Natural atomic orbitals

In the previous discussion of contracted basis functions, the general contraction scheme of Raffenetti, in which every primitive can contribute to every contracted function, was mentioned. The alternate approach produces functions that are sometimes referred to as segmented contractions since the primitives are partitioned into disjoint or almost disjoint sets. Because FORTRAN programs to efficiently implement the general contraction scheme were not very common in the 1960s and 1970s, most basis sets are of the segmented variety. For example, all of the Pople-style basis sets are of this type. 

Almlof and Taylor propose using all ANOs with comparable occupation 

These authors maintain that properties, such as the dipole moment, polarizabilities, and infrared intensities, can be reproduced with near Hartree— Fock accuracy using a relatively small DZP + diffuse basis. In the review by Davidson and Feller the results from an atom-fixed ANO basis are compared with results obtained from many other types of basis sets for a variety of energy-related and 1-elearon properties of formaldehyde. 

Other recent applications of ANO basis sets include the work of Bausch-licher and Langhoff on the A ground state of FeH. Large multiconfiguration SCF (MCSCF)/MR SD-CI calculations were carried out with a (20s,15p,10d, 6f,4g/8s,6p,4d) primitive basis contracted to [8s,7p,5d,3f,2g/4s,3p,2d]. Exponents for the f and g funaions were chosen in an even-tempered fashion (Of 0.0696, ttg = 0.2088, pf,g = 2.5). 

Some applications of perturbation theory to molecular problems would benefit from the simplicity of an extended floating spherical Gaussian basis. Adamowicz and Bartlett ° have developed a procedure for projecting large conventional basis set wave functions onto a floating spherical Gaussian basis. 

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Atomic natural orbital (ANO) basis sets [44] are fonned by contracting Gaussian fiinctions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with... 

There are several types of basis functions listed below. Over the past several decades, most basis sets have been optimized to describe individual atoms at the EIF level of theory. These basis sets work very well, although not optimally, for other types of calculations. The atomic natural orbital, ANO, basis sets use primitive exponents from older EIF basis sets with coefficients obtained from the natural orbitals of correlated atom calculations to give a basis that is a bit better for correlated calculations. The correlation-consistent basis sets have been completely optimized for use with correlated calculations. Compared to ANO basis sets, correlation consistent sets give a comparable accuracy with significantly fewer primitives and thus require less CPU time. 

One popular way of obtaining general contraction coefficients is from Atomic Natural Orbitals (ANO), to be discussed in section 5.4.4. The difference between segmented and general contraction may be illustrated as shown in Figure 5.2. 

Finally, we mention the very encouraging successes combining atomic natural orbitals and full Cl calculations for small molecules (Almlof, Bauschllcher, and Taylor). With this method the singlet-triplet splittings... 

Atomic natural orbitals, use, 18 Attached processors FPS-164, 238-239 IBM hosts, 239 Aufbau principle, 51-52 Axial momentum, conservation of, CVD reactor, 337... 

It is not possible to use normal AO basis sets in relativistic calculations The relativistic contraction of the inner shells makes it necessary to design new basis sets to account for this effect. Specially designed basis sets have therefore been constructed using the DKH Flamiltonian. These basis sets are of the atomic natural orbital (ANO) type and are constructed such that semi-core electrons can also be correlated. They have been given the name ANO-RCC (relativistic with core correlation) and cover all atoms of the Periodic Table.36-38 They have been used in most applications presented in this review. ANO-RCC are all-electron basis sets. Deep core orbitals are described by a minimal basis set and are kept frozen in the wave function calculations. The extra cost compared with using effective core potentials (ECPs) is therefore limited. ECPs, however, have been used in some studies, and more details will be given in connection with the specific application. The ANO-RCC basis sets can be downloaded from the home page of the MOLCAS quantum chemistry software (http //www.teokem.lu.se/molcas). 

Calculations of ionization energies and electron affinities were performed with a modified development version of Gaussian 99 [48], Pople and Effective Core Potential (ECP) basis sets are provided in this software [49], Dunning and Atomic Natural Orbital (ANO) basis sets were obtained from the EMSL Gaussian Basis Set Library [50],... 

All calculations were carried out with the software MOLCAS-6.0 [16]. Scalar relativistic effects were included using a DKH Hamiltonian [14,15]. Specially designed basis sets of the atomic natural orbital type were used. These basis sets have been optimized with the scalar DKH Hamiltonian. They were generated using the CASSCF/CASPT2 method. The semi-core electrons (ns, np, n — 3,4, 5) were included in the correlation treatment. More details can be found in Refs. [17-19]. The size of the basis sets is presented in Table 1. All atoms have been computed with basis sets including up to g-type function. For the first row TMs we also studied the effect of adding two h-type functions. 

Almlof, J., Taylor, P.R. Atomic natural orbital (ANO) basis-sets for quantum-chemical calculations. Adv. Quantum Chem. 1991, 22, 301-73. 

Pierloot, K., Dumez, B., Widmark, P.-O., Roos, B.O. Density-matrix averaged atomic natural orbital (ANO) basis-sets for correlated molecular wave-functions. IV. Medium-size basis-sets for the atoms H-Kr. Theor. Chim. Acta 1995, 90, 87-114. 

Sources. Results taken from Ref. 69 the near-HF SCF Slater bases are from Ref. 70. The 6-31IG basis is that of Ref. 16. The contracted ANO (atomic natural orbital) bases [72] are indicated in [69], as well as the (13r 2d If) basis constructed with the help of van Duijneveldt s (13i 8p) basis [18] augmented with d and / functions taken from Ref. 17. 

SDCI results obtained [69] with the ANO (atomic natural orbital) [Is6p3d] basis given in Ref. 86. Taken as minus the appropriate sum of ionization potentials [80]. 

Gaussian Basis Sets. I. Atomic Natural Orbitals for First- and Second-Row Atoms. 

Three basis sets were used in the CCSD calculations. The first, designated ANOl, is an atomic natural orbital set consisting of 4s3pld contracted functions on C, 2slp on H, and a set of spd diffuse functions positioned at the center of the molecule. The... 

Almlof, J., and P. R. Taylor (1987). General contraction of Gaussian basis sets. I. Atomic natural orbitals for first- and second-row atoms. J. Chem. Phys. 86, 4070-77. 

ANO Atomic Natural Orbitals. A basis set constructed from maximization of the... 

Modihed JNeglect of Diatomic Overlap fMNDO) 3.10.4 Austin Model 1 (AMI) 86 87 5.4.3 MINI, MIDI and MAXI Basis Sets 5.4.4 Atomic Natural Orbitals Basis Sets 161 161... 

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