585:
indicates that all "light" atoms also receive polarization functions (this adds a set of 2p orbitals to the basis for each hydrogen atom). Eventually it became desirable to add more polarization to the basis sets, and a new notation was developed in which the number and types of polarization functions are given explicitly in parentheses in the order (heavy,light) but with the principal quantum numbers of the orbitals implicit. For example, the * notation becomes (d) and the ** notation is now given as (d,p). If instead 3d and 4f functions were added to each heavy atom and 2p, 3p, 3d functions were added to each light atom, the notation would become (df,2pd).
479:. For example, while the minimal basis set for hydrogen is one function approximating the 1s atomic orbital, a simple polarized basis set typically has two s- and one p-function (which consists of three basis functions: px, py and pz). This adds flexibility to the basis set, effectively allowing molecular orbitals involving the hydrogen atom to be more asymmetric about the hydrogen nucleus. This is very important for modeling chemical bonding, because the bonds are often polarized. Similarly, d-type functions can be added to a basis set with valence p orbitals, and f-functions to a basis set with d-type orbitals, and so on.
529:
functions). Basis sets in which there are multiple basis functions corresponding to each valence atomic orbital are called valence double, triple, quadruple-zeta, and so on, basis sets (zeta, ζ, was commonly used to represent the exponent of an STO basis function). Since the different orbitals of the split have different spatial extents, the combination allows the electron density to adjust its spatial extent appropriate to the particular molecular environment. In contrast, minimal basis sets lack the flexibility to adjust to different molecular environments.
1338:. The properties of the Fourier Transform allow a vector representing the gradient of the total energy with respect to the plane-wave coefficients to be calculated with a computational effort that scales as NPW*ln(NPW) where NPW is the number of plane-waves. When this property is combined with separable pseudopotentials of the Kleinman-Bylander type and pre-conditioned conjugate gradient solution techniques, the dynamic simulation of periodic problems containing hundreds of atoms becomes possible.
467:
1376:(LAPW) basis sets. These are based on a partitioning of space into nonoverlapping spheres around each atom and an interstitial region in between the spheres. An LAPW basis function is a plane wave in the interstitial region, which is augmented by numerical atomic functions in each sphere. The numerical atomic functions hereby provide a linearized representation of wave functions for arbitrary energies around automatically determined energy parameters.
773:
functions have been used in second hyperpolarizability calculations in the literature. Because of the rigorous construction of these basis sets, extrapolation can be done for almost any energetic property. However, care must be taken when extrapolating energy differences as the individual energy components converge at different rates: the
Hartree–Fock energy converges exponentially, whereas the correlation energy converges only polynomially.
1345:, so that the plane waves are only used to describe the valence charge density. This is because core electrons tend to be concentrated very close to the atomic nuclei, resulting in large wavefunction and density gradients near the nuclei which are not easily described by a plane-wave basis set unless a very high energy cutoff, and therefore small wavelength, is used. This combined method of a plane-wave basis set with a core
1041:
486:. These are extended Gaussian basis functions with a small exponent, which give flexibility to the "tail" portion of the atomic orbitals, far away from the nucleus. Diffuse basis functions are important for describing anions or dipole moments, but they can also be important for accurate modeling of intra- and inter-molecular bonding.
946: = 1). Using cc-pVDZ, orbitals are (where ' represents the added in polarisation orbitals), with 4 s orbitals (4 basis functions), 3 sets of p orbitals (3 × 3 = 9 basis functions), and 1 set of d orbitals (5 basis functions). Adding up the basis functions gives a total of 18 functions for Ar with the cc-pVDZ basis-set.
1427:
parts of the system, so that more points are used close to the nuclei where the wave function undergoes rapid changes and where most of the total energies lie, whereas a coarser representation is sufficient far away from nuclei; this feature is extremely important as it can be used to make all-electron calculations tractable.
1383:
The plane waves in the interstitial region imply three-dimensional periodic boundary conditions, though it is possible to introduce additional augmentation regions to reduce this to one or two dimensions, e.g., for the description of chain-like structures or thin films. The atomic-like representation
665:
The Pople basis sets were originally developed for use in
Hartree-Fock calculations. Since then, correlation-consistent or polarization-consistent basis sets (see below) have been developed which are usually more appropriate for correlated wave function calculations. For Hartree–Fock or density
1023:
Gaussian-type orbital basis sets are typically optimized to reproduce the lowest possible energy for the systems used to train the basis set. However, the convergence of the energy does not imply convergence of other properties, such as nuclear magnetic shieldings, the dipole moment, or the electron
1426:
A common feature of all real-space methods is that the accuracy of the numerical basis set is improvable, so that the complete basis set limit can be reached in a systematical manner. Moreover, in the case of wavelets and finite elements, it is easy to use different levels of accuracy in different
1333:
In addition, certain integrals and operations are much easier to program and carry out with plane-wave basis functions than with their localized counterparts. For example, the kinetic energy operator is diagonal in the reciprocal space. Integrals over real-space operators can be efficiently carried
968:
Adopting a similar methodology to the correlation-consistent series, Frank Jensen introduced polarization-consistent (pc-n) basis sets as a way to quickly converge density functional theory calculations to the complete basis set limit. Like the
Dunning sets, the pc-n sets can be combined with basis
1317:
basis sets can also be used in quantum-chemical simulations. Typically, the choice of the plane wave basis set is based on a cutoff energy. The plane waves in the simulation cell that fit below the energy criterion are then included in the calculation. These basis sets are popular in calculations
528:
During most molecular bonding, it is the valence electrons which principally take part in the bonding. In recognition of this fact, it is common to represent valence orbitals by more than one basis function (each of which can in turn be composed of a fixed linear combination of primitive
Gaussian
462:
calculation on the free atom. For atoms such as lithium, basis functions of p type are also added to the basis functions that correspond to the 1s and 2s orbitals of the free atom, because lithium also has a 1s2p bound state. For example, each atom in the second period of the periodic system (Li –
1379:
Similarly to plane-wave basis sets an LAPW basis set is mainly determined by a cutoff parameter for the plane-wave representation in the interstitial region. In the spheres the variational degrees of freedom can be extended by adding local orbitals to the basis set. This allows representations of
1304:
must be optimized, significantly reducing the dimension of the search space or even avoiding the exponent optimization problem. In order to properly describe electronic delocalized states, a previously optimized standard basis set can be complemented with additional delocalized
Gaussian functions
1031:
Completeness-optimized basis sets are tailored to a specific property. This way, the flexibility of the basis set can be focused on the computational demands of the chosen property, typically yielding much faster convergence to the complete basis set limit than is achievable with energy-optimized
772:
Diffuse functions can also be added for describing anions and long-range interactions such as Van der Waals forces, or to perform electronic excited-state calculations, electric field property calculations. A recipe for constructing additional augmented functions exists; as many as five augmented
584:
Polarization functions are denoted by two different notations. The original Pople notation added "*" to indicate that all "heavy" atoms (everything but H and He) have a small set of polarization functions added to the basis (in the case of carbon, a set of 3d orbital functions). The "**" notation
502:
representing the number of
Gaussian primitive functions used to represent each Slater-type orbital. Minimal basis sets typically give rough results that are insufficient for research-quality publication, but are much cheaper than their larger counterparts. Commonly used minimal basis sets of this
1363:
Due to the assumption of periodic boundary conditions, plane-wave basis sets are less well suited to gas-phase calculations than localized basis sets. Large regions of vacuum need to be added on all sides of the gas-phase molecule in order to avoid interactions with the molecule and its periodic
1387:
The disadvantage of LAPW basis sets is its complex definition, which comes with many parameters that have to be controlled either by the user or an automatic recipe. Another consequence of the form of the basis set are complex mathematical expressions, e.g., for the calculation of a
Hamiltonian
1027:
Manninen and Vaara have proposed completeness-optimized basis sets, where the exponents are obtained by maximization of the one-electron completeness profile instead of minimization of the energy. Completeness-optimized basis sets are a way to easily approach the complete basis set limit of any
1329:
to the target wavefunction. In contrast, when localized basis sets are used, monotonic convergence to the basis set limit may be difficult due to problems with over-completeness: in a large basis set, functions on different atoms start to look alike, and many eigenvalues of the overlap matrix
764:
While the usual
Dunning basis sets are for valence-only calculations, the sets can be augmented with further functions that describe core electron correlation. These core-valence sets (cc-pCVXZ) can be used to approach the exact solution to the all-electron problem, and they are necessary for
1201:
768:
Weighted core-valence sets (cc-pwCVXZ) have also been recently suggested. The weighted sets aim to capture core-valence correlation, while neglecting most of core-core correlation, in order to yield accurate geometries with smaller cost than the cc-pCVXZ sets.
760:
For period-3 atoms (Al–Ar), additional functions have turned out to be necessary; these are the cc-pV(N+d)Z basis sets. Even larger atoms may employ pseudopotential basis sets, cc-pVNZ-PP, or relativistic-contracted
Douglas-Kroll basis sets, cc-pVNZ-DK.
474:
A minimal basis set may already be exact for the gas-phase atom at the self-consistent field level of theory. In the next level, additional functions are added to describe polarization of the electron density of the atom in molecules. These are called
305:
1305:
with small exponent values, generated by the even-tempered scheme. This approach has also been employed to generate basis sets for other types of quantum particles rather than electrons, like quantum nuclei, negative muons or positrons.
450:
Dozens of
Gaussian-type orbital basis sets have been published in the literature. Basis sets typically come in hierarchies of increasing size, giving a controlled way to obtain more accurate solutions, however at a higher cost.
1051:
717: = triples, etc.). The 'cc-p', stands for 'correlation-consistent polarized' and the 'V' indicates they are valence-only basis sets. They include successively larger shells of polarization (correlating) functions (
181:
443:(GTOs) instead. Because the product of two GTOs can be written as a linear combination of GTOs, integrals with Gaussian basis functions can be written in closed form, which leads to huge computational savings (see
2068:
Bardo, Richard D.; Ruedenberg, Klaus (February 1974). "Even‐tempered atomic orbitals. VI. Optimal orbital exponents and optimal contractions of Gaussian primitives for hydrogen, carbon, and oxygen in molecules".
1364:
copies. However, the plane waves use a similar accuracy to describe the vacuum region as the region where the molecule is, meaning that obtaining the truly noninteracting limit may be computationally costly.
427:
at the nucleus, meaning that they are able to accurately describe electron density near the nucleus. However, hydrogen-like atoms lack many-electron interactions, thus the orbitals do not accurately describe
1918:"Development of new auxiliary basis functions of the Karlsruhe segmented contracted basis sets including diffuse basis functions (def2-SVPD, def2-TZVPPD, and def2-QVPPD) for RI-MP2 and RI-CC calculations"
666:
functional theory, however, Pople basis sets are more efficient (per unit basis function) as compared to other alternatives, provided that the electronic structure program can take advantage of combined
1810:
Moran, Damian; Simmonett, Andrew C.; Leach, Franklin E. III; Allen, Wesley D.; Schleyer, Paul v. R.; Schaefer, Henry F. (2006). "Popular theoretical methods predict benzene and arenes to be nonplanar".
2404:
Moran, Damian; Simmonett, Andrew C.; Leach, Franklin E.; Allen, Wesley D.; Schleyer, Paul v. R.; Schaefer, Henry F. (2006). "Popular Theoretical Methods Predict Benzene and Arenes To Be Nonplanar".
354:. When the finite basis is expanded towards an (infinite) complete set of functions, calculations using such a basis set are said to approach the complete basis set (CBS) limit. In this context,
1396:
Real-space approaches offer powerful methods to solve electronic structure problems thanks to their controllable accuracy. Real-space basis sets can be thought to arise from the theory of
1523:
2433:
Choi, Sunghwan; Kwangwoo, Hong; Jaewook, Kim; Woo Youn, Kim (2015). "Accuracy of Lagrange-sinc functions as a basis set for electronic structure calculations of atoms and molecules".
1048:
In 1974 Bardo and Ruedenberg proposed a simple scheme to generate the exponents of a basis set that spans the Hilbert space evenly by following a geometric progression of the form:
1775:
Ditchfield, R; Hehre, W.J; Pople, J. A. (1971). "Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules".
1423:
algorithms are also often included in this category, even though precisely speaking, they do not form a proper basis set and are not variational unlike e.g. finite element methods.
588:
In all cases, diffuse functions are indicated by either adding a + before the letter G (diffuse functions on heavy atoms only) or ++ (diffuse functions are added to all atoms).
105:
961:. However, the correlation-consistent basis sets described above are suboptimal for density-functional theory, because the correlation-consistent sets have been designed for
1275:
1302:
1044:
s-type Gaussian functions using six different exponent values obtained from an even-tempered scheme starting with α = 0.1 and β = sqrt(10). Plot generated with Gnuplot.
211:
1617:
1248:
216:
2299:
All the many basis sets discussed here along with others are discussed in the references below which themselves give references to the original journal articles:
1586:
1563:
1543:
1456:
1221:
2150:
Nakai, Hiromi (2002). "Simultaneous determination of nuclear and electronic wave functions without Born-Oppenheimer approximation: Ab initio NO+MO/HF theory".
1525:. The complete basis set can thereby be reached either by going to smaller and smaller elements (i.e. dividing space in smaller and smaller subdivisions;
729:, etc.). More recently these 'correlation-consistent polarized' basis sets have become widely used and are the current state of the art for correlated or
1356:
Furthermore, as all functions in the basis are mutually orthogonal and are not associated with any particular atom, plane-wave basis sets do not exhibit
654:
In summary; the 6-31G* basis set (defined for the atoms H through Zn) is a split-valence double-zeta polarized basis set that adds to the 6-31G set five
1955:
Manninen, Pekka; Vaara, Juha (2006). "Systematic Gaussian basis-set limit using completeness-optimized primitive sets. A case for magnetic properties".
330:, or numerical atomic orbitals. Out of the three, Gaussian-type orbitals are by far the most often used, as they allow efficient implementations of
114:
1846:
Dunning, Thomas H. (1989). "Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen".
638:
6-31G(3df,3pd) – 3 sets of d functions and 1 set of f functions on heavy atoms and 3 sets of p functions and 1 set of d functions on hydrogen
1384:
in the spheres allows to treat each atom with its potential singularity at the nucleus and to not rely on a pseudopotential approximation.
1196:{\displaystyle \alpha _{i,l}=\alpha _{l}\beta _{l}^{i-1},\quad \alpha _{l},\beta _{l}>0,\quad \beta _{l}\neq 1\quad i=1,2,\dots ,N_{l}}
2185:
Moncada, Félix; Cruz, Daniel; Reyes, Andrés (June 2012). "Muonic alchemy: Transmuting elements with the inclusion of negative muons".
2115:
Cherkes, Ira; Klaiman, Shachar; Moiseyev, Nimrod (2009-11-05). "Spanning the Hilbert space with an even tempered Gaussian basis set".
373:, the components of which correspond to coefficients of the basis functions in the linear expansion. In such a basis, one-electron
322:
which are typically used within the solid state community, or real-space approaches. Several types of atomic orbitals can be used:
2398:
1373:
561:
indicate that the valence orbitals are composed of two basis functions each, the first one composed of a linear combination of
2389:
2370:
2332:
2313:
393:
315:
17:
569:
primitive Gaussian functions. In this case, the presence of two numbers after the hyphens implies that this basis set is a
458:. A minimal basis set is one in which, on each atom in the molecule, a single basis function is used for each orbital in a
1360:. However, the plane-wave basis set is dependent on the size of the simulation cell, complicating cell size optimization.
894:
671:
2489:
2351:
1729:
935:. Thus, there are five spatial orbitals in total. Note that each orbital can hold two electrons of opposite spin.
2538:
1461:
1644:"A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules"
670:
shells, and are still widely used for molecular structure determination of large molecules and as components of
2543:
1400:, as the central idea is to represent the (unknown) orbitals in terms of some set of interpolation functions.
498:, where n is an integer. The STO-nG basis sets are derived from a minimal Slater-type orbital basis set, with
1597:
1357:
965:, while density-functional theory exhibits much more rapid basis set convergence than wave function methods.
63:
1434:
methods (FEMs), the wave function is represented as a linear combination of a set of piecewise polynomials.
1438:(LIPs) are a commonly-used basis for FEM calculations. The local interpolation error in LIP basis of order
1319:
1014:
def2-QZVPPD – Valence quadruple-zeta with two sets of polarization functions and a set of diffuse functions
617:
3-21+G** – Polarization functions on heavy atoms and hydrogen, as well as diffuse functions on heavy atoms
1372:
A combination of some of the properties of localized basis sets and plane-wave approaches is achieved by
435:
Unfortunately, calculating integrals with STOs is computationally difficult and it was later realized by
1002:
def2-TZVPPD – Valence triple-zeta with two sets of polarization functions and a set of diffuse functions
75:
2533:
1722:
Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics
1341:
In practice, plane-wave basis sets are often used in combination with an 'effective core potential' or
362:
are sometimes used interchangeably, although the basis functions are usually not true atomic orbitals.
877:
To understand how to get the number of functions, consider the cc-pVDZ basis set for H: There are two
690:
calculations systematically to the complete basis set limit using empirical extrapolation techniques.
553:
represents the number of primitive Gaussians comprising each core atomic orbital basis function. The
954:
420:
59:
2257:
Lehtola, Susi (2019). "Fully numerical Hartree–Fock and density functional calculations. I. Atoms".
1917:
2025:
Lehtola, Susi (2015). "Automatic algorithms for completeness-optimization of Gaussian basis sets".
1253:
958:
416:
343:
69:
The use of basis sets is equivalent to the use of an approximate resolution of the identity: the
55:
35:
1588:-adaptive FEM). The use of high-order LIPs has been shown to be highly beneficial for accuracy.
1280:
753:
aug-cc-pVDZ, etc. – Augmented versions of the preceding basis sets with added diffuse functions.
404:
2399:
https://web.archive.org/web/20070830043639/http://www.chem.swin.edu.au/modules/mod8/basis1.html
1335:
429:
300:{\textstyle c_{\mu i}=\sum _{\nu }\langle \mu |\nu \rangle ^{-1}\langle \nu |\psi _{i}\rangle }
186:
43:
1404:
980:
Some of the various valence adaptations of Karlsruhe basis sets are briefly described below.
962:
730:
687:
520:
There are several other minimum basis sets that have been used such as the MidiX basis sets.
331:
31:
2218:"The any particle molecular orbital approach: A short review of the theory and applications"
2442:
2190:
2124:
2078:
1890:
1855:
1784:
1226:
658:-type Cartesian-Gaussian polarization functions on each of the atoms Li through Ca and ten
400:
378:
66:
of the model into algebraic equations suitable for efficient implementation on a computer.
2498:
1403:
Various methods have been proposed for constructing the solution in real space, including
573:
basis set. Split-valence triple- and quadruple-zeta basis sets are also used, denoted as
8:
2481:
1435:
327:
2508:
2446:
2194:
2128:
2082:
1894:
1859:
1788:
1568:
2284:
2050:
1980:
1745:
1702:
1655:
1612:
1548:
1528:
1441:
1206:
737:
prefix is added if diffuse functions are included in the basis. Examples of these are:
463:
Ne) would have a basis set of five functions (two s functions and three p functions).
408:
374:
370:
108:
2458:
2421:
2385:
2366:
2347:
2328:
2309:
2239:
2167:
2094:
2042:
1984:
1972:
1937:
1828:
1725:
1706:
1420:
495:
412:
347:
2288:
984:
def2-SV(P) – Split valence with polarization functions on heavy atoms (not hydrogen)
662:-type Cartesian Gaussian polarization functions on each of the atoms Sc through Zn.
2450:
2413:
2274:
2266:
2229:
2198:
2159:
2132:
2086:
2054:
2034:
2007:
1964:
1929:
1898:
1863:
1820:
1792:
1757:
1694:
1665:
1602:
1325:
The main advantage of a plane-wave basis is that it is guaranteed to converge in a
683:
459:
440:
388:
When molecular calculations are performed, it is common to use a basis composed of
323:
2518:
2493:
2202:
1607:
1346:
1342:
1024:
momentum density, which probe different aspects of the electronic wave function.
436:
2503:
1545:-adaptive FEM), by switching to the use of higher and higher order polynomials (
1431:
389:
351:
311:
70:
47:
2513:
972:
The pc-n sets can be augmented with diffuse functions to obtain augpc-n sets.
411:, and decay exponentially far away from the nucleus. It can be shown that the
2527:
2486:
2243:
2171:
2098:
1998:
Chong, Delano P. (1995). "Completeness profiles of one-electron basis sets".
1941:
1412:
1397:
318:
approach), which is the usual choice within the quantum chemistry community;
51:
1028:
property at any level of theory, and the procedure is simple to automatize.
565:
primitive Gaussian functions, the other composed of a linear combination of
2462:
2425:
2046:
1976:
1832:
1011:
def2-QZVPP – Valence quadruple-zeta with two sets of polarization functions
424:
366:
1748:; Feller, David (1986). "Basis set selection for molecular calculations".
466:
176:{\textstyle |\psi _{i}\rangle \approx \sum _{\mu }c_{\mu i}|\mu \rangle }
2514:
Stuttgart/Cologne energy-consistent (ab initio) pseudopotentials Library
2279:
1881:
Jensen, Frank (2001). "Polarization consistent basis sets: Principles".
1761:
999:
def2-TZVPP – Valence triple-zeta with two sets of polarization functions
1933:
1314:
1008:
def2-QZVPD – Valence quadruple-zeta polarization with diffuse functions
591:
Here is a list of commonly used split-valence basis sets of this type:
542:
444:
319:
2454:
2417:
2270:
2234:
2217:
2136:
2090:
2038:
1968:
1902:
1824:
1796:
1698:
1670:
1643:
423:
also exhibit exponential decay. Furthermore, S-type STOs also satisfy
2163:
1867:
1250:
is the number of primitives functions. Here, only the two parameters
2011:
996:
def2-TZVPD – Valence triple-zeta polarization with diffuse functions
1660:
1416:
1408:
693:
For first- and second-row atoms, the basis sets are cc-pVNZ where
2476:
2308:. Englewood Cliffs, New jersey: Prentice Hall. pp. 461–466.
382:
2382:
A Guide to Molecular Mechanics and Quantum Chemical Calculations
1774:
682:
Some of the most widely used basis sets are those developed by
396:
27:
Set of functions used to represent the electronic wave function
1367:
990:
def2-SVPD – Split valence polarization with diffuse functions
2327:. Chichester: John Wiley & Sons, Ltd. pp. 154–168.
601:
3-21G** – Polarization functions on heavy atoms and hydrogen
2432:
2216:
Reyes, Andrés; Moncada, Félix; Charry, Jorge (2019-01-15).
1618:
List of quantum chemistry and solid state physics software
1040:
439:
that STOs could be approximated as linear combinations of
2384:. Irvine, California: Wavefunction, Inc. pp. 40–47.
482:
Another common addition to basis sets is the addition of
385:), whereas two-electron operators are rank four tensors.
2403:
1809:
1565:-adaptive FEM), or by a combination of both strategies (
686:
and coworkers, since they are designed for converging
607:
3-21++G – Diffuse functions on heavy atoms and hydrogen
2114:
765:
accurate geometric and nuclear property calculations.
219:
117:
1744:
1571:
1551:
1531:
1464:
1444:
1283:
1256:
1229:
1209:
1054:
949:
189:
78:
1637:
1635:
1633:
1018:
677:
1685:Jensen, Frank (2013). "Atomic orbital basis sets".
969:set extrapolation techniques to obtain CBS values.
2215:
1580:
1557:
1537:
1517:
1450:
1296:
1269:
1242:
1215:
1195:
299:
205:
175:
99:
2250:
1916:Hellweg, Arnim; Rappoport, Dmitrij (2014-12-10).
1630:
1380:wavefunctions beyond the linearized description.
350:calculations are performed using a finite set of
2525:
2504:Peterson Group Correlation Consistent Basis Sets
2363:Molecular Modelling: Principles and Applications
2184:
1915:
1481:
392:, centered at each nucleus within the molecule (
2067:
1719:
1005:def2-QZVP – Valence quadruple-zeta polarization
399:). The physically best motivated basis set are
598:3-21G* – Polarization functions on heavy atoms
470:A d-polarization function added to a p orbital
2509:Sapporo Segmented Gaussian Basis Sets Library
1954:
993:def2-TZVP – Valence triple-zeta polarization
756:cc-pCVDZ – Double-zeta with core correlation
294:
273:
261:
246:
170:
133:
94:
1518:{\displaystyle h^{n+1}\max f^{(n+1)}(\xi )}
1035:
523:
2222:International Journal of Quantum Chemistry
2152:International Journal of Quantum Chemistry
2117:International Journal of Quantum Chemistry
1368:Linearized augmented-plane-wave basis sets
942: = 0) and 2 sets of p orbitals (
938:As another example, Ar has 3 s orbitals (
2346:. John Wiley and Sons. pp. 150–176.
2278:
2233:
1669:
1659:
604:3-21+G – Diffuse functions on heavy atoms
2406:Journal of the American Chemical Society
1391:
1308:
1039:
465:
310:The basis set can either be composed of
2344:Introduction to Computational Chemistry
2256:
2024:
1845:
1641:
975:
107:are expanded within the basis set as a
14:
2526:
2365:. Singapore: Longman. pp. 68–77.
2341:
2322:
2303:
1880:
1684:
2379:
2360:
2325:Essentials of Computational Chemistry
2149:
2110:
2108:
1997:
1313:In addition to localized basis sets,
987:def2-SVP – Split valence polarization
614:diffuse functions on heavy atoms only
541:basis sets arising from the group of
516:STO-3G* – Polarized version of STO-3G
494:The most common minimal basis set is
394:linear combination of atomic orbitals
316:linear combination of atomic orbitals
1922:Physical Chemistry Chemical Physics
957:has recently become widely used in
672:quantum chemistry composite methods
532:
454:The smallest basis sets are called
403:(STOs), which are solutions to the
183:, where the expansion coefficients
24:
2105:
1436:Lagrange interpolating polynomials
950:Polarization-consistent basis sets
100:{\displaystyle |\psi _{i}\rangle }
25:
2555:
2519:ChemViz – Basis Sets Lab Activity
2470:
1019:Completeness-optimized basis sets
678:Correlation-consistent basis sets
489:
50:) that is used to represent the
2435:The Journal of Chemical Physics
2323:Cramer, Christopher J. (2002).
2209:
2178:
2143:
2071:The Journal of Chemical Physics
2061:
2018:
1991:
1948:
1374:linearized augmented-plane-wave
1158:
1141:
1108:
337:
1909:
1874:
1839:
1803:
1768:
1738:
1720:Errol G. Lewars (2003-01-01).
1713:
1678:
1512:
1506:
1501:
1489:
750:cc-pV5Z – Quintuple-zeta, etc.
280:
253:
163:
119:
80:
64:partial differential equations
13:
1:
1623:
1598:Basis set superposition error
1358:basis-set superposition error
2487:CRYSTAL – Basis Sets Library
2203:10.1016/j.cplett.2012.04.062
1320:periodic boundary conditions
1318:involving three-dimensional
7:
2482:TURBOMOLE basis set library
1591:
1270:{\displaystyle \alpha _{l}}
908:= −1,0,1) corresponding to
430:electron state correlations
10:
2560:
2380:Hehre, Warren J.. (2003).
1724:(1st ed.). Springer.
1349:is often abbreviated as a
1297:{\displaystyle \beta _{l}}
1203:for each angular momentum
365:Within the basis set, the
2361:Leach, Andrew R. (1996).
1388:matrix or atomic forces.
955:Density-functional theory
571:split-valence double-zeta
421:density-functional theory
206:{\displaystyle c_{\mu i}}
60:density-functional theory
2499:Dyall Basis Sets Library
2187:Chemical Physics Letters
1327:smooth, monotonic manner
1036:Even-tempered basis sets
893:= 1) orbital that has 3
747:cc-pVQZ – Quadruple-zeta
524:Split-valence basis sets
52:electronic wave function
2539:Computational chemistry
2477:EMSL Basis Set Exchange
2304:Levine, Ira N. (1991).
1413:Lagrange sinc-functions
1336:fast Fourier transforms
959:computational chemistry
610:3-21+G* – Polarization
344:computational chemistry
111:of the basis functions
36:computational chemistry
2342:Jensen, Frank (1999).
1687:WIREs Comput. Mol. Sci
1642:Lehtola, Susi (2019).
1582:
1559:
1539:
1519:
1452:
1298:
1271:
1244:
1217:
1197:
1045:
885:= 0) orbitals and one
477:polarization functions
471:
441:Gaussian-type orbitals
324:Gaussian-type orbitals
301:
207:
177:
101:
2544:Theoretical chemistry
1583:
1560:
1540:
1520:
1453:
1392:Real-space basis sets
1309:Plane-wave basis sets
1299:
1272:
1245:
1243:{\displaystyle N_{l}}
1218:
1198:
1043:
744:cc-pVTZ – Triple-zeta
741:cc-pVDZ – Double-zeta
713: = double,
537:The notation for the
469:
425:Kato's cusp condition
302:
208:
178:
102:
62:in order to turn the
18:Polarization function
2259:Int. J. Quantum Chem
2189:. 539–540: 209–213.
1648:Int. J. Quantum Chem
1569:
1549:
1529:
1462:
1442:
1281:
1254:
1227:
1207:
1052:
976:Karlsruhe basis sets
405:Schrödinger equation
401:Slater-type orbitals
369:is represented as a
328:Slater-type orbitals
217:
187:
115:
76:
2447:2015JChPh.142i4116C
2195:2012CPL...539..209M
2129:2009IJQC..109.2996C
2083:1974JChPh..60..918B
1895:2001JChPh.115.9113J
1860:1989JChPh..90.1007D
1789:1971JChPh..54..724D
1762:10.1021/cr00074a002
1104:
733:calculations. The
409:hydrogen-like atoms
56:Hartree–Fock method
2492:2020-02-11 at the
1934:10.1039/C4CP04286G
1613:Molecular orbitals
1581:{\displaystyle hp}
1578:
1555:
1535:
1515:
1448:
1294:
1267:
1240:
1213:
1193:
1084:
1046:
549:. In this case,
472:
456:minimal basis sets
413:molecular orbitals
297:
245:
203:
173:
148:
109:linear combination
97:
2534:Quantum chemistry
2455:10.1063/1.4913569
2418:10.1021/ja0630285
2391:978-1-890661-18-2
2372:978-0-582-23933-3
2334:978-0-471-48552-0
2315:978-0-205-12770-2
2306:Quantum Chemistry
2271:10.1002/qua.25945
2235:10.1002/qua.25705
2137:10.1002/qua.22090
2123:(13): 2996–3002.
2091:10.1063/1.1681168
2039:10.1002/jcc.23802
1969:10.1002/jcc.20358
1903:10.1063/1.1413524
1889:(20): 9113–9125.
1825:10.1021/ja0630285
1819:(29): 9342–9343.
1797:10.1063/1.1674902
1699:10.1002/wcms.1123
1671:10.1002/qua.25968
1558:{\displaystyle p}
1538:{\displaystyle h}
1451:{\displaystyle n}
1421:Finite difference
1216:{\displaystyle l}
963:post-Hartree–Fock
875:
874:
731:post-Hartree–Fock
688:post-Hartree–Fock
484:diffuse functions
381:(a.k.a. rank two
332:post-Hartree–Fock
236:
139:
16:(Redirected from
2551:
2466:
2429:
2395:
2376:
2357:
2338:
2319:
2293:
2292:
2282:
2254:
2248:
2247:
2237:
2213:
2207:
2206:
2182:
2176:
2175:
2164:10.1002/qua.1106
2147:
2141:
2140:
2112:
2103:
2102:
2065:
2059:
2058:
2022:
2016:
2015:
1995:
1989:
1988:
1952:
1946:
1945:
1928:(2): 1010–1017.
1913:
1907:
1906:
1878:
1872:
1871:
1868:10.1063/1.456153
1854:(2): 1007–1023.
1843:
1837:
1836:
1813:J. Am. Chem. Soc
1807:
1801:
1800:
1772:
1766:
1765:
1746:Davidson, Ernest
1742:
1736:
1735:
1717:
1711:
1710:
1682:
1676:
1675:
1673:
1663:
1639:
1603:Angular momentum
1587:
1585:
1584:
1579:
1564:
1562:
1561:
1556:
1544:
1542:
1541:
1536:
1524:
1522:
1521:
1516:
1505:
1504:
1480:
1479:
1457:
1455:
1454:
1449:
1430:For example, in
1303:
1301:
1300:
1295:
1293:
1292:
1276:
1274:
1273:
1268:
1266:
1265:
1249:
1247:
1246:
1241:
1239:
1238:
1222:
1220:
1219:
1214:
1202:
1200:
1199:
1194:
1192:
1191:
1151:
1150:
1131:
1130:
1118:
1117:
1103:
1092:
1083:
1082:
1070:
1069:
776:
775:
533:Pople basis sets
348:quantum chemical
306:
304:
303:
298:
293:
292:
283:
272:
271:
256:
244:
232:
231:
212:
210:
209:
204:
202:
201:
182:
180:
179:
174:
166:
161:
160:
147:
132:
131:
122:
106:
104:
103:
98:
93:
92:
83:
21:
2559:
2558:
2554:
2553:
2552:
2550:
2549:
2548:
2524:
2523:
2494:Wayback Machine
2473:
2392:
2373:
2354:
2335:
2316:
2297:
2296:
2255:
2251:
2214:
2210:
2183:
2179:
2148:
2144:
2113:
2106:
2066:
2062:
2027:J. Comput. Chem
2023:
2019:
2012:10.1139/v95-011
1996:
1992:
1957:J. Comput. Chem
1953:
1949:
1914:
1910:
1879:
1875:
1844:
1840:
1808:
1804:
1773:
1769:
1743:
1739:
1732:
1718:
1714:
1683:
1679:
1640:
1631:
1626:
1608:Atomic orbitals
1594:
1570:
1567:
1566:
1550:
1547:
1546:
1530:
1527:
1526:
1488:
1484:
1469:
1465:
1463:
1460:
1459:
1458:is of the form
1443:
1440:
1439:
1405:finite elements
1394:
1370:
1347:pseudopotential
1343:pseudopotential
1330:approach zero.
1311:
1288:
1284:
1282:
1279:
1278:
1261:
1257:
1255:
1252:
1251:
1234:
1230:
1228:
1225:
1224:
1208:
1205:
1204:
1187:
1183:
1146:
1142:
1126:
1122:
1113:
1109:
1093:
1088:
1078:
1074:
1059:
1055:
1053:
1050:
1049:
1038:
1021:
978:
952:
934:
925:
916:
907:
680:
650:6-311+G(2df,2p)
535:
526:
492:
390:atomic orbitals
352:basis functions
340:
312:atomic orbitals
288:
284:
279:
264:
260:
252:
240:
224:
220:
218:
215:
214:
194:
190:
188:
185:
184:
162:
153:
149:
143:
127:
123:
118:
116:
113:
112:
88:
84:
79:
77:
74:
73:
48:basis functions
28:
23:
22:
15:
12:
11:
5:
2557:
2547:
2546:
2541:
2536:
2522:
2521:
2516:
2511:
2506:
2501:
2496:
2484:
2479:
2472:
2471:External links
2469:
2468:
2467:
2430:
2412:(29): 9342–3.
2401:
2396:
2390:
2377:
2371:
2358:
2353:978-0471980858
2352:
2339:
2333:
2320:
2314:
2295:
2294:
2265:(19): e25945.
2249:
2208:
2177:
2158:(6): 511–517.
2142:
2104:
2077:(3): 918–931.
2060:
2033:(5): 335–347.
2017:
1990:
1963:(4): 434–445.
1947:
1908:
1873:
1838:
1802:
1783:(2): 724–728.
1767:
1756:(4): 681–696.
1737:
1731:978-1402072857
1730:
1712:
1693:(3): 273–295.
1677:
1654:(19): e25968.
1628:
1627:
1625:
1622:
1621:
1620:
1615:
1610:
1605:
1600:
1593:
1590:
1577:
1574:
1554:
1534:
1514:
1511:
1508:
1503:
1500:
1497:
1494:
1491:
1487:
1483:
1478:
1475:
1472:
1468:
1447:
1432:finite element
1393:
1390:
1369:
1366:
1310:
1307:
1291:
1287:
1264:
1260:
1237:
1233:
1212:
1190:
1186:
1182:
1179:
1176:
1173:
1170:
1167:
1164:
1161:
1157:
1154:
1149:
1145:
1140:
1137:
1134:
1129:
1125:
1121:
1116:
1112:
1107:
1102:
1099:
1096:
1091:
1087:
1081:
1077:
1073:
1068:
1065:
1062:
1058:
1037:
1034:
1020:
1017:
1016:
1015:
1012:
1009:
1006:
1003:
1000:
997:
994:
991:
988:
985:
977:
974:
951:
948:
930:
921:
912:
905:
873:
872:
869:
866:
863:
859:
858:
855:
852:
849:
845:
844:
841:
838:
835:
831:
830:
827:
824:
821:
817:
816:
813:
810:
807:
803:
802:
799:
796:
793:
789:
788:
785:
782:
779:
758:
757:
754:
751:
748:
745:
742:
679:
676:
652:
651:
648:
645:
642:
639:
636:
633:
630:
627:
624:
621:
618:
615:
608:
605:
602:
599:
596:
534:
531:
525:
522:
518:
517:
514:
511:
508:
491:
488:
377:correspond to
360:atomic orbital
356:basis function
339:
336:
314:(yielding the
296:
291:
287:
282:
278:
275:
270:
267:
263:
259:
255:
251:
248:
243:
239:
235:
230:
227:
223:
200:
197:
193:
172:
169:
165:
159:
156:
152:
146:
142:
138:
135:
130:
126:
121:
96:
91:
87:
82:
26:
9:
6:
4:
3:
2:
2556:
2545:
2542:
2540:
2537:
2535:
2532:
2531:
2529:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2491:
2488:
2485:
2483:
2480:
2478:
2475:
2474:
2464:
2460:
2456:
2452:
2448:
2444:
2441:(9): 094116.
2440:
2436:
2431:
2427:
2423:
2419:
2415:
2411:
2407:
2402:
2400:
2397:
2393:
2387:
2383:
2378:
2374:
2368:
2364:
2359:
2355:
2349:
2345:
2340:
2336:
2330:
2326:
2321:
2317:
2311:
2307:
2302:
2301:
2300:
2290:
2286:
2281:
2276:
2272:
2268:
2264:
2260:
2253:
2245:
2241:
2236:
2231:
2228:(2): e25705.
2227:
2223:
2219:
2212:
2204:
2200:
2196:
2192:
2188:
2181:
2173:
2169:
2165:
2161:
2157:
2153:
2146:
2138:
2134:
2130:
2126:
2122:
2118:
2111:
2109:
2100:
2096:
2092:
2088:
2084:
2080:
2076:
2072:
2064:
2056:
2052:
2048:
2044:
2040:
2036:
2032:
2028:
2021:
2013:
2009:
2005:
2001:
1994:
1986:
1982:
1978:
1974:
1970:
1966:
1962:
1958:
1951:
1943:
1939:
1935:
1931:
1927:
1923:
1919:
1912:
1904:
1900:
1896:
1892:
1888:
1884:
1883:J. Chem. Phys
1877:
1869:
1865:
1861:
1857:
1853:
1849:
1848:J. Chem. Phys
1842:
1834:
1830:
1826:
1822:
1818:
1814:
1806:
1798:
1794:
1790:
1786:
1782:
1778:
1777:J. Chem. Phys
1771:
1763:
1759:
1755:
1751:
1747:
1741:
1733:
1727:
1723:
1716:
1708:
1704:
1700:
1696:
1692:
1688:
1681:
1672:
1667:
1662:
1657:
1653:
1649:
1645:
1638:
1636:
1634:
1629:
1619:
1616:
1614:
1611:
1609:
1606:
1604:
1601:
1599:
1596:
1595:
1589:
1575:
1572:
1552:
1532:
1509:
1498:
1495:
1492:
1485:
1476:
1473:
1470:
1466:
1445:
1437:
1433:
1428:
1424:
1422:
1418:
1414:
1410:
1409:basis splines
1406:
1401:
1399:
1398:interpolation
1389:
1385:
1381:
1377:
1375:
1365:
1361:
1359:
1354:
1353:calculation.
1352:
1348:
1344:
1339:
1337:
1331:
1328:
1323:
1321:
1316:
1306:
1289:
1285:
1262:
1258:
1235:
1231:
1210:
1188:
1184:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1155:
1152:
1147:
1143:
1138:
1135:
1132:
1127:
1123:
1119:
1114:
1110:
1105:
1100:
1097:
1094:
1089:
1085:
1079:
1075:
1071:
1066:
1063:
1060:
1056:
1042:
1033:
1029:
1025:
1013:
1010:
1007:
1004:
1001:
998:
995:
992:
989:
986:
983:
982:
981:
973:
970:
966:
964:
960:
956:
947:
945:
941:
936:
933:
929:
924:
920:
915:
911:
904:
900:
896:
892:
888:
884:
880:
870:
867:
864:
861:
860:
856:
853:
850:
847:
846:
842:
839:
836:
833:
832:
828:
825:
822:
819:
818:
814:
811:
808:
805:
804:
800:
797:
794:
791:
790:
786:
783:
780:
778:
777:
774:
770:
766:
762:
755:
752:
749:
746:
743:
740:
739:
738:
736:
732:
728:
724:
720:
716:
712:
708:
704:
700:
697: =
696:
691:
689:
685:
675:
673:
669:
663:
661:
657:
649:
646:
643:
640:
637:
634:
631:
628:
625:
622:
619:
616:
613:
609:
606:
603:
600:
597:
594:
593:
592:
589:
586:
582:
580:
576:
572:
568:
564:
560:
556:
552:
548:
545:is typically
544:
540:
539:split-valence
530:
521:
515:
512:
509:
506:
505:
504:
501:
497:
490:STO hierarchy
487:
485:
480:
478:
468:
464:
461:
457:
452:
448:
446:
442:
438:
433:
431:
426:
422:
418:
414:
410:
406:
402:
398:
395:
391:
386:
384:
380:
376:
372:
368:
363:
361:
357:
353:
349:
345:
335:
333:
329:
325:
321:
317:
313:
308:
289:
285:
276:
268:
265:
257:
249:
241:
237:
233:
228:
225:
221:
213:are given by
198:
195:
191:
167:
157:
154:
150:
144:
140:
136:
128:
124:
110:
89:
85:
72:
67:
65:
61:
57:
53:
49:
45:
41:
37:
33:
19:
2438:
2434:
2409:
2405:
2381:
2362:
2343:
2324:
2305:
2298:
2280:10138/311128
2262:
2258:
2252:
2225:
2221:
2211:
2186:
2180:
2155:
2151:
2145:
2120:
2116:
2074:
2070:
2063:
2030:
2026:
2020:
2006:(1): 79–83.
2003:
2000:Can. J. Chem
1999:
1993:
1960:
1956:
1950:
1925:
1921:
1911:
1886:
1882:
1876:
1851:
1847:
1841:
1816:
1812:
1805:
1780:
1776:
1770:
1753:
1749:
1740:
1721:
1715:
1690:
1686:
1680:
1651:
1647:
1429:
1425:
1402:
1395:
1386:
1382:
1378:
1371:
1362:
1355:
1350:
1340:
1332:
1326:
1324:
1312:
1047:
1032:basis sets.
1030:
1026:
1022:
979:
971:
967:
953:
943:
939:
937:
931:
927:
922:
918:
913:
909:
902:
898:
890:
886:
882:
878:
876:
862:aug-cc-pVQZ
848:aug-cc-pVTZ
834:aug-cc-pVDZ
771:
767:
763:
759:
734:
726:
722:
718:
714:
710:
706:
702:
698:
694:
692:
681:
667:
664:
659:
655:
653:
611:
590:
587:
583:
578:
574:
570:
566:
562:
558:
554:
550:
546:
538:
536:
527:
519:
499:
493:
483:
481:
476:
473:
460:Hartree–Fock
455:
453:
449:
434:
417:Hartree–Fock
387:
367:wavefunction
364:
359:
355:
341:
338:Introduction
309:
68:
42:is a set of
39:
29:
871:→ 84 func.
868:→ 80 func.
865:→ 46 func.
857:→ 50 func.
854:→ 46 func.
851:→ 23 func.
843:→ 27 func.
840:→ 23 func.
829:→ 59 func.
826:→ 55 func.
823:→ 30 func.
815:→ 34 func.
812:→ 30 func.
809:→ 14 func.
801:→ 18 func.
798:→ 14 func.
320:plane waves
32:theoretical
2528:Categories
1661:1902.01431
1624:References
1334:out using
1315:plane-wave
897:along the
895:components
837:→ 9 func.
795:→ 5 func.
709:,5,6,... (
543:John Pople
503:type are:
445:John Pople
437:Frank Boys
342:In modern
2244:0020-7608
2172:0020-7608
2099:0021-9606
1985:206030278
1942:1463-9084
1750:Chem. Rev
1707:124142343
1510:ξ
1286:β
1259:α
1178:…
1153:≠
1144:β
1124:β
1111:α
1098:−
1086:β
1076:α
1057:α
581:, etc.
375:operators
334:methods.
295:⟩
286:ψ
277:ν
274:⟨
266:−
262:⟩
258:ν
250:μ
247:⟨
242:ν
238:∑
226:μ
196:μ
171:⟩
168:μ
155:μ
145:μ
141:∑
137:≈
134:⟩
125:ψ
95:⟩
86:ψ
44:functions
40:basis set
2490:Archived
2463:25747070
2426:16848464
2289:85516860
2047:25487276
1977:16419020
1833:16848464
1592:See also
1417:wavelets
1223:, where
820:cc-pVQZ
806:cc-pVTZ
792:cc-pVDZ
647:6-311+G*
379:matrices
71:orbitals
46:(called
2443:Bibcode
2191:Bibcode
2125:Bibcode
2079:Bibcode
2055:5726685
1891:Bibcode
1856:Bibcode
1785:Bibcode
901:-axis (
684:Dunning
644:6-311G*
635:6-31+G*
579:X-YZWVg
383:tensors
54:in the
2461:
2424:
2388:
2369:
2350:
2331:
2312:
2287:
2242:
2170:
2097:
2053:
2045:
1983:
1975:
1940:
1831:
1728:
1705:
1415:, and
787:Na-Ar
784:Li-Ne
641:6-311G
632:6-31G*
575:X-YZWg
513:STO-6G
510:STO-4G
507:STO-3G
496:STO-nG
397:ansatz
371:vector
2285:S2CID
2051:S2CID
1981:S2CID
1703:S2CID
1656:arXiv
781:H-He
629:6-31G
626:6-21G
623:4-31G
620:4-21G
595:3-21G
547:X-YZg
2459:PMID
2422:PMID
2386:ISBN
2367:ISBN
2348:ISBN
2329:ISBN
2310:ISBN
2240:ISSN
2168:ISSN
2095:ISSN
2043:PMID
1973:PMID
1938:ISSN
1829:PMID
1726:ISBN
1351:PSPW
1277:and
1133:>
926:and
735:aug-
557:and
419:and
358:and
38:, a
34:and
2451:doi
2439:142
2414:doi
2410:128
2275:hdl
2267:doi
2263:119
2230:doi
2226:119
2199:doi
2160:doi
2133:doi
2121:109
2087:doi
2035:doi
2008:doi
1965:doi
1930:doi
1899:doi
1887:115
1864:doi
1821:doi
1817:128
1793:doi
1758:doi
1695:doi
1666:doi
1652:119
1482:max
612:and
447:).
415:of
407:of
58:or
30:In
2530::
2457:.
2449:.
2437:.
2420:.
2408:.
2283:.
2273:.
2261:.
2238:.
2224:.
2220:.
2197:.
2166:.
2156:86
2154:.
2131:.
2119:.
2107:^
2093:.
2085:.
2075:60
2073:.
2049:.
2041:.
2031:36
2029:.
2004:73
2002:.
1979:.
1971:.
1961:27
1959:.
1936:.
1926:17
1924:.
1920:.
1897:.
1885:.
1862:.
1852:90
1850:.
1827:.
1815:.
1791:.
1781:54
1779:.
1754:86
1752:.
1701:.
1689:.
1664:.
1650:.
1646:.
1632:^
1419:.
1411:,
1407:,
1322:.
917:,
725:,
721:,
674:.
668:sp
577:,
432:.
346:,
326:,
307:.
2465:.
2453::
2445::
2428:.
2416::
2394:.
2375:.
2356:.
2337:.
2318:.
2291:.
2277::
2269::
2246:.
2232::
2205:.
2201::
2193::
2174:.
2162::
2139:.
2135::
2127::
2101:.
2089::
2081::
2057:.
2037::
2014:.
2010::
1987:.
1967::
1944:.
1932::
1905:.
1901::
1893::
1870:.
1866::
1858::
1835:.
1823::
1799:.
1795::
1787::
1764:.
1760::
1734:.
1709:.
1697::
1691:3
1674:.
1668::
1658::
1576:p
1573:h
1553:p
1533:h
1513:)
1507:(
1502:)
1499:1
1496:+
1493:n
1490:(
1486:f
1477:1
1474:+
1471:n
1467:h
1446:n
1290:l
1263:l
1236:l
1232:N
1211:l
1189:l
1185:N
1181:,
1175:,
1172:2
1169:,
1166:1
1163:=
1160:i
1156:1
1148:l
1139:,
1136:0
1128:l
1120:,
1115:l
1106:,
1101:1
1095:i
1090:l
1080:l
1072:=
1067:l
1064:,
1061:i
944:L
940:L
932:z
928:p
923:y
919:p
914:x
910:p
906:L
903:m
899:z
891:L
889:(
887:p
883:L
881:(
879:s
727:g
723:f
719:d
715:T
711:D
707:Q
705:,
703:T
701:,
699:D
695:N
660:f
656:d
567:Z
563:Y
559:Z
555:Y
551:X
500:n
290:i
281:|
269:1
254:|
234:=
229:i
222:c
199:i
192:c
164:|
158:i
151:c
129:i
120:|
90:i
81:|
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.