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Covalent bonding in a molecule of ammonia : Each hydrogen atom needs one more electron to complete its valence energy shell. The nitrogen atom needs three more electrons to complete its valence energy shell.

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Therefore, three pairs of electrons must be shared between the four atoms involved. The nitrogen atom will share three of its electrons so that each of the hydrogen atoms now has a complete valence shell. Each of the hydrogen atoms will share its electron with the nitrogen atom to complete its valence shell. Explain the process of hybridization as it applies to the formation of sp 3 hybridized atoms.

Molecular Orbital Theory, Bonding & Antibonding MO, Bond Order, Homonuclear Diatomic Molecules

In a tetravalent molecule, four outer atoms are bonded to a central atom. Perhaps the most common and important example of this bond type is methane, CH 4. In the ground state of the free carbon atom, there are two unpaired electrons in separate 2p orbitals.

The single 2s orbital is spherical, different from the dumbbell-shaped 2p orbitals. The bonds between carbon and hydrogen can form the backbone of very complicated and extensive chain hydrocarbon molecules. The simplest of these is ethane C 2 H 6 , in which an sp 3 orbital on each of the two carbon atoms joins overlaps to form a carbon-carbon bond; then, the remaining carbon sp 3 orbital overlaps with six hydrogen 1s orbitals to form the ethane molecule. Ethane : Ethane can form by replacing one of the hydrogen atoms in CH 4 with another sp 3 hybridized carbon fragment. If lone electron pairs are present on the central atom, thet can occupy one or more of the sp 3 orbitals.

For example, in the ammonia molecule, the fourth of the sp 3 hybrid orbitals on the nitrogen contains the two remaining outer-shell electrons, which form a non-bonding lone pair.

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In the water molecule, the oxygen atom can form four sp 3 orbitals. Two of these are occupied by the two lone pairs on the oxygen atom, while the other two are used for bonding. The observed H-O-H bond angle in water Boron trifluoride BF 3 has a boron atom with three outer-shell electrons in its normal or ground state, as well as three fluorine atoms, each with seven outer electrons. One of the three boron electrons is unpaired in the ground state. In order to explain the bonding, the 2s orbital and two of the 2p orbitals called sp 2 hybrids hybridize; one empty p-orbital remains.

Boron configuration diagram : One of the three boron electrons is unpaired in its ground state. These particular orbitals are called sp 2 hybrids, meaning that this set of orbitals derives from one s- orbital and two p-orbitals of the free atom. The Lewis structure for ethene : The carbon atoms are sp 2 hybridized. Two sp 2 hybrids bond with the hydrogen atoms, and the other forms a sigma bond with the other carbon atom. Ethene C 2 H 4 has a double bond between the carbons.

In this case, carbon will sp 2 hybridize; in sp 2 hybridization, the 2s orbital mixes with only two of the three available 2p orbitals, forming a total of three sp hybrid orbitals with one p-orbital remaining. The three hybridized orbitals explain the three sigma bonds that each carbon forms. The two carbon atoms form a sigma bond in the molecule by overlapping two sp 2 orbitals. The pi bond between the carbon atoms perpendicular to the molecular plane is formed by 2p—2p overlap.

Formation of sp 2 hybrid orbitals : This illustration shows how an s-orbital mixes with two p orbitals to form a set of three sp 2 hybrid orbitals. Notice again how the three atomic orbitals yield the same number of hybrid orbitals. In sp hybridization, the s orbital overlaps with only one p orbital. Any central atom surrounded by just two regions of valence electron density in a molecule will exhibit sp hybridization. This last example will be discussed in more detail below.

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Second, the spins of the electrons must be opposed when the bonds are formed, so that they do not contribute to the magnetic properties of the substance. And third, the two electrons that form a shared pair cannot take part in forming additional pairs. These rules systematized the understanding of chemical bonding that was emerging from the rapidly developing quantum theory. They exemplify, more than any other single discovery, the extraordinary chemical intuition that, in one area after another, led Pauling to simple and elegant explanations of extremely complex phenomena.

The rules were justified, in the paper, by sketchy mathematical and qualitative arguments; their real justification lies in the numerous chemical structures that have been correctly inferred from them.

The trick is always to make the right approximation — not to overlook the important points. So, if there are two orbitals competing for a bond with a certain atom, the winner will be the one that overlaps more with that atom. In addition, the direction of the bond formed by an orbital will tend to be the same as the direction that the orbital is concentrated in. However, despite its lack of precedents, the rule smacks of common sense.

Greater overlap makes a stronger bond, and the bond is in the direction of the orbital that is bonding — these are very natural, intuitive conclusions. This rule is mathematically similar to the fifth rule but tends to have fewer direct applications. In this way atoms join together to make molecules, the basic elements of matter.

This is a natural, intuitive idea, almost visceral in its simplicity, and it cuts through the complexity of interacting quantum wave functions in a most remarkable way. The pivotal concept in the theory is the highly technical, highly innovative idea of the hybridization of orbitals, based on the concept of resonance among different electrons. A simplification which made it very easy to get the results. And I was so excited and happy, I think I stayed up all night making, writing out, solving the equations which were so simple that I could solve them in a few minutes.

Solve one equation and get the answer and solve another equation … I just kept getting more and more euphorious as time went by, and it didn't take me long to write a long paper about the nature of the chemical bond. That was a great experience.

The correlation theory of the chemical bond

And, years later, Pauling remembered believing that it would have the journal editor, Arthur Beckett Lamb,. First proof of quantum computer advantage Oct 18, Nov 07, Nov 05, IBM says it's reached milestone in quantum computing Nov 10, Jul 24, Feb 24, Recommended for you. New research brings scientists one step closer to a fully functioning quantum computer 49 minutes ago. Sep 24, Quantum observers may be entitled to their own facts Sep 24, User comments.

Jan 02, One of the first problems I tackled in high school in the 's was calculating the Schroedinger equation for a single point. Brings back memories of Fortran and card decks and an old IBM computer with 16k words of memory. Even with the simplifications found in this latest work, the number of qubits required for practical problems probably runs into the thousands anyone with more accurate info than my speculation please correct me. I am confident that quantum computers of that size will be eventually built, but not today. I am recently retired after 45 years as a professional software developer and I one of the things I most hope to see in my lifetime is such computers coming into widespread enough use I will be able to program one.

Probably not, but I am eternally optimistic.

Quantum chemistry on quantum computers

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