LCAO local-spin-density and Xα calculations for Cr<sub>2</sub>and Mo<sub>2</sub>

Baykara, N. A.; McMaster, Blair N.; Salahub, Dennis R.

doi:10.1080/00268978400101641

Cited by 91 publications

(40 citation statements)

References 38 publications

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“…In addi-tion, a number of truly noncollinear starting spin configurations ͑typically 20͒ are considered. This includes the magnetic order reported in previous studies, 20,21,[23][24][25]38 random orientations of the ជ i , together with the NC spin orders obtained by varying the parameters of a self-consistent d-band Hamiltonian model. 39,40 It is important to remark that in all cases, i.e., for all S z and for all starting noncollinear configurations, the geometry has been optimized following the forces resulting from the self-consistent solution of the KS equations.…”

Section: Theoretical Methodsmentioning

confidence: 99%

Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

et al. 2010

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The magnetic properties of small Cr N clusters ͑N Յ 6͒ are investigated in the framework of densityfunctional theory. The interplay between electron correlations, cluster structure, and magnetic order is quantified by performing fully spin-unrestricted calculations allowing for noncollinear spin arrangements within both the local-spin-density approximation ͑LSDA͒ and the generalized-gradient approximation ͑GGA͒. The possible transition or saddle-point states are identified by determining the vibrational frequencies from diagonalizing the dynamical matrix. In agreement with previous studies, a dimer-based growth pattern is found in all considered low-lying isomers with very short equilibrium bond lengths ͑typically d eq GGA = 1.55-1.65 Å͒ alternating with relative long ones ͑typically d eq GGA = 2.75-2.85 Å͒ in the relaxed geometries. Strong local magnetic moments ជ i are, in general, obtained for the relaxed geometries ͑e.g., ͉ i GGA ͉Ӎ2 B in Cr 4 ͒, which show a collinear magnetic order with antiparallel ͑parallel͒ alignment of the ជ i along the short ͑long͒ bonds. In contrast to the GGA, the LSDA yields vanishing magnetization density in some cases ͉͑ i LSDA ͉ =0 ∀ i for N = 2 and 4͒. Despite quantitative differences, both LSDA and GGA functionals always yield collinear ground-state solutions for the fully relaxed structures. In fact, noncollinear spin arrangements are found only for particular symmetric ͑nondimerized͒ geometries. However, the structures are not local minima and involve considerably large excitation energies. The results clearly indicate that the magnetic frustration, which one would physically expect in compact antiferromagnetic spin systems, is solved by dimerization rather than by noncollinearity of the local moments.

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Section: Theoretical Methodsmentioning

confidence: 99%

Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

et al. 2010

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“…To accurately account for these effects has proven to be an intricate computational task. Many different theoretical methods have been used in the past in attempts to reproduce the spectroscopic quantities experimentally measured: generalized valence bond [1,2], density functional theory [3][4][5][6][7][8][9][10][11][12], coupled cluster methods [3], multi-reference perturbation theory [13][14][15][16][17][18][19][20][21][22], multi-reference configuration interaction (MRCI), and its variants like multi-reference average coupled-pair functionals (MRACPF) [23][24][25]. For the specific purpose of this paper the studies that use multi-reference configuration interaction and multireference perturbation theory are of particular interest.…”

Section: Introductionmentioning

confidence: 99%

The CIPT2 method: Coupling of multi-reference configuration interaction and multi-reference perturbation theory. Application to the chromium dimer

et al. 2004

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The potential energy function of Cr 2 (X 1 AE þ g ) is computed using the MRCI þ Q (multi-reference configuration interaction with Davidson correction) and CASPT2 (complete active space second-order multi-reference perturbation theory) methods and very large basis sets. In addition, a new hybrid method denoted CIPT2, in which excitations solely from the active space are treated by MRCI and the remaining ones by perturbation theory, is proposed and applied. These methods are used to analyse valence and core correlation effects on the potential energy function. MRCI calculations which fully include correlation of the 3p, 3d, and 4s electrons yield excellent agreement with experimental values for the equilibrium distance R e and the harmonic vibrational constant ! e . Correlation of the (3p) orbitals is found to be very important. At the MRCI þ Q level this reduces R e by 0.08 Å and increases ! e by about 200 cm À1 . These effects are not correctly reproduced in CASPT2 and CIPT2. It is shown that in CASPT2 the valence correlation effects are significantly overestimated and the distance dependence of the core correlation is incorrect. The basis set limit of the dissociation energies for MRCI þ Q and CASPT 2 is estimated to be 1.3 eV and 1.9 eV, respectively. The remaining error (% 0:2 À 0:3 eV) of the MRCI þ Q dissociation energy is attributed to unlinked cluster and higher excitation effects, which are only approximately accounted for by the Davidson correction. IntroductionThe calculation of the dissociation energy and spectroscopic properties of the Cr 2 dimer is a severe test for ab initio electron correlation methods. Its (formally) hextuple 1 AE þ g bond dissociates along the ground-state potential curve to two high-spin Cr atoms with d 5 s 1 ( 7 S) configuration. This leads to very large differential electron correlation effects. In addition, near the equilibrium distance there is a subtle competition between bonding of the 4s and 3d electrons, and repulsion of the 3p-electrons, which makes it necessary to correlate all electrons in the 3p, 3d, and 4s orbitals. To accurately account for these effects has proven to be an intricate computational task. Many different theoretical methods have been used in the past in attempts to reproduce the spectroscopic quantities experimentally measured: generalized valence bond [1, 2], density functional theory [3][4][5][6][7][8][9][10][11][12], coupled cluster methods [3], multi-reference perturbation theory [13][14][15][16][17][18][19][20][21][22], multi-reference configuration

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“…relativistic pseudopotentials PP . Finally, Salahub w x et al 8,9 studied Mo using the model potential 2 …”

Section: Introduction Ommercial Catalysts Based On Molybdenummentioning

confidence: 99%

Density functional study of small molybdenum clusters

Diez

2000

Int. J. Quant. Chem.

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Small molybdenum clusters up to the tetramer are investigated within the framework of the density functional theory. Both the geometry and the spin state are optimized for the dimer, trimer, and the tetramer. Moreover, all those calculations are followed by a vibrational analysis to discriminate between real minima and saddle points on the potential energy surfaces. Several low-lying excited states are found to be stable after the vibrational analysis. Equilibrium geometries, electronic configurations, binding energies, magnetic moments, and harmonic frequencies of the stable conformers are reported.

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LCAO local-spin-density and Xα calculations for Cr₂and Mo₂

Cited by 91 publications

References 38 publications

Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

The CIPT2 method: Coupling of multi-reference configuration interaction and multi-reference perturbation theory. Application to the chromium dimer

Density functional study of small molybdenum clusters

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LCAO local-spin-density and Xα calculations for Cr2and Mo2

Cited by 91 publications

References 38 publications

Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

Magnetism of small Cr clusters: Interplay between structure, magnetic order, and electron correlations

The CIPT2 method: Coupling of multi-reference configuration interaction and multi-reference perturbation theory. Application to the chromium dimer

Density functional study of small molybdenum clusters

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LCAO local-spin-density and Xα calculations for Cr₂and Mo₂