Symmetry aspects of diatomics-in-molecules (DIM) calculations. II. Construction of symmetry-adapted diatomic fragment subspaces

A new general procedure is presented for the construction of symmetry adapted diatomic fragment sub-spaces of spin-adapted polyatomic DIM bases obtained by direct diagonalization of the polyatomic spin-square operator. The spin part of the construction is accomplished by the diagonalization in the DIM basis of the diatomic spin-square operators. The spatial part of relevant transformations is given in terms of quantum numbers of the constituent atomic functions. Simple expressions for the spatial symmetry and spin designation of the resulting symmetry-adapted diatomic fragment states are obtained. Special attention is paid to consistent phases of diatomic fragment functions corresponding to equivalent fragments. The approach eliminates such mental operations from the construction of symmetry-adapted diatomic fragment subspaces which are difficult to formulate in a way suitable for straightforward computer implementation.     

Reactant subspaces and kinetics of chemical reaction networks

This paper studies a chemical reaction network’s (CRN) reactant subspace, i.e. the linear subspace generated by its reactant complexes, to elucidate its role in the system’s kinetic behaviour. We introduce concepts such as reactant rank and reactant deficiency and compare them with their analogues currently used in chemical reaction network theory. We construct a classification of CRNs based on the type of intersection between the reactant subspace R and the stoichiometric subspace S and identify the subnetwork of S-complexes, i.e. complexes which, when viewed as vectors, are contained in S, as a tool to study the network classes, which play a key role in the kinetic behaviour. Our main results on new connections between reactant subspaces and kinetic properties are (1) determination of kinetic characteristics of CRNs with zero reactant deficiency by considering the difference between (network) deficiency and reactant deficiency, (2) resolution of the coincidence problem between the reactant and kinetic subspaces for complex factorizable kinetics via an analogue of the generalized Feinberg–Horn theorem, and (3) construction of an appropriate subspace for the parametrization and uniqueness of positive equilibria for complex factorizable power law kinetics, extending the work of Müller and Regensburger.     

Coupled cluster response theory in parameter subspaces

We introduce a response function formalism that enables smaller number of parameters than that defined in standard coupled cluster response theory. This is essential in the development of reduced scaling methods. The formalism is general and it applies to all parameterizations at all levels of the coupled cluster hierarchy. We show that to achieve physically reasonable results the parameterization must fulfill certain criteria. The linear response functions are derived and discussed in the context of optimized virtual orbitals and Cholesky decomposition of the cluster amplitudes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The kinetic energy operator in the subspaces of wavelet analysis

At any resolution level of wavelet expansions the physical observable of the kinetic energy is represented by an infinite matrix which is “canonically” chosen as the projection of the operator  − Δ/2 onto the subspace of the given resolution. It is shown, that this canonical choice is not optimal, as the regular grid of the basis set introduces an artificial consequence of its periodicity, and it is only a particular member of possible operator representations. We present an explicit method of preparing a near optimal kinetic energy matrix which leads to more appropriate results in numerical wavelet based calculations. This construction works even in those cases, where the usual definition is unusable (i.e., the derivative of the basis functions does not exist). It is also shown, that building an effective kinetic energy matrix is equivalent to the renormalization of the kinetic energy by a momentum dependent effective mass compensating for artificial periodicity effects.     

Gaussian expansions from STOs by the distance between subspaces

Expansions of STO orbitals with GTO s for the first-row atoms have been obtained by the method of the distance between subspaces. The expansion coefficients and exponential parameters were simultaneously varied when the distance between subspaces, which are generated from STO and GTO functions, is minimized. The ζ; exponents (or scale factors) for the atomic orbitals that are optimized for these atoms are also shown to be almost independent of the number of Gaussian functions. Comparisons carried out with Stewart's least-squares method produce equivalent results when exponents for 2s and 2p functions are different. Some examples and applications for several atomic properties of the first-row atoms are included: energies and expectation values of rⁱ and pⁱ for the several expansions. These new minimal basis sets were tested for diatomic and polyatomic molecules containing these atoms. © 1993 John Wiley & Sons, Inc.     

Analysis of the stability of finite subspaces in density functional theory

We have studied photodissociation of the A state of the H₂S⁺ ion using the quantum-chemical CAS methods, and the 1² A″ (X ² B ₁) and 1⁴ A″ states are involved in photodissociation of the 1² A′ (A ² A ₁) state (the electronic states in dissociation were studied in the C _s symmetry). The CASPT2 S-loss dissociation potential energy curve (PEC) calculations indicate that the 1² A″ and 1² A′ states correlate with the second limit [H₂ + S⁺(² D)] while the 1⁴ A″ state correlates with the first limit [H₂ + S⁺(⁴S)] and that there are a transition state and a local minimum along the 1² A′ PEC and the repulsive 1⁴ A″ PEC crosses the 1² A″ and 1² A′ PECs. The CASPT2 H-loss dissociation PEC calculations indicate that the 1² A″ and 1⁴ A″ states correlate with the first limit [HS⁺(X ³Σ^?) + H] while the 1² A′ state correlates with the second limit [HS⁺(a ¹Δ) + H] and that the repulsive 1⁴ A″ PEC crosses the 1² A′ PEC. For the crossing doublet and quartet states in pairs, we performed CASSCF minimum energy crossing point (MECP) calculations, and the CASSCF spin-orbit couplings and CASPT2 energies at the MECP geometries were calculated. We examined the two previously proposed mechanisms (mechanisms I and II) for dissociation of the A state to the S⁺ ion, based on our calculation results. We suggest processes for dissociation of the A state to the S⁺ ion (processes I and II, based on mechanisms I and II, respectively) and to the SH⁺ ion (process III) and conclude that photodissociation of the A state mainly leads to the S⁺ ion via the most energetically favorable process II: A ² A ₁ (1² A′) (2.38 eV) → barrier at the linearity (2.96 eV) → X ² B ₁ (1² A″) (0.0 eV) → the 1² A″/1⁴ A″ MECP (3.50 eV, large spin-orbit coupling) → H₂ $ (X^{ 1} \Upsigma_{\text{g}}^{ + } ) $  + S⁺(⁴S) (2.92 eV) (the CASPT2 relative energy values to X ² B ₁ are given in parentheses and the largest value is 3.50 eV at the MECP).     

Microwave-assisted orthogonal synthesis of PNA-peptide conjugates

Microwave heating facilitates peptide nucleic acid synthesis offering a fully automated and efficient synthetic strategy to PNA-peptide conjugates.     

Computational design of orthogonal nucleoside kinases

We report the computational enzyme design of an orthogonal nucleoside analog kinase for 3'-deoxythymidine. The best kinase variant shows an 8500-fold change in substrate specificity, resulting from a 4.6-fold gain in catalytic efficiency for the nucleoside analog and a 2000-fold decline for the native substrate thymidine.     

Wavelength-controlled orthogonal photolysis of protecting groups

The selective control of a chemical process by the use of an electromagnetic wave has been a challenging goal for several decades. In this article, we describe for the first time the use of a monochromatic light beam to differentiate two different reactive centers. A direct application of this concept is found in the chemistry of protecting groups. Two different photolabile protecting groups were tuned to be responsive to a specific wavelength (e.g., 254 or 420 nm). Using derivatives of the 2-nitroveratryl fragment (such as 10, sensitive at 420 nm) and 3',5'-dimethoxybenzoin fragment (such as 4, sensitive at 254 nm), it was shown that energy transfer phenomena did not erode the selectivity. Both the inter- and the intramolecular cases were studied and showed selectivities within the synthetically useful range. Hence, we could replace the traditional chemical orthogonality by a chromatic orthogonality.     

Multifunctionalization of dendrimers through orthogonal transformations

A straightforward methodology for the synthesis of multifunctionalized dendrimers that is based on an orthogonal functionalization strategy has been developed. Polyamide-based dendrimers that possess both a single aldehyde and a single azide moiety on their periphery have been synthesized by using a convergent synthetic strategy. These dendrimers can be functionalized quantitatively with small organic and biological molecules that contain hydrazide and/or alkyne groups in which each functional moiety is completely specific for its complementary motif. This orthogonal functionalization strategy has the potential to be used to synthesize multifunctional dendrimers for a variety of applications, which range from targeted biological delivery vehicles to optical materials.     

Multiplication theorems for orthogonal polynomials

In this paper, a general method is presented that allows the derivation of the expansion coefficients of the product of two orthogonal functions provided the generating function is known. For the three classical orthogonal polynomials, the Laguerre, the Hermite, and the Legendre polynomials, the coefficients b_lmn with ?_m?_n = ∑_lb_lmn?_l are derived. © 1993 John Wiley & Sons, Inc.     

Cellular logic with orthogonal ribosomes

The creation and use of unnatural molecules to control cellular function is a long standing goal of the chemical community, but in general, these efforts have been directed at finding molecules to inhibit or activate a particular molecular target or function, or to elicit a particular phenotype. Here we show that multiple unnatural molecules (orthogonal ribosomes) can be used combinatorially, in a single cell, to program Boolean logic functions. These experiments show how attention to the molecular specificity of noncovalent interactions between unnatural macromolecules allows the synthesis of complex function from the "bottom-up" in living matter.     

Dehydropeptides from orthogonal ligation of unprotected peptides

A facile method has been developed to synthesize linear and cyclic dehydropeptides from unprotected peptide precursors. This method exploits an N-terminal Cys for a Cys-thioester ligation to generate an unprotected peptide and as a precursor for conversion to DeltaAla by beta-elimination under mild conditions.     

Information theoretic spreading measures of orthogonal functions

We calculate information theoretic spreading measures of orthogonal functions associated with solutions of quantum mechanical isospectral potentials. In particular, Shannon, Renyi and Fisher lengths have been evaluated for potentials isospectral to the linear harmonic oscillator and the symmetric Rosen-Morse potentials. We have also compared the behaviour of different lengths for the orthogonal functions and the associated orthogonal polynomials.