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Mathematical function
molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the linear combination
Gaussian_orbital
Function used in quantum chemistry
be evaluated by Slater orbitals. However, taking the integral of a Gaussian is much easier. For example, the Slater-type orbital for 1s is: ϕ 1 s STO (
Slater-type_orbital
Computational chemistry software
methods Gaussian 70, Gaussian 76, Gaussian 80, Gaussian 82, Gaussian 86, Gaussian 88, Gaussian 90, Gaussian 92, Gaussian 92/DFT, Gaussian 94, and Gaussian 98
Gaussian_(software)
Mathematical function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}
Gaussian_function
Monochrome light beam whose amplitude envelope is a Gaussian function
optics, a Gaussian beam is an idealized beam of electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function;
Gaussian_beam
Function describing an electron in an atom
{\displaystyle m_{s}} . The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number ℓ = 0, 1, 2
Atomic_orbital
Quantum number denoting orbital angular momentum
number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum
Azimuthal_quantum_number
coordinate system Gaussian grid Gauss lens Double-Gauss lens Gaussian optics Gauss's principle of least constraint For orbit determination in orbital mechanics:
List of things named after Carl Friedrich Gauss
List_of_things_named_after_Carl_Friedrich_Gauss
Constant used in orbital mechanics
The Gaussian gravitational constant (symbol k) is a parameter used in the orbital mechanics of the Solar System. It relates the orbital period to the
Gaussian gravitational constant
Gaussian_gravitational_constant
British theoretical chemist (1925–2004)
quantum chemistry community. The Gaussian molecular orbital methods were described in the 1986 book Ab initio molecular orbital theory by Warren Hehre, Leo
John_Pople
Computer simulation of chemical systems
applications, including factoring and solving linear systems of equations. In Gaussian orbital basis sets, phase estimation algorithms have been optimized empirically
Quantum computational chemistry
Quantum_computational_chemistry
Set of functions used to represent the electronic wave function
Slater-type orbital basis set, with n representing the number of Gaussian primitive functions used to represent each Slater-type orbital. Minimal basis
Basis_set_(chemistry)
Random matrix with gaussian entries
the Gaussian ensembles are specific probability distributions over self-adjoint matrices whose entries are independently sampled from the gaussian distribution
Gaussian_ensemble
Unit of time equaling 365.2568983 days
A Gaussian year is defined as 365.2563835 days. It was adopted by Carl Friedrich Gauss as the length of the sidereal year in his studies of the dynamics
Gaussian_year
Type of angular momentum in light
Laguerre-Gaussian mode with rotational mode number l ≠ 0 {\displaystyle l\neq 0} has such a helical wavefront. The classical expression of the orbital angular
Orbital angular momentum of light
Orbital_angular_momentum_of_light
Force of attraction or repulsion between molecules and neighboring particles
Science Books. ISBN 0-935702-99-7. Blustin PH (1978). "A Floating Gaussian Orbital calculation on argon hydrochloride (Ar·HCl)". Theoretica Chimica Acta
Intermolecular_force
Angular speed required for a body to complete one orbit
the orbital period, as above. Astronomy portal Gaussian gravitational constant Kepler orbit Mean anomaly Mean longitude Mean motion resonance Orbital elements
Mean_motion
Wave-like behavior of an electron in a molecule
region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary
Molecular_orbital
Topics referred to by the same term
preliminary orbit determination Gauss's Easter algorithm Gauss separation algorithm This disambiguation page lists articles associated with the title Gaussian algorithm
Gaussian_algorithm
Indian theoretical and computational chemist
state of Odisha, he studied molecules using molecular orbital and floating spherical gaussian orbital methods and his work on the nature of electron density
Naba_Kishore_Ray
Basis sets used in quantum chemistry
(1969). "Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals". Journal of Chemical Physics. 51 (6):
STO-nG_basis_sets
British chemist
introduction of Gaussian orbitals into ab initio quantum chemistry. Almost all basis sets used in computational chemistry now employ these orbitals. Frank Boys
Samuel_Francis_Boys
Technique in quantum chemistry
molecular orbitals, which can be numbered i = 1 to n and which may not all be the same. The expression (linear expansion) for the i th molecular orbital would
Linear combination of atomic orbitals
Linear_combination_of_atomic_orbitals
Branch of chemistry
ATMOL, Gaussian, IBMOL, and POLYAYTOM, began to be used to speed ab initio calculations of molecular orbitals. Of these four programs, only Gaussian, now
Computational_chemistry
Physical quantity carried in photons
Spreeuw, R.; Woerdman, J. (1992). "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes". Phys. Rev. A. 45 (11):
Angular_momentum_of_light
Algorithm that estimates unknowns from a series of measurements over time
assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear." Regardless of Gaussianity, however, if the process
Kalman_filter
Time taken by the Earth to orbit the Sun once with respect to the fixed stars
sidus 'asterism, star'), also called a sidereal orbital period, is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed
Sidereal_year
Hungarian chemist (1932–2022)
(POLYATOM was the first software package for ab initio calculations using Gaussian orbitals, developed in John C. Slater's Solid State and Molecular Theory Group
Imre_Gyula_Csizmadia
Gauss optics Gaussian beam Gaussian broadening Gaussian fixed point Gaussian gravitational constant Gaussian noise Gaussian orbital Gaussian polar coordinates
Index_of_physics_articles_(G)
Optical phenomenon
consisting of the Bessel function. Photons in a hypergeometric-Gaussian beam have an orbital angular momentum of mħ. The integer m also gives the strength
Optical_vortex
German polymath and scholar (1777–1855)
the Gaussian gravitational constant. Since the new asteroids had been discovered, Gauss occupied himself with the perturbations of their orbital elements
Carl_Friedrich_Gauss
list. Slater-type orbitals (STOs) as basis functions for both molecular and periodic calculations, in contrast to Gaussian orbitals (GTOs) and plane waves
Amsterdam_Density_Functional
Unit of magnetic induction
known as magnetic induction or magnetic field). The unit is part of the Gaussian system of units, which inherited it from the older centimetre–gram–second
Gauss_(unit)
Equations in quantum chemistry
which can be of Gaussian-type or Slater-type. It applies to closed-shell molecules or atoms where all molecular orbitals or atomic orbitals, respectively
Roothaan_equations
Computational chemistry software program
systems with hundreds of atoms. All the methods used are based on Gaussian orbitals, in order to improve performance on contemporary (2010s) computer
TeraChem
Unit of magnetic moment
{\displaystyle \mu _{\mathrm {B} }={\frac {e\hbar }{2m_{\mathrm {e} }}}} and in the Gaussian CGS units as μ B = e ℏ 2 m e c , {\displaystyle \mu _{\mathrm {B} }={\frac
Bohr_magneton
Type of covalent bond in organic chemistry
Bent's rule states that there should be more p-orbital character in the C–F bond and more s-orbital character in the C–H bonds, compared to the equal
Bent_bond
Physical constant for the strength of gravity induced by a mass
years. Physics portal Gravity of Earth Standard gravity Gaussian gravitational constant Orbital mechanics Escape velocity Gravitational potential Gravitational
Gravitational_constant
3D reconstruction technique
mipmap). Rather than sampling a single ray per pixel, the technique fits a gaussian to the conical frustum cast by the camera. This improvement effectively
Neural_radiance_field
Quantized magnetization of charged particles
In quantum mechanics, orbital magnetization, Morb, refers to the magnetization induced by orbital motion of charged particles, usually electrons in solids
Orbital_magnetization
Academic journal
Self-consistent molecular-orbital methods. 12. Further extensions of Gaussian-type basis sets for use in molecular-orbital studies of organic molecules
The Journal of Chemical Physics
The_Journal_of_Chemical_Physics
Parameter introduced by the Minor Planet Center
the future motion of near-Earth objects. Orbital uncertainty is related to several parameters used in the orbit determination process including the number
Uncertainty_parameter
of Density Functional Theory programs is being built making use of Gaussian orbital expansions for the basis set (not yet available). The way PLATO performs
PLATO (computational chemistry)
PLATO_(computational_chemistry)
mission because the reflected light variation with orbital phase is largely independent of orbital inclination and does not require the planet to pass
Methods of detecting exoplanets
Methods_of_detecting_exoplanets
using an additional set of d-orbitals in the basis set and with two-center core–core parameters, rather than the Gaussian functions used to modify the
AM1*
"Investigating the Reactivity and Spectra of Large Molecules with ONIOM | Gaussian.com". gaussian.com. Retrieved 2023-04-13. S. Dapprich; I. Komaromi; K.S. Byun;
ONIOM
Stochastic processes
Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. A stationary Gauss–Markov process is unique[citation
Gauss–Markov_process
Unit of time based on Earth's orbit
and its duration is very close to the Julian year of 365.25 days. The Gaussian year is the sidereal year for a planet of negligible mass (relative to
Year
Extrasolar planet in the constellation Cancer
Justin; Dodson-Robinson, Sarah E (2025-10-27). "High-pass Filtering and Gaussian Process Regularization: Stellar Activity Characterization Techniques Applied
55_Cancri_Ab
Type of non-Euclidean geometry
pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they
Hyperbolic_geometry
Mathematics of smooth surfaces
curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss, who showed that
Differential geometry of surfaces
Differential_geometry_of_surfaces
Combining multiple simulation methods
called Gaussian-1 (G1) introduced by John Pople. This was quickly replaced by the Gaussian-2 (G2) which has been used extensively. The Gaussian-3 (G3)
Quantum chemistry composite methods
Quantum_chemistry_composite_methods
Topics referred to by the same term
the album Walk the Earth Gate turn-off thyristor Gaussian-type orbital Geostationary transfer orbit Golgi tendon organ Gorton railway station, in Greater
GTO
Motion of charged particles
SI units. In some cases, the cyclotron frequency is given in Gaussian units. In Gaussian units, the Lorentz force differs by a factor of 1/c, the speed
Cyclotron_motion
Class of physical phenomena
the CGS-Gaussian unit of magnetic field (denoted B). oersted – the CGS-Gaussian unit of magnetizing field (denoted H) maxwell – the CGS-Gaussian unit for
Magnetism
Australian quantum chemist (born 1962)
Head-Gordon-Pople scheme for the evaluation of integrals, and the orbital rotation picture of orbital optimization. At Berkeley, Head-Gordon supervises a group
Martin_Head-Gordon
Concept in the physics of electromagnetism
are added to get a total spin, and individual orbital angular momenta are added to get a total orbital angular momentum. These two then are added using
Magnetic_moment
Standard unit of mass in astronomy
stars can be calculated in units of Solar mass directly from the orbital radius and orbital period of the planet or stars using Kepler's third law. The mass
Solar_mass
Hot Super-Earth orbiting 55 Cancri A
Cancri Ae orbits very close to its parent star; with average orbital distance of 0.01544 ± 0.00005 AU, it takes only 18 hours to complete an orbit. Analysis
55_Cancri_Ae
most common choice for this basis set is Gaussian orbitals (GTOs) however for linear molecules Slater orbitals (STOs) can be used. The Schrödinger equation
Yoshimine_sort
2007 book by Nassim Nicholas Taleb
studying. Mediocristan environments can safely use Gaussian distribution. In Extremistan environments, a Gaussian distribution should be used at one's own peril
The Black Swan: The Impact of the Highly Improbable
The_Black_Swan:_The_Impact_of_the_Highly_Improbable
Software used for simulations and modeling in materials science
Atomistic and electronic structure simulations Open-source CRYSTAL Gaussian-type orbital DFT for periodic systems Commercial DMol3 Density functional theory
List of materials science software
List_of_materials_science_software
Quantum chemistry software program
orbital (GIAO) NMR program by Wolinski, who additionally included a highly efficient integral package. Bofill executed an unhindered natural orbital-complete
PQS_(software)
Indirect method for finding extrasolar planets and brown dwarfs
(or estimate) of the inclination of the planet's orbit to determine the planet's mass. If the orbital plane of the planet happens to line up with the line-of-sight
Doppler_spectroscopy
American/Canadian research chemist
machines. GAUSSIAN, Quantum Chemistry Program Exchange, Indiana University, Bloomington, Indiana, 1984. Available today commercially through Gaussian, Inc
William_J._Pietro
Approximation method in quantum physics
_{k}} and ϵ k {\displaystyle \epsilon _{k}} are called molecular orbital and orbital energy respectively. Although Hartree-Fock equation appears in the
Hartree–Fock_method
Gabedit is a graphical user interface to GAMESS (US), Gaussian, MOLCAS, MOLPRO, MPQC, OpenMopac, PC GAMESS, ORCA and Q-Chem computational chemistry packages
Gabedit
G5V star in the constellation Cygnus
of co-orbital planets. However, follow-up study of the system revealed that an alternative configuration, with the four planets having orbital periods
Kepler-223
Candidate extrasolar planet in the constellation Cancer
thought to be on a fairly low eccentricity orbit similar to Jupiter in the Solar System, though the orbital elements were not well determined. As more
55_Cancri_Ad
Mathematical model of the time dependence of a point in space
arXiv:2510.01089 [cs.LG]. Gaussian multiplicative chaos revisited https://hal.science/hal-00293830v1/document Complex Gaussian multiplicative chaos https://ui
Dynamical_system
Set of points equidistant from a center
have constant mean curvature. The sphere has constant positive Gaussian curvature. Gaussian curvature is the product of the two principal curvatures. It
Sphere
Molecule containing main group elements with more than eight valence electrons
molecular orbital framework, was proposed. The 3c–4e bond is described as three molecular orbitals formed by the combination of a p atomic orbital on the
Hypervalent_molecule
Mean distance between Earth and the Sun
of Gaussian gravitational constant and D is the time period of one day. The Sun is constantly losing mass by radiating away energy, so the orbits of the
Astronomical_unit
Quantum chemistry rule regarding vibronic transitions
solvent-chromophore interaction energies, represented in the figure by a Gaussian distribution function. The solvent-chromophore interaction is drawn as
Franck–Condon_principle
Orbits where planets may have liquid surface water
January 2015. Bortle, Anna; et al. (2021), "A Gaussian Process Regression Reveals No Evidence for Planets Orbiting Kapteyn's Star", The Astronomical Journal
Habitable_zone
American physical chemist (born 1966)
function kernel, a gaussian algorithm used to support vector machines, is applied to determine electronic and molecular orbitals. The NEO approach is
Sharon_Hammes-Schiffer
Measure for hazard from asteroid or comet impacts on Earth
imprecision, the orbit calculation has an uncertainty, which can be quantified for the close approach distance. Assuming a two-dimensional Gaussian probability
Torino_scale
Dynamic disturbance in a medium or field
have a Gaussian shape and is called a Gaussian wave packet. Gaussian wave packets also are used to analyze water waves. For example, a Gaussian wavefunction
Wave
American mathematician
generalizing the Rogers–Ramanujan identities. He also posed the still-unsolved Gaussian moat problem in 1962. Gordon was drafted into the US Army, where he worked
Basil_Gordon
Binary star with at least five exoplanets 41 light-years away
result relies on orbital parameters which have been substantially revised since this was published. The observed transits of e suggest an orbit normal inclined
55_Cancri
Periodic comet with 19 year orbit
comet with randomly Gaussian distributed orbital elements (using their mean values and their sigma-values) was created and the orbital development of this
39P/Oterma
Hot Jupiter exoplanet in the constellation Vulpecula
Jupiter and a radius 11.4% greater, HD 189733 b orbits its host star once every 2.2 days at an orbital speed of 152.0 kilometers per second (340,000 miles
HD_189733_b
Distance from the Earth surface to a point near its center
^{2}\varphi }},} where K is the Gaussian curvature, K = κ 1 κ 2 . {\displaystyle K=\kappa _{1}\,\kappa _{2}.} The Gaussian radius of curvature is defined
Earth_radius
Extrasolar planet in the constellation Cancer
Justin; Dodson-Robinson, Sarah E (2025-10-27). "High-pass Filtering and Gaussian Process Regularization: Stellar Activity Characterization Techniques Applied
55_Cancri_Ac
Way of describing a molecule's charge distribution
charge at the ‘overlap center’ of the two Gaussian functions. The product of an s orbital and a p orbital has only charge and dipole components, and
Distributed multipole analysis
Distributed_multipole_analysis
Triple star system in the constellation of Lyra
- an ancient planetary system in Messier 4 The eccentricity has a non-Gaussian posterior distribution and so the median is an overestimate of the true
Kepler-444
measurement only allows for an estimate on the exoplanet's orbital parameters, but not on their orbital inclination (i). As such, most exoplanets only have an
List_of_nearest_exoplanets
Particle effect
is to study the evolution of a Gaussian wavepacket. In the non-relativistic case, using Schrödinger equation a Gaussian wavepacket disperses uniformly
Zitterbewegung
Aspect of algebraic number theory
take K = Q and L = Q(i), so OK is simply Z, and OL = Z[i] is the ring of Gaussian integers. Although this case is far from representative — after all, Z[i]
Splitting of prime ideals in Galois extensions
Splitting_of_prime_ideals_in_Galois_extensions
Net potential energy encountered in orbital mechanics
N.; Ballauff, M.; Lindner, P.; Werner, N.; Vögtle, F.; et al. (2002). "Gaussian effective interaction between flexible dendrimers of fourth generation:
Effective_potential
Approximation in many-body systems
plane-wave (FP-LAPW) method FHI-aims - numeric atom-centered orbitals method Fiesta - Gaussian all-electron method GAP - an all-electron GW code based on
GW_approximation
Signal-processing operation
If the imaging beam has a Gaussian distribution, then when the truncation ratio (the ratio of the diameter of the Gaussian beam to the diameter of the
Apodization
Main-belt asteroid
prediction · Orbital info · Proper elements · Observational info 1001 Gaussia at the JPL Small-Body Database Close approach · Discovery · Ephemeris · Orbit viewer ·
1001_Gaussia
Phenomenon in quantum systems
the quantum spectrum is extracted by propagating a Gaussian wave packet along a periodic orbit. Nowadays, this seminal idea is known as the linear theory
Quantum_scar
Galaxy that orbits a larger galaxy due to gravitational attraction
matter) and Newton's laws of gravity. For example, measurements of the orbital speed of stars and gas within spiral galaxies result in a velocity curve
Satellite_galaxy
Molecular orbitals and vibrational frequencies are among the properties displayed. Support for importing results from NWChem, Gaussian 94, Gaussian 98, and
Extensible Computational Chemistry Environment
Extensible_Computational_Chemistry_Environment
Curve whose normals converge asymptotically
normalized to have Gaussian curvature −1, then the horocycle is a curve of geodesic curvature 1 at every point. Every horocycle is the orbit of a unipotent
Horocycle
Physics phenomenon
{\displaystyle 1\oplus n} -mode Gaussian states, but no longer sufficient for 2 ⊕ 2 {\displaystyle 2\oplus 2} -mode Gaussian states. Simon's condition can
Quantum_entanglement
Quantization of cyclotron orbits
{\displaystyle n=0} consists of arbitrary analytic functions multiplying a Gaussian, ψ ( x , y ) = f ( w ) e − | w | 2 / 4 {\displaystyle \psi (x,y)=f(w)e^{-|w|^{2}/4}}
Landau_levels
Justin; Dodson-Robinson, Sarah E. (November 2025). "High-pass Filtering and Gaussian Process Regularization: Stellar Activity Characterization Techniques Applied
List of proper names of exoplanets
List_of_proper_names_of_exoplanets
GAUSSIAN ORBITAL
GAUSSIAN ORBITAL
Male
Russian
Variant spelling of Russian Irinei, IRINEY means "peaceful."
Boy/Male
Australian, French, German, Irish
Curly-headed
Male
Russian
Variant spelling of Russian Afanasiy, AFANASY means "immortal."
Male
Russian
Variant spelling of Russian Vasiliy, VASILY means "king."
Male
Russian
Variant spelling of Russian Vikentiy, VIKENTI means "conquering."
Male
Russian
Variant spelling of Russian Vasiliy, VASILI means "king."
Male
Russian
Variant spelling of Russian Gennadiy, GENNADY means "noble."
Male
Russian
(Паша) Russian pet form of Czech/Russian Pavel, PASHA means "small."
Male
Russian
(Russian ИÑидор): Russian form of Greek Isidoros, ISIDOR means "gift of Isis."
Male
Russian
Variant spelling of Russian Gennadiy, GENNADI means "noble."
Male
Russian
Variant spelling of Russian Faddei, FADEI means "courageous."
Male
Russian
Variant spelling of Russian Arseniy, ARSENIY means "virile."
Female
Russian
(Людмила) Russian feminine form of Czech/Russian Ludmil, LUDMILA means "people's favor."Â
Female
Russian
(Russian Ева): Armenian and Russian form of Greek Eva, YEVA means "life."Â
Male
Russian
(РоÑÑ) Russian pet form of Czech/Russian Rostislav, ROSTYA means "usurp-glory."
Male
Russian
Variant spelling of Russian Arseniy, ARSENI means "virile."
Male
Russian
Variant spelling of Russian Aleksey, ALEXEY means "defender."
Male
Russian
Variant spelling of Russian Afanasiy, AFANASII means "immortal."
Male
Russian
Variant spelling of Russian Afanasiy, AFANASEI means "immortal."
Male
Russian
Variant spelling of Russian Vasiliy, VASSILY means "king."
GAUSSIAN ORBITAL
GAUSSIAN ORBITAL
GAUSSIAN ORBITAL
GAUSSIAN ORBITAL
GAUSSIAN ORBITAL
GAUSSIAN ORBITAL
GAUSSIAN ORBITAL