Kernel energy method: Basis functions and quantum methods

The kernel energy method (KEM) has been illustrated with peptides and has been shown to reduce the computational difficulty associated with obtaining ab initio quality quantum chemistry results for large biological compounds. In a recent paper, the method was illustrated by application to 15 different peptides, ranging in size from 4 to 19 amino acid residues, and was found to deliver accurate Hartree–Fock (HF) molecular energies within the model, using Slater‐type orbital (STO)‐3G basis functions. A question arises concerning whether the results obtained from the use of KEM are wholly dependent on the STO‐3G basis functions that were employed, because of their relative simplicity, in the first applications. In the present work, it is shown that the accuracy of KEM does not depend on a particular choice of basis functions. This is done by calculating the ground‐state energy of a representative peptide, ADPGV7B, containing seven amino acid residues, using seven different commonly employed basis function sets, ranging in size from small to medium to large. It is shown that the accuracy of the KEM does not vary in any systematic way with the size or mathematical completeness of the basis set used, and good accuracy is maintained over the entire variety of basis sets that have been tested. Both approximate HF and density functional theory (DFT) calculations are made. We conclude that the accuracy inherent in the KEM is not dependent on a particular choice of basis functions. The first application, to 15 different peptides mentioned above, employed only HF calculations. A second question that arises is whether the results obtained with the use of KEM will be accurate only within the HF approximation. Therefore, in the present work we also study whether KEM is applicable across a variety of quantum computational methods, characterized by differing levels of accuracy. The peptide, Zaib4, containing 74 atoms, was used to calculate its energy at seven different levels of accuracy. These include the semi‐empirical methods, AM1 and PM5, a DFT B3LYP model, and ab initio HF, MP2, CID, and CCSD calculations. KEM was found to be widely applicable across the spectrum of quantum methods tested. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Kernel energy method illustrated with peptides

We describe a kernel energy method (KEM) for applying quantum crystallography to large molecules, with an emphasis on the calculation of the molecular energy of peptides. The computational difficulty of representing the system increases only modestly with the number of atoms. The calculations are carried out on modern parallel supercomputers. By adopting the approximation that a full biological molecule can be represented by smaller “kernels” of atoms, the calculations are greatly simplified. Moreover, collections of kernels are, from a computational point of view, well suited for parallel computation. The result is a modest increase in computational time as the number of atoms increases, while retaining the ab initio character of the calculations. We describe a test of our method, and establish its accuracy using 15 different peptides of biological interest. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The Clar covering polynomial of hexagonal systems Ⅱ.An application to resonance energy of condensed aromatic hydrocarbons

The Clar covering polynomial of hexagonal systems is a recently proposed1,2 concept which contains much more topological properties of condensed aromatic hydrocarbons, such as Kekule structure count, Clar number, first Herndon number, etc. It is shown that this polynomial can be used for calculating the resonance energy of condensed aromatic hydrocarbons with better accuracy.     

The concept of protobranching and its many paradigm shifting implications for energy evaluations

Branched alkanes like isobutane and neopentane are more stable than their straight chain isomers, n-butane and n-pentane (by 2 and 5 kcal mol(-1), respectively). Electron correlation is largely responsible. Branched alkanes have a greater number of net attractive 1,3-alkyl-alkyl group interactions, there are three such stabilizing 1,3 "protobranching" dispositions in isobutane, but only two in n-butane. Neopentane has six protobranches but n-pentane only three. Propane has one protobranch and is stabilized appreciably, by 2.8 kcal mol(-1), relative to methane and ethane. This value per protobranch also applies to the n-alkanes and cyclohexane. Consequently, energy evaluations employing alkane reference standards, for example, of small ring strain and stabilizations due to conjugation, hyperconjugation, and aromaticity, should be corrected for protobranching, for example, by employing Pople's isodesmic bond separation reaction method. This reduces the ring strain of cyclopropane to 19.2 from the conventional 27.7 kcal mol(-1), while the stabilization energies of alkenes and alkynes due to hyperconjugation (5.5 and 7.7 kcal mol(-1) for propene and propyne) and conjugation (14.8 and 27.1 kcal mol(-1) for butadiene and butadiyne) are considerably larger than the traditional estimates. Widely diverging literature evaluations of benzene resonance energy all give approximately 65 kcal mol(-1) after adjusting for conjugation, hyperconjugation, and protobranching "contaminations." The BLW (block localized wavefunction) method, which localizes pi bonds and precludes their interactions, largely confirms these stabilization estimates for hyperconjugation, conjugation, and aromaticity. Protobranching is seriously underestimated by theoretical computations at the HF and most DFT levels, which do not account for electron correlation satisfactorily. Such levels give bond separation energies, which can differ greatly from experimental values.     

Kohn-Sham Density Matrix and the Kernel Energy MethodSCI北大核心CSCD

The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.     

Modification of the integral isoconversional method to account for variation in the activation energy

Integral isoconversional methods may give rise to noticeable systematic error in the activation energy when the latter strongly varies with the extent of conversion. This error is eliminated by using an integration technique that properly accounts for the variation in the activation energy. The technique is implemented as a modification of the earlier proposed advanced isoconversional method [Vyazovkin, S. J Comput Chem 1997, 18, 393]. The applications of the modified method are illustrated by simulations as well as by processing of data on the thermal decomposition of calcium oxalate monohydrate and ammonium nitrate. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 178–183, 2001     

Presentation of a new index for estimation of aromaticity in halo‐ and cyanobenzenes: The role of potential energy in aromaticity

A linear correlation has been obtained between average values of Hamiltonian kinetic energy ( ) and potential energy ( ) calculated at the bond critical points using atoms in molecules method. This relation was used to introduce a new index ( ) for estimation of aromaticity in halo‐ and cyanobenzenes. Potential energy has different terms such as attraction between nuclei and electrons, also repulsion of electrons which affect the inertia and mobility of electrons, respectively. Therefore, contribution of potential energy in this relation must be controlled. Contribution of potential energy in aromaticity has been managed using a fitting parameter. This parameter was obtained by fitting the aromaticity stabilization energy data with values of aromaticity calculated by index for halo‐ and cyanobenzenes. The contribution of potential energy in index is complete when molecule is nonaromatic and is negligible when molecule is antiaromatic. Indeed, molecule is aromatic when contribution of potential energy in index lies between above limits. © 2013 Wiley Periodicals, Inc.     

Synthesis of A2B6‐Type [36]Octaphyrins: Copper(II)‐Metalation‐Induced Fragmentation Reactions to Porphyrins and N‐Fusion Reactions of meso‐(3‐Thienyl) Substituents

5,10,15‐Tris(pentafluorophenyl)tetrapyrromethane was efficiently prepared through a route involving stepwise diaroylation of 5‐pentafluorophenyldipyrromethane. A₂B₆‐type [36]octaphyrins were prepared by the cross condensation of the tetrapyrromethane with aryl aldehydes in moderate yields. A₂B₆‐type [36]octaphyrins bearing 2,4,6‐trifluorophenyl, 2,6‐dichlorophenyl, and phenyl substituents underwent Cu^II‐metalation‐induced fragmentation to give two molecules of AB₃‐type Cu^II porphyrins. A₂B₆‐type [36]octaphyrin bearing 3‐thienyl substituents underwent thermal N‐thienyl fusion reactions to provide a modestly aromatic [38]octaphyrin, which, upon treatment with MnO₂, underwent further N‐thienyl fusion and subsequent oxidation to give a nonaromatic doubly N‐thienyl fused [36]octaphyrin.     

Analytic energy derivatives for the equation-of-motion coupled-cluster method: Algebraic expressions,implementation and application to theS 1 state of HFCO

Summary The general theory of analytic derivatives for the equation-of-motion coupled cluster (EOM-CC) method is reviewed. Special attention is paid to the EOM-CC singles and doubles (EOM-CCSD) approximation, which has the same computational scaling properties as the coupled-cluster singles doubles (CCSD) ground state method and is therefore applicable to a wide range of molecular systems. The detailed spin orbital equations that must be solved in EOM-CCSD gradient calculations are presented for the first time, and some guidelines are discussed regarding their computational implementation. Finally, use of the EOM-CCSD gradient method is illustrated by determining the structure, dipole moment components, harmonic frequencies and infrared intensities of formyl fluoride (HFCO) in its singlet excited (n, *) state.     

A new method for partition of interaction energy. Relation between stabilization energy and orbital mixing

A new method for partition of interaction energy is proposed. The scheme given here easily connects the calculated stabilization energy with the orbital mixing in analyzing orbital interactions of molecules. The method can reveal the relation between the change of electron distribution and stabilization energy. As an example, orbital interaction energies are estimated for diazocompounds, diazomethane and diazirine.     

“To Twist or Not to Twist”: Figure‐of‐Eight and Planar Structures of Octaphyrins

Amongst the various porphyrinoids, octaphyrin has attracted significant attention owing to its diverse syntheses, conformations, and metal‐ligation properties. Octaphyrin is a higher homologue of porphyrin and is formed by linking together heterocycles such as pyrrole, furan, thiophene, and selenophene through α‐α or α‐meso carbon bonds. The planar conformation is mainly achieved through inversion of the heterocyclic units from the center of macrocycle; avoiding meso ‐bridges; introducing a para ‐quinodimethane bridge; employing a neo‐confusion approach; protonation; and by generating dianionic species. In this Focus Review, recent synthetic advancements in the field of octaphyrins are summarized. The twisted conformation of the octaphyrin binds to two metal ions in a tetracoordinate geometry. The diphosphorus complex of octaphyrin represents the first example of a stable expanded isophlorin.     

A method for molecular correlation energy calculations. Application to the determination of dissociation energies of diatomic and polyatomic molecules

A simple and economical method for molecular correlation energy calculations is developed. In this method, the internal part of the correlation energy is calculated by means of a CI in a minimal basis set and the non-internal part (semi-internal and all-external) is evaluated using an original atoms-in-molecule method. It is successfully applied to the determination of dissociation energies of some diatomic (H₂, NH, C₂, CN, N₂, CO, NO, O₂, F₂) and polyatomic (H₂O, N₂O, CO₂, N₃H, CH₂N₂, CH₂CO, C₂N₂) molecules. The results are compared to those obtained using very elaborate variational methods.Aspirant du Fonds National Belge de la Recherche Scientifique.     

An approximate but efficient method to calculate free energy trends by computer simulation: Application to dihydrofolate reductase-inhibitor complexes

Summary Derivatives of free energy differences have been calculated by molecular dynamics techniques. The systems under study were ternary complexes of Trimethoprim (TMP) with dihydrofolate reductases of E. coli and chicken liver, containing the cofactor NADPH. Derivatives are taken with respect to modification of TMP, with emphasis on altering the 3-, 4- and 5-substituents of the phenyl ring. A linear approximation allows the encompassing of a whole set of modifications in a single simulation, as opposed to a full perturbation calculation, which requires a separate simulation for each modification. In the case considered here, the proposed technique requires a factor of 1000 less computing effort than a full free energy perturbation calculation. For the linear approximation to yield a significant result, one has to find ways of choosing the perturbation evolution, such that the initial trend mirrors the full calculation. The generation of new atoms requires a careful treatment of the singular terms in the non-bonded interaction. The result can be represented by maps of the changed molecule, which indicate whether complex formation is favoured under movement of partial charges and change in atom polarizabilities. Comparison with experimental measurements of inhibition constants reveals fair agreement in the range of values covered. However, detailed comparison fails to show a significant correlation. Possible reasons for the most pronounced deviations are given.     

The NICS‐XY‐Scan: Identification of Local and Global Ring Currents in Multi‐Ring Systems

Nucleus‐independent chemical shift (NICS)‐based methods are very popular for the determination of the induced magnetic field under an external magnetic field. These methods are used mostly (but not only) for the determination of the aromaticity and antiaromaticity of molecules and ions, both qualitatively and quantitatively. The ghost atom that serves as the NICS probe senses the induced magnetic field and reports it in the form of an NMR chemical shift. However, the source of the field cannot be determined by NICS. Thus, in a multi‐ring system that may contain more than one induced current circuit (and therefore more than one source of the induced magnetic field) the NICS value may represent the sum of many induced magnetic fields. This may lead to wrong assignments of the aromaticity (and antiaromaticity) of the systems under study. In this paper, we present a NICS‐based method for the determination of local and global ring currents in conjugated multi‐ring systems. The method involves placing the NICS probes along the X axis, and if needed, along the Y axis, at a constant height above the system under study. Following the change in the induced field along these axes allows the identification of global and local induced currents. The best NICS type to use for these scans is NICS_πZZ, but it is shown that at a height of 1.7 Å above the molecular plane, NICS_ZZ provides the same qualitative picture. This method, namely the NICS‐XY‐scan, gives information equivalent to that obtained through current density analysis methods, and in some cases, provides even more details.     

A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.