PRINCIPLE). Because of this, scientists resort to statistical approach and speak of the probability of finding an electron within specified region in space ( ATOMIC ORBITAL). So, quantum numbers are used to designate the electronic arrangements in all atoms (ELECTRONIC CONFIGURATIONS) and play important roles in describing the energy levels and the shapes of orbitals that describe the distributions of electrons in space.
Each electron is said to occupy an atomic orbital defined by the set of quantum numbers . The main shell of the atomic orbital is indicated by the principal quantum number. These shells are referred to as the electron energy levels. Each shell has s subshell. Beginning with the 2nd energy level, it has a p subshell. Each shell has also p subshell. Each of these subshells contains a set of three p atomic orbitals. Each set of atomic p orbitals resembles three mutually perpendicular equal arm dumbbells. The nucleus defines the origin of a set of cartesian coordinates with the usual x, y and z axes which indicate the axis along which each of the orbitals is directed. Beginning with the 3rd shell, each shell also contain a third subshell d, composed of five atomic orbitals. In each of the fourth shell and larger shells, there is also a fourth subshell f, which composed of seven atomic orbitals.
We also learned that wave function represents atomic orbital. The overall sign on the wave function that describes an atomic orbital is not important but when we combine two orbitals ( covalent bond- sharing of electron), their signs become very significant. When waves are combined, they may interact constructively and destructively. Constructive interaction of waves occurs in the region between the nuclei while destructive interaction of waves reduces the probability of finding electrons between the nuclei. These interactions occur in the bonding of MOLECULAR ORBITAL.
ATOMIC ORBITALS  The energy levels about the nucleus contain group of these atomic orbitals.  Each orbital ( designated as s, p, d, and f) has a unique energy associated with it, can contain a maximum of two electrons and varies in shape and spatial orientation.  We are mainly concerned with the s and p orbitals since most of the elements found in organic molecules have their electrons in the 1s, 2s, and 2p orbitals.  For the shapes of f orbitals, are quite complicated.  Higher d and f orbitals are utilized by elements further down in the periodic table . These are further discussed by inorganic chemists.  The s orbital is spherical, like a fuzzy hollow ball with its center at the nucleus of the atom.  The are three p orbitals of equal energy, designated px, py, and pz.  Each p orbital is dumbbell shaped. Each consists of two lobes with atomic nucleus lying between them and each has a nodal plane at the nucleus, where the probability of the electron’s location is zero.
Shape of the s orbital It contains no nodes because it is the closest to the nucleus. It has the lowest energy of all the atomic orbitals 1s
Shape of the s orbital The 2s atomic orbital has a small region of . electron density surrounding the nucleus, but most of the eletron density is farther from the nucleus, beyond a node. 2s
Shape of the s orbital 3s
 For any atom there is only one 1s orbital. The "1" represents the fact that the orbital is in the energy level closest to the nucleus. The "s" refers to the shape of the orbital. S orbitals are spherically symmetrical around the nucleus.  For any atom there is only one 2s orbital. This is similar to a 1s orbital except that the region where there is the greatest chance of finding the electron is further from the nucleus - this is an orbital at the second energy level. There is a also a region of slightly higher electron density nearer the nucleus called a spherical node.  For any atom there is only one 3s orbital. The intensity of colouration indicates the positions where the electron is likely to be found on any plane cutting through the nucleus. There are two spherical nodes in the 3s orbital.
Shapes of the p orbitals
 The three p orbitals in the second shell of electrons are totally different from the 1s and 2s orbitals. Each p orbital consists of a “dumbbell” or “teardrop” shape on either side of the nodal plane that runs through the center of the nucleus.  Their orientation is 90 ˚ from each other in the three spatial direction and have identical energies and shapes.  Chemists call them as degenerate orbitals.  Because electrons in the three 2p orbitals are farther from the nucleus than those in the 2s orbital, they are at a higher energy level.
Shapes of d orbitals
Shapes of the f orbitals 4fy3 - 3x2y 4fxyz 4f5yz2 - yr2
Shapes of the f orbitals 4fz3 - 3zr2 4fzx2 - zy2 4f5xz2 - xr2 4fx3 - 3xy2
 The 4f y3 - 3x2y orbital corresponds to n=4, =3, and m=-3. Six lobes point to the corners of a regular hexagon in the xy plane, with one pair of lobes along the x-axis. Three nodal planes pass between the lobes and intersect at the z axis.  The 4fxyz orbital corresponds to n=4, =3, and m=-2. Eight lobes point to the corners of a cube, with four lobes above and four lobes below the xy plane. The x and y axes pass through the centers of four of the cube's faces (between the lobes). The three nodal planes are defined by the x, y, and z axes.  The 4f5yz2 - yr2 orbital corresponds to n=4, =3, and m=-1. Six lobes point to the corners of a regular hexagon in the yz plane, with one pair of lobes along the x-axis. The three nodal planes pass between the lobes and intersect at the y axis.  The 4fz3 - 3zr2 orbital corresponds to n=4, =3, and m=0. Two lobes point along the z-axis, with two bowl-shaped rings above and below the xy plane. The nodal surfaces are the xy plane and a conical surface passing through the nucleus and between the rings and the lobes.
 The 4f5xz2 - xr2 corresponds to n=4, =3, and m=+1. Six lobes point to the corners of a regular hexagon in the xz plane, with one pair of lobes along the y-axis. The three nodal planes pass between the lobes and intersect at the x axis.  The 4fzx2 - zy2 orbital corresponds to n=4, =3, and m=+2. It has the same shape as the 4fxyz orbital, but the corners of the cube are in the planes defined by the x, y, and z axes and the three nodal planes cut between the lobes and intersect along the z axis.  The 4fx3 - 3xy2 orbital corresponds to n=4, =3, and m=+3. It is identical to the orbital with m_=-3 except that a lobe lies along the y axis instead of along the x axis.
MOLECULAR ORBITALS  Bonding between atoms occurs when they come into close enough proximity for their orbitals to overlap. Thus, when two atoms are brought close enough together to permit overlap of their orbitals, their electron pair and go into a single orbital encompassing both nuclei.  As two atoms form a bond, they interact very much like waves on a body of water. When two waves are traveling in the same directions and one overtakes the other the amplitude of the new wave is greater than the amplitude of either of the two that created it. In contrast, when two waves travel in opposite directions, and they meet, their amplitudes cancel each other.  A pair of electrons encompassing two or more nuclei is said to occupy a MOLECULAR ORBITAL.  As with atomic orbitals, a molecular orbital may not contain more than two electrons.  The molecular orbital represents a lower energy state for the system than do two separate atomic orbitals at the characteristic internuclear distance.  Energy is liberated during the overlap, and a stable covalent bond is formed.
MOLECULAR ORBITALS  During bonding, atoms overlap either in-phase or out-of-phase. In-phase overlap if there is constructive bonding (added, wave functions with the same signs), while out-of-phase overlap if there is destructive bonding (subtracted, wave functions of opposite signs).  In the in-phase overlap, the wave functions reinforce one another. This reinforcement increases the probability of finding the electrons in the region between the nuclei. This is so-called the BONDING MOLECULAR ORBITAL.  An out-of-phase overlap forms an ANTIBONDING MOLECULAR ORBITAL. A node develops between the two nuclei. It is also formed for each bonding molecular orbital that forms.  BONDING MOLECULAR ORBITAL always has lower energy than the energies of combining atomic orbitals and the more stable the molecule or ion becomes.  ANTIBONDING MOLECULAR ORBITAL always has a higher energy than the energies of the two separate atomic orbitals, leading to the repulsion between two atoms, and the less stable the molecule or ion becomes.  In a bonding MO, the electron density is high between two atoms where it stabilizes the arrangement by attracting both nuclei.
Types of Molecular Orbital
TYPES OF MOLECULAR ORBITAL 1.) Sigma (σ) molecular orbital – orbital that is symmetrical about the molecular axis. The two electrons in it are called the σ bonds. A sigma molecular orbital may be formed by the direct or head-on overlap the following orbitals. a.) Two 1s atomic orbitals + → 1s 1s 1s-1s σ bond s-s σ MO b.) Two px atomic orbitals + → → px px px-px σ bond px-px σ MO
c.) 1s and px atomic orbitals 1s px s-px σbond → s-px σ MO
Atomic and molecular orbitals
2.) Pi (π) molecular orbital – In a π molecular orbital, the electron density is concentrated above and below the line joining the two nuclei of the bonding atoms. The electrons in it are called π electrons and the bond is referred to as π bond. A double bond is one σ bond and one π bond, a triple bond consists of one σ bond and two π bonds. A π molecular orbital may be formed by the sideways overlap of the following orbitals. a.) Two pz atomic orbitals + → pz pz pz – pz π MO
b.) Two py atomic orbitals + → py py py – py π MO + →
c.) py or pz and dxz atomic orbitals + → dxz pz dxz – pz π MO + →
Atomic and molecular orbitals
Atomic and molecular orbitals
Atomic and molecular orbitals
Atomic and molecular orbitals

More Related Content

Atomic and molecular orbitals

  • 1. ORGANIC CHEMISTRY ATOMIC ORBITALS and MOLECULAR ORBITALS by: J. B. Andres-Catipon
  • 2. OBJECTIVE Be able to know about atomic orbitals and molecular orbitals and understand them through bond formation.
  • 3. TERMS AND DEFINITIONS  Orbitals - They represent the probability of finding an electron in any one place. They correspond to different energies. So an electron in an orbital has definite energy. Orbitals are best described with quantum mechanics.  Atomic Orbitals – the region in space just outside the nucleus of the atom where the probability of finding the electrons is at the highest (95%).  Molecular Orbitals – formed as a result from the overlap of two atomic orbitals, wherein a pair of electrons occupying.  Electron Density – a measure of the probability of finding an electron in an orbital.  Wave Function – mathematical description of the volume of space occupied by an electron having a certain amount of energy.  A node in an orbital – is the place where a crest and a trough meet.  Quantum Mechanics is based on the wave properties of matter. Quantization of energy is the consequence of these properties.
  • 4. FOREWORD As it has been studied previously, electrons in atoms treated as waves effectively than as compact particles in circular or elliptical orbits. Such particles like electrons, atoms or molecules do not obey Isaac Newton’s Law but rather obeys a different kind of mechanics called quantum mechanics. One of the underlying principles of quantum mechanics is that we cannot determine precisely the paths that electrons follow as they move about atomic nuclei (HEISENBERG UNCERTAINTY PRINCIPLE). Because of this, scientists resort to statistical approach and speak of the probability of finding an electron within specified region in space ( ATOMIC ORBITAL). So, quantum numbers are used to designate the electronic arrangements in all atoms (ELECTRONIC CONFIGURATIONS) and play important roles in describing the energy levels and the shapes of orbitals that describe the distributions of electrons in space.
  • 5. Each electron is said to occupy an atomic orbital defined by the set of quantum numbers . The main shell of the atomic orbital is indicated by the principal quantum number. These shells are referred to as the electron energy levels. Each shell has s subshell. Beginning with the 2nd energy level, it has a p subshell. Each shell has also p subshell. Each of these subshells contains a set of three p atomic orbitals. Each set of atomic p orbitals resembles three mutually perpendicular equal arm dumbbells. The nucleus defines the origin of a set of cartesian coordinates with the usual x, y and z axes which indicate the axis along which each of the orbitals is directed. Beginning with the 3rd shell, each shell also contain a third subshell d, composed of five atomic orbitals. In each of the fourth shell and larger shells, there is also a fourth subshell f, which composed of seven atomic orbitals.
  • 6. We also learned that wave function represents atomic orbital. The overall sign on the wave function that describes an atomic orbital is not important but when we combine two orbitals ( covalent bond- sharing of electron), their signs become very significant. When waves are combined, they may interact constructively and destructively. Constructive interaction of waves occurs in the region between the nuclei while destructive interaction of waves reduces the probability of finding electrons between the nuclei. These interactions occur in the bonding of MOLECULAR ORBITAL.
  • 7. ATOMIC ORBITALS  The energy levels about the nucleus contain group of these atomic orbitals.  Each orbital ( designated as s, p, d, and f) has a unique energy associated with it, can contain a maximum of two electrons and varies in shape and spatial orientation.  We are mainly concerned with the s and p orbitals since most of the elements found in organic molecules have their electrons in the 1s, 2s, and 2p orbitals.  For the shapes of f orbitals, are quite complicated.  Higher d and f orbitals are utilized by elements further down in the periodic table . These are further discussed by inorganic chemists.  The s orbital is spherical, like a fuzzy hollow ball with its center at the nucleus of the atom.  The are three p orbitals of equal energy, designated px, py, and pz.  Each p orbital is dumbbell shaped. Each consists of two lobes with atomic nucleus lying between them and each has a nodal plane at the nucleus, where the probability of the electron’s location is zero.
  • 8. Shape of the s orbital It contains no nodes because it is the closest to the nucleus. It has the lowest energy of all the atomic orbitals 1s
  • 9. Shape of the s orbital The 2s atomic orbital has a small region of . electron density surrounding the nucleus, but most of the eletron density is farther from the nucleus, beyond a node. 2s
  • 10. Shape of the s orbital 3s
  • 11.  For any atom there is only one 1s orbital. The "1" represents the fact that the orbital is in the energy level closest to the nucleus. The "s" refers to the shape of the orbital. S orbitals are spherically symmetrical around the nucleus.  For any atom there is only one 2s orbital. This is similar to a 1s orbital except that the region where there is the greatest chance of finding the electron is further from the nucleus - this is an orbital at the second energy level. There is a also a region of slightly higher electron density nearer the nucleus called a spherical node.  For any atom there is only one 3s orbital. The intensity of colouration indicates the positions where the electron is likely to be found on any plane cutting through the nucleus. There are two spherical nodes in the 3s orbital.
  • 12. Shapes of the p orbitals
  • 13.  The three p orbitals in the second shell of electrons are totally different from the 1s and 2s orbitals. Each p orbital consists of a “dumbbell” or “teardrop” shape on either side of the nodal plane that runs through the center of the nucleus.  Their orientation is 90 ˚ from each other in the three spatial direction and have identical energies and shapes.  Chemists call them as degenerate orbitals.  Because electrons in the three 2p orbitals are farther from the nucleus than those in the 2s orbital, they are at a higher energy level.
  • 14. Shapes of d orbitals
  • 15. Shapes of the f orbitals 4fy3 - 3x2y 4fxyz 4f5yz2 - yr2
  • 16. Shapes of the f orbitals 4fz3 - 3zr2 4fzx2 - zy2 4f5xz2 - xr2 4fx3 - 3xy2
  • 17.  The 4f y3 - 3x2y orbital corresponds to n=4, =3, and m=-3. Six lobes point to the corners of a regular hexagon in the xy plane, with one pair of lobes along the x-axis. Three nodal planes pass between the lobes and intersect at the z axis.  The 4fxyz orbital corresponds to n=4, =3, and m=-2. Eight lobes point to the corners of a cube, with four lobes above and four lobes below the xy plane. The x and y axes pass through the centers of four of the cube's faces (between the lobes). The three nodal planes are defined by the x, y, and z axes.  The 4f5yz2 - yr2 orbital corresponds to n=4, =3, and m=-1. Six lobes point to the corners of a regular hexagon in the yz plane, with one pair of lobes along the x-axis. The three nodal planes pass between the lobes and intersect at the y axis.  The 4fz3 - 3zr2 orbital corresponds to n=4, =3, and m=0. Two lobes point along the z-axis, with two bowl-shaped rings above and below the xy plane. The nodal surfaces are the xy plane and a conical surface passing through the nucleus and between the rings and the lobes.
  • 18.  The 4f5xz2 - xr2 corresponds to n=4, =3, and m=+1. Six lobes point to the corners of a regular hexagon in the xz plane, with one pair of lobes along the y-axis. The three nodal planes pass between the lobes and intersect at the x axis.  The 4fzx2 - zy2 orbital corresponds to n=4, =3, and m=+2. It has the same shape as the 4fxyz orbital, but the corners of the cube are in the planes defined by the x, y, and z axes and the three nodal planes cut between the lobes and intersect along the z axis.  The 4fx3 - 3xy2 orbital corresponds to n=4, =3, and m=+3. It is identical to the orbital with m_=-3 except that a lobe lies along the y axis instead of along the x axis.
  • 19. MOLECULAR ORBITALS  Bonding between atoms occurs when they come into close enough proximity for their orbitals to overlap. Thus, when two atoms are brought close enough together to permit overlap of their orbitals, their electron pair and go into a single orbital encompassing both nuclei.  As two atoms form a bond, they interact very much like waves on a body of water. When two waves are traveling in the same directions and one overtakes the other the amplitude of the new wave is greater than the amplitude of either of the two that created it. In contrast, when two waves travel in opposite directions, and they meet, their amplitudes cancel each other.  A pair of electrons encompassing two or more nuclei is said to occupy a MOLECULAR ORBITAL.  As with atomic orbitals, a molecular orbital may not contain more than two electrons.  The molecular orbital represents a lower energy state for the system than do two separate atomic orbitals at the characteristic internuclear distance.  Energy is liberated during the overlap, and a stable covalent bond is formed.
  • 20. MOLECULAR ORBITALS  During bonding, atoms overlap either in-phase or out-of-phase. In-phase overlap if there is constructive bonding (added, wave functions with the same signs), while out-of-phase overlap if there is destructive bonding (subtracted, wave functions of opposite signs).  In the in-phase overlap, the wave functions reinforce one another. This reinforcement increases the probability of finding the electrons in the region between the nuclei. This is so-called the BONDING MOLECULAR ORBITAL.  An out-of-phase overlap forms an ANTIBONDING MOLECULAR ORBITAL. A node develops between the two nuclei. It is also formed for each bonding molecular orbital that forms.  BONDING MOLECULAR ORBITAL always has lower energy than the energies of combining atomic orbitals and the more stable the molecule or ion becomes.  ANTIBONDING MOLECULAR ORBITAL always has a higher energy than the energies of the two separate atomic orbitals, leading to the repulsion between two atoms, and the less stable the molecule or ion becomes.  In a bonding MO, the electron density is high between two atoms where it stabilizes the arrangement by attracting both nuclei.
  • 22. TYPES OF MOLECULAR ORBITAL 1.) Sigma (σ) molecular orbital – orbital that is symmetrical about the molecular axis. The two electrons in it are called the σ bonds. A sigma molecular orbital may be formed by the direct or head-on overlap the following orbitals. a.) Two 1s atomic orbitals + → 1s 1s 1s-1s σ bond s-s σ MO b.) Two px atomic orbitals + → → px px px-px σ bond px-px σ MO
  • 23. c.) 1s and px atomic orbitals 1s px s-px σbond → s-px σ MO
  • 25. 2.) Pi (π) molecular orbital – In a π molecular orbital, the electron density is concentrated above and below the line joining the two nuclei of the bonding atoms. The electrons in it are called π electrons and the bond is referred to as π bond. A double bond is one σ bond and one π bond, a triple bond consists of one σ bond and two π bonds. A π molecular orbital may be formed by the sideways overlap of the following orbitals. a.) Two pz atomic orbitals + → pz pz pz – pz π MO
  • 26. b.) Two py atomic orbitals + → py py py – py π MO + →
  • 27. c.) py or pz and dxz atomic orbitals + → dxz pz dxz – pz π MO + →