Density functional theory stability

The stability of SCF solutions for unknown systems should always be tested. Stability considerations apply to and may be tested for in calculations using Density Functional Theory methods as well. 

As a final note, be aware that Hartree-Fock calculations performed with small basis sets are many times more prone to finding unstable SCF solutions than are larger calculations. Sometimes this is a result of spin contamination in other cases, the neglect of electron correlation is at the root. The same molecular system may or may not lead to an instability when it is modeled with a larger basis set or a more accurate method such as Density Functional Theory. Nevertheless, wavefunctions should still be checked for stability with the SCF=Stable option. ... 

Fischer-type carbene complexes, generally characterized by the formula (CO)5M=C(X)R (M=Cr, Mo, W X=7r-donor substitutent, R=alkyl, aryl or unsaturated alkenyl and alkynyl), have been known now for about 40 years. They have been widely used in synthetic reactions [37,51-58] and show a very good reactivity especially in cycloaddition reactions [59-64]. As described above, Fischer-type carbene complexes are characterized by a formal metal-carbon double bond to a low-valent transition metal which is usually stabilized by 7r-acceptor substituents such as CO, PPh3 or Cp. The electronic structure of the metal-carbene bond is of great interest because it determines the reactivity of the complex [65-68]. Several theoretical studies have addressed this problem by means of semiempirical [69-73], Hartree-Fock (HF) [74-79] and post-HF [80-83] calculations and lately also by density functional theory (DFT) calculations [67, 84-94]. Often these studies also compared Fischer-type and... 

Only the structures of di- and trisulfane have been determined experimentally. For a number of other sulfanes structural information is available from theoretical calculations using either density functional theory or ab initio molecular orbital theory. In all cases the unbranched chain has been confirmed as the most stable structure but these chains can exist as different ro-tamers and, in some cases, as enantiomers. However, by theoretical methods information about the structures and stabilities of additional isomeric sul-fane molecules with branched sulfur chains and cluster-like structures was obtained which were identified as local minima on the potential energy hypersurface (see later). 

Geometries, hyperfme structure, and relative stabilities of the different positional isomers of monodeuterated benzene cations have been studied theoretically by density functional theory, using the B3-LYP functional, and experimentally by ESR and ENDOR spectroscopy. A comparison between theoretical and experimental results at 30 K gives acceptable agreement, but further experiments on multiply deuterated species should improve the analysis by making the effects of deuteration larger. 

ROsch N (1999) A Critical Assessment of Density Functional Theory with Regard to Applications in Organometallic Chemistry. 4 109-163 Roucoux A (2005) Stabilized Noble Metal Nanoparticles An Unavoidable Family of Catalysts for Arene Derivative Hydrogenation. 16 261-279... 

Density functional theory study of aqueous-phase rate acceleration and endo/exo selectivity of the butadiene and acrolein Diels-Alder reaction72 shows that approximately 50% of the rate acceleration and endo/exo selectivity is attributed to hydrogen bonding and the remainder to bulk-phase effects, including enforced hydrophobic interactions and cosolvent effects. This appears to be supported by the experimental results of Engberts where a pseudothermodynamic analysis of the rate acceleration in water relative to 1-propanol and 1-propanol-water mixtures indicates that hydrogen-bond stabilization of the polarized activated complex and the decrease of the hydrophobic surface area of the reactants during the activation process are the two main causes of the rate enhancement in water.13... 

The crystal structures of raer-[lr(en)(enl I )C13]C1 1120 and mer-[Ir(en)(en )Cl3] show that the coordination geometry of Ir is almost identical in the two complexes, with the only difference being in the conformation of the unidentate en and enH+ groups.122 Density functional theory and ab initio calculations have been performed on the two complexes and the calculated confirmations agree well with the X-ray diffraction values.123 The enH+ ligand is stabilized via intramolecular N—H - - Cl hydrogen bonds. 

A recent ab initio quantum mechanical study (Han et al, 1998) used B3LYP/6-31G density functional theory to examine the relative stabilities of eight conformers of AAMA with four explicit water... 

Elementary reaction mechanisms for nitrous oxide (N20) dissociation were studied on Fc"( i-0)( i-0H)Fc" + exchanged in ZSM-5, using density functional theory (DFT). The effect of the cluster size on the energetics and on the reaction routes of N20 dissociation were investigated over di-iron core inserted inside two different Z cluster (Z ) and (Z oh)- The results show that while the relative stability changes with the cluster termination, the height of the energetic barriers are similar. 

The protocol developed by Jacobsen and Katsuki for the salen-Mn catalyzed asymmetric epoxidation of unfunctionalized alkenes continues to dominate the field. The mechanism of the oxygen transfer has not yet been fully elucidated, although recent molecular orbital calculations based on density functional theory suggest a radical intermediate (2), whose stability and lifetime dictate the degree of cis/trans isomerization during the epoxidation <00AG(E)589>. 

The results indicate that the formation of long-lived trimethyl substituted silyl cations, in the presence of aromatic solvents, as claimed by Lambert et al.95 is not feasible under these conditions. Persistent silicenium ions require sterically more shielding substituents at silicon or hypercoordinative stabilization.96 98 13C and 29Si NMR chemical shifts were calculated for a series of disilylated arenium ions 85 using density functional theory (DFT). The calculations predict consistently the unsaturated carbon atoms to be too deshielded by 8-15 ppm. Applying an empirical correction, the deviation between experiment and theory was reduced to -0.4 to 9 ppm, and the 13C NMR chemical shift of the highly diagnostic cipso is reproduced by the calculations (Ad = -3.8 to 2.7 ppm).99... 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

When a molecule accepts electrons, the electrons tend to go to places where/1 (r) is large because it is at these locations that the molecule is most able to stabilize additional electrons. Therefore a molecule is susceptible to nucleophilic attack at sites where/ "(r) is large. Similarly, a molecule is susceptible to electrophilic attack at sites where f (r) is large, because these are the regions where electron removal destabilizes the molecule the least. In chemical density functional theory (DFT), the Fukui functions are the key regioselectivity indicators for electron-transfer controlled reactions. 

Model computational studies aimed at understanding structure-reactivity relationships and substituent effects on carbocation stability for aza-PAHs derivatives were performed by density functional theory (DFT). Comparisons were made with the biological activity data when available. Protonation of the epoxides and diol epoxides, and subsequent epoxide ring opening reactions were analyzed for several families of compounds. Bay-region carbocations were formed via the O-protonated epoxides in barrierless processes. Relative carbocation stabilities were determined in the gas phase and in water as solvent (by the PCM method). 

The problem is that relaxation energies 7 (PhO ) and 7 (EtO ) just calculated do not contain the electronic stabilization of the radicals they merely account for the structural rearrangements of PhO and EtO when they relax to their ground states. In fact, when the density functional theory is used to compute the energies of the fragments PhO and EtO the molecular orbital framework is the same as in the relaxed radicals PhO and EtO. Therefore, the energies of PhO and EtO already include most of the electronic stabilization of the radicals. 

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