Molecular orbitals are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms.

Molecular orbitals ( MOs ) represent regions in a molecule where an electron is likely to be found.

Molecular orbitals are obtained from the combination of atomic orbitals, which predict the location of an electron in an atom.

Molecular orbitals were first introduced by Friedrich Hund and Robert S. Mulliken in 1927 and 1928.

Molecular orbitals are said to be degenerate if they have the same energy.

Molecular orbitals

Molecular orbitals require different quantum numbers, because the Hamiltonian and its symmetries are quite different.

Molecular fragments joined by a pi bond cannot rotate about that bond without breaking the pi bond, because rotation involves destroying the parallel orientation of the constituent p orbitals.

Molecular orbital ( MO ) theory uses a linear combination of atomic orbitals ( LCAO ) to represent molecular orbitals involving the whole molecule.

Molecular orbitals are further divided according to the types of atomic orbitals combining to form a bond.

His prize-winning work focused on the role of frontier orbitals in chemical reactions: specifically that molecules share loosely bonded electrons which occupy the frontier orbitals, that is the Highest Occupied Molecular Orbital ( HOMO ) and the Lowest Unoccupied Molecular Orbital ( LUMO ).

Molecular orbital scheme, illustrating the linear combination of P – R σ * and P 3d orbitals to form PR3 π acceptor orbitals

Molecular evidence suggests that the Phycodnaviridae may have evolved from the family Iridoviridae.

Molecular evidence indicates that the lineage of gibbons ( family Hylobatidae ) diverged from Great Apes some 18-12 million years ago, and that of orangutans ( subfamily Ponginae ) diverged from the other Great Apes at about 12 million years ; there are no fossils that clearly document the ancestry of gibbons, which may have originated in a so-far-unknown South East Asian hominoid population, but fossil proto-orangutans may be represented by Sivapithecus from India and Griphopithecus from Turkey, dated to around 10 million years ago.

Molecular evidence suggests that between 8 and 4 million years ago, first the gorillas, and then the chimpanzees ( genus Pan ) split off from the line leading to the humans ; human DNA is approximately 98. 4 % identical to that of chimpanzees when comparing single nucleotide polymorphisms ( see human evolutionary genetics ).

Molecular diffusion from a microscopic and macroscopic point of view.

Early Tertiary Out-of-India Dispersal of Crypteroniaceae: Evidence from Phylogeny and Molecular Dating.

Drexler argues that we may need to wait until our conventional nanotechnology improves before solving these issues: " Molecular manufacturing will result from a series of advances in molecular machine systems, much as the first Moon landing resulted from a series of advances in liquid-fuel rocket systems.

Molecular studies, however, have shown that the Cetacea descend from the Artiodactyl ancestors, although the precise phylogeny within the order remains uncertain.

A study conducted by the Centre for Cellular and Molecular Biology in 2009 ( in collaboration with Harvard Medical School, Harvard School of Public Health and the Broad Institute of Harvard and MIT ) analyzed half a million genetic markers across the genomes of 132 individuals from 25 ethnic groups from 13 states in India across multiple caste groups.

Molecular excitons have several interesting properties, one of which is energy transfer ( see Förster resonance energy transfer ) whereby if a molecular exciton has proper energetic matching to a second molecule's spectral absorbance, then an exciton may transfer ( hop ) from one molecule to another.

Molecular analysis suggests that the hexapods diverged from their sister group, the Anostraca ( fairy shrimps ), at around the start of the Silurian period-coinciding with the appearance of vascular plants on land.

") Molecular phylogenetics have clarified the relatedness of some associated genera, and at least nine genera that were previously included in Cornaceae have been eliminated from the order Cornales entirely, but the circumscription of Cornaceae is still unclear.

Molecular clock and fossil dating suggest echidnas split from platypuses 19 – 48 million years ago.

Molecular data indicate Vespertilionidae diverged from Molossidae in the early Eocene period.

Molecular genetics study suggests that surviving Amerindian populations derived from a theoretical single founding population, possibly from only 50 to 70 genetic contributors Preliminary research, restricted to only 9 genomic regions ( or loci ) have shown a genetic link between original Americas and Asia populations.

* Molecular dynamics, a form of computer simulation where atoms and molecules are allowed to interact for a period of time under known laws of physics

Molecular genetics allowed much greater insight into this previously intractable problem.

Molecular cloning allowed for the discovery of similar channels in many other tissues.

Docking @ Home, hosted by University of Delaware, one of the projects which use an opensource platform for the distributed computing, BOINC, adopts CHARMM to analyze the atomic details of protein-ligand interactions in terms of Molecular Dynamics ( MD ) simulations and minimizations.

The Quantized Valence Bonds ' Molecular Mechanics ( QVBMM ) force field ( implemented in Exorga, Incorporated's StruMM3D product, once named STR3DI32 ) is unique in molecular mechanics as the only one to directly use all lone pair interactions in all of its energy calculations.

Many faculty in the department conduct research on plant-microbe interactions. The faculty and graduate students also cooperate with faculty from other UC Berkeley departments, such as the Molecular and Cell Biology Department, on researches pertaining to plant genetics and microbial biology.

* Molecular Interaction Maps, a graphic formalism to depict cellular and molecular interactions

Molecular biology chiefly concerns itself with understanding the interactions between the various systems of a cell, including the interrelationship of DNA, RNA and protein synthesis and learning how these interactions are regulated.

* Molecular interactions

Molecular interactions can occur between molecules belonging to different biochemical families ( proteins, nucleic acids, lipids, carbohydrates, etc.

Molecular neuropharmacology involves the study of neurons and their neurochemical interactions, with the overall goal of developing drugs that have beneficial effects on neurological function.

Molecular neuropharmacology involves the study of neurons and their neurochemical interactions, and receptors on neurons, with the goal of developing new drugs that will treat neurological disorders such as pain, neurodegenerative diseases, and psychological disorders ( also known in this case as neuropsychopharmacology ).

Molecular diffusion in tissues is not free, but reflects interactions with many obstacles, such as macromolecules, fibers, membranes, etc.

Molecular chemistry deals with the laws governing the interaction between molecules that results in the formation and breakage of chemical bonds, while molecular physics deals with the laws governing their structure and properties.

According to Robert Freitas of the Institute for Molecular Manufacturing, a typical blood borne medical nanorobot would be between 0. 5-3 micrometres in size, because that is the maximum size possible due to capillary passage requirement.

* Molecular binding, an attractive interaction between two molecules

Molecular physics is the study of the physical properties of molecules, the chemical bonds between atoms as well as the molecular dynamics.

Molecular evidence suggests that the Shoebill and the Hamerkop form a sister group to the pelicans, though there is some doubt as to the exact relationship between the three lineages.

* Johansson, Ulf S. & Ericson, Per G. P. ( 2003 ): Molecular support for a sister group relationship between Pici and Galbulae ( Piciformes sensu Wetmore 1960 ).

* Johansson, Ulf S. & Ericson, Per G. P. ( 2003 ): Molecular support for a sister group relationship between Pici and Galbulae ( Piciformes sensu Wetmore 1960 ).

( 2003 ): Molecular support for a sister group relationship between Pici and Galbulae ( Piciformes sensu Wetmore 1960 ).

Molecular studies of the pipits suggest that the genus arose in East Asia around seven million years ago ( mya ), during the Miocene, and that the genus had spread to the Americas, Africa and Europe between 5 and 6 mya.

Molecular evidence indicates that the steppe polecat and black-footed ferret diverged from Mustela stromeri sometime between 500, 000 and 2, 000, 000 years ago, perhaps in Beringia.

* ( 2003 ): Molecular support for a sister group relationship between Pici and Galbulae ( Piciformes sensu Wetmore 1960 ).

Molecular trees have had some difficulty resolving relationships between the different groups.

Molecular analysis of 39 leopard cat tissue samples suggested distinction between northern leopard cats from Tsushima, Korea, Siberia, China and Taiwan, and southeast Asian leopard cats.

Molecular polarity is dependent on the difference in electronegativity between atoms in a compound and the asymmetry of the compound's structure.

Molecular hyperfine structure is generally dominated by these two effects, but also includes the energy associated with the interaction between the magnetic moments associated with different magnetic nuclei in a molecule, as well as between the nuclear magnetic moments and the magnetic field generated by the rotation of the molecule.

Notably, Thomson ScienceWatch, which quantifies citations-per-paper for work published between 2005 – 2009, ranked UTSW 1st in the world for published research in Clinical Medicine, 1st in Biology & Biochemistry, 2nd in Neurobiology / Behavior, and 3rd in Molecular Biology / Genetics.

Molecular set theory ( MST ) is a mathematical formulation of the wide-sense chemical kinetics of biomolecular reactions in terms of sets of molecules and their chemical transformations represented by set-theoretical mappings between molecular sets.

Molecular physics is the study of the physical properties of molecules, the chemical bonds between atoms as well as the molecular dynamics.

He was professor of physical chemistry at Kyoto University from 1951 to 1982, president of the Kyoto Institute of Technology between 1982 and 1988, and a member of the International Academy of Quantum Molecular Science and honorary member of the International Academy of Science.