We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

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The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by medium-range correlation energy, such as van der Waals attraction, aromatic−aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid)...

Density functionals with broad applicability in chemistry.

We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993

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A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions.

Molpro (available at http://www.molpro.net) is a general-purpose quantum chemical program. The original focus was on high-accuracy wave function calculations for small molecules, but using local approximations combined with explicit correlation treatments, highly accurate coupled-cluster calculations are now possible for molecules with up to approximately 100 atoms. Recently, multireference correlation treatments were also made applicable to larger molecules. Furthermore, an efficient implementation of density functional theory is available.

Molpro: a general-purpose quantum chemistry program package

The phenyl cation is known to have two low-energy minima, corresponding to 1
A
1 and 3
B
1 states, the first of which is more stable by ca. 25 kcal/mol. The minimum energy crossing point between these two surfaces, located at various levels including a hybrid method first described here, lies just above the minimum of the triplet, 0.12 kcal/mol at the CCSD(T)/cc-pVDZ//B3LYP/SV level, and there is significant spin-orbit coupling between the surfaces at this point. On the basis of these results, the lifetime of the triplet is expected to be very short.

The singlet and triplet states of phenyl cation. A hybrid approach for locating minimum energy crossing points between non-interacting potential energy surfaces

The complexes trans-RuH(Cl)(tmen)(R-binap) (1) and (OC-6-43)-RuH(Cl)(tmen)(PPh(3))(2) (2) are prepared by the reaction of the diamine NH(2)CMe(2)CMe(2)NH(2) (tmen) with RuH(Cl)(PPh(3))(R-binap) and RuH(Cl)(PPh(3))(3), respectively. Reaction of KHB(sec)Bu(3) with 1 yields trans-Ru(H)(2)(R-binap)(tmen) (5) while reaction of KHB(sec)Bu(3) or KO(t)Bu with 2 under Ar yields the new hydridoamido complex RuH(PPh(3))(2)(NH(2)CMe(2)CMe(2)NH) (4). Complex 4 has a distorted trigonal bipyramidal geometry with the amido nitrogen in the equatorial plane. Loss of H(2) from 5 results in the related complex RuH(R-binap)(NH(2)CMe(2)CMe(2)NH) (3). Reaction of H(2) with 4 yields the trans-dihydride (OC-6-22)-Ru(H)(2)(PPh(3))(2)(tmen)(6). Calculations support the assignment of the structures. The hydrogenation of acetophenone is catalyzed by 5 or 4 in benzene or 2-propanol without the need for added base. For 5 in benzene at 293 K over the ranges of concentrations [5] = 10(-)(4) to 10(-)(3) M, [ketone] = 0.1 to 0.5 M, and of pressures of H(2) = 8 to 23 atm, the rate law is rate = k[5][H(2)] with k = 3.3 M(-1) s(1), DeltaH++ = 8.5 +/- 0.5 kcal mol(-1), DeltaS++ = -28 +/- 2 cal mol(-1) K(-1). For 4 in benzene at 293 K over the ranges of concentrations [4] = 10(-4) to 10(-3) M, [ketone] 0.1 to 0.7 M, and of pressures of H(2) = 1 to 6 atm, the preliminary rate law is rate = k[4][H(2)] with k = 1.1 x 10(2) M(-1) s(-1), DeltaH++ = 7.6 +/- 0.3 kcal mol(-1), DeltaS++ = -23 +/- 1 cal mol(-1) K(-1). Both theory and experiment suggest that the intramolecular heterolytic splitting of dihydrogen across the polar Ru=N bond of the amido complexes 3 and 4 is the turn-over limiting step. A transition state structure and reaction energy profile is calculated. The transfer of H(delta+)/H(delta-) to the ketone from the RuH and NH groups of 5 in a Noyori metal-ligand bifunctional mechanism is a fast process and it sets the chirality as (R)-1-phenylethanol (62-68% ee) in the hydrogenation of acetophenone. The rate of hydrogenation of acetophenone catalyzed by 5 is slower and the ee of the product is low (14% S) when 2-propanol is used as the solvent, but both the rate and ee (up to 55% R) increase when excess KO(t)Bu is added. The formation of ruthenium alkoxide complexes in 2-propanol might explain these observations. Alkoxide complexes [RuP(2)]H(OR)(tmen), [RuP(2)] = Ru(R-binap) or Ru(PPh(3))(2), R= (i) Pr, CHPhMe, (t)Bu, are observed by reacting the alcohols (i)PrOH, phenylethanol, and (t)BuOH with the dihydrides 5 and 6, respectively, under Ar. In the absence of H(2), the amido complexes 3 and 4 react with acetophenone to give the ketone adducts [RuP(2)]H(O=CPhMe)(NH(2)CMe(2)CMe(2)NH) in equilibrium with the enolate complexes trans- [RuP(2)](H)(OCPh=CH(2))(tmen) and eventually the decomposition products [RuP(2)]H(eta(5)-CH(2)CPhCHCPhO), with the binap complex characterized crystallographically. In general, proton transfer from the weakly acidic molecules dihydrogen, alcohol, or acetophenone to the amido nitrogen of complexes 3 and 4 is favored in two ways when the molecule coordinates to ruthenium: (1) an increase in acidity of the molecule by the Lewis acidic metal and (2) an increase in the basicity of the amido nitrogen caused by its pyramidalization. The formato complexes trans-[RuP(2)]H(OCHO)(tmen) were prepared by reacting the respective complex 4 or 5 with formic acid. The crystal structure of RuH(OCHO)(PPh(3))(2)(tmen) displays similar features to the calculated transition state for H(delta+)/H(delta-) transfer to the ketone in the catalytic cycle.

Mechanism of the hydrogenation of ketones catalyzed by trans-dihydrido(diamine)ruthenium II complexes.

Many reactions of transition metal compounds involve a change in spin. These reactions may proceed faster, slower—or at the same rate as—otherwise equivalent processes in which spin is conserved. For example, ligand substitution in [CpMo(Cl)2(PR3)2] is faster than expected, whereas addition of dinitrogen to [Cp*Mo(Cl)(PMe3)2] is slow. Spin-forbidden oxidative addition of ethylene to [Cp*Ir(PMe3)] occurs competitively with ligand association. To explain these observations, we discuss the shape of the different potential energy surfaces (PESs) involved, and the energy of the minimum energy crossing points (MECPs) between them. This computational approach is of great help in understanding the mechanisms of spin-forbidden reactions, provided that accurate calculations can be used to predict the relevant PESs. Density functional theory, especially using gradient-corrected and hybrid functionals, performs reasonably well for the difficult problem of predicting the energy splitting between different spin states of transition metal complexes, although careful calibration is needed.

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Spin forbidden chemical reactions of transition metal compounds. New ideas and new computational challenges

Many chemical reactions involve a change in spin-state and are formally forbidden. This article summarises a number of previously published applications showing that a form of Transition State Theory (TST) can account for the kinetics of these reactions. New calculations for the emblematic spin-forbidden reaction HC + N2 are also reported. The observed reactivity is determined by two factors. The first is the critical energy required for reaction to occur, which in spin-forbidden reactions is often defined by the relative energy of the Minimum Energy Crossing Point (MECP) between potential energy surfaces corresponding to the different spin states. The second factor is the probability of hopping from one surface to the other in the vicinity of the crossing region, which is largely defined by the spin–orbit coupling matrix element between the two electronic wavefunctions. The spin-forbidden transition state theory takes both factors into account and gives good results. The shortcomings of the theory, which are largely analogous to those of standard TST, are discussed. Finally, it is shown that in cases where the surface-hopping probability is low, the kinetics of spin-forbidden reactions will be characterised by unusually unfavourable entropies of activation. As a consequence, reactions involving a spin-state change can be expected to compete poorly with spin-allowed reactions at high temperatures (or energies).

Understanding the kinetics of spin-forbidden chemical reactions

Density Functional Theory has become very widely used to study the electronic structure and related properties of transition metal complexes. Despite the many successes obtained using modern functionals, care is still needed as quite large errors can occur. These can be best understood by taking into consideration how density functional theory works, and how well it performs for the simpler case of main-group compounds. This serves to highlight the critical role of the exchange functional, which describes such varied effects as electron self-interaction, static (or non-dynamic) correlation, and dynamic correlation. A poor balance between these effects can lead to significant errors even for main-group compounds. This is even truer for transition metal compounds. Benchmark data published in the last year suggest that all existing functionals can lead to severe errors for some transition metal compounds. There is a slight trend for systems involving more static correlation to be treated better using second- or third-generation gradient-corrected or kinetic energy density functionals, rather than hybrid functionals. This trend is however quite variable from one type of compound to another. Computed spin-state splittings are highly variable from one functional to another, and this is also diagnostic of differences in the extent of static correlation. The increasing awareness of transition metal compounds by the developers of new exchange–correlation functionals should lead in the medium term to more accurate and hence (even) more useful functionals.

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Jeremy N. Harvey

Papers

The singlet and triplet states of phenyl cation. A hybrid approach for locating minimum energy crossing points between non-interacting potential energy surfaces

Mechanism of the hydrogenation of ketones catalyzed by trans-dihydrido(diamine)ruthenium II complexes.

Spin forbidden chemical reactions of transition metal compounds. New ideas and new computational challenges

Understanding the kinetics of spin-forbidden chemical reactions

On the accuracy of density functional theory in transition metal chemistry