Intruder states in multireference perturbation theory: the ground state of manganese dimer

A detailed analysis of a severe intruder state problem in the multistate multireference perturbation theory (MS-MRPT) calculations on the ground state of manganese dimer is presented. An enormous number of detected intruder states (> 5000) do not permit finding even an approximate shape of the X(1)Sigma(g) (+) potential energy curve. The intruder states are explicitly demonstrated to originate from quasidegeneracies in the zeroth-order Hamiltonian spectrum. The electronic configurations responsible for appearance of the quasidegeneracies are identified as single and double excitations from the active orbitals to the external orbitals. It is shown that the quasidegeneracy problem can be completely eliminated using shift techniques despite of its severity. The resultant curves are smooth and continuous. Unfortunately, strong dependence of the spectroscopic parameters of the X(1)Sigma(g) (+) state on the shift parameter is observed. This finding rises serious controversies regarding validity of employing shift techniques for solving the intruder state problem in MS-MRPT. Various alternative approaches of removing intruder states (e.g., modification of the basis set or changing the active space) are tested. None of these conventional techniques is able to fully avoid the quasidegeneracies. We believe that the MS-MRPT calculations on the three lowest A(g) states of manganese dimer constitute a perfect benchmark case for studying the behavior of MRPT in extreme situations.     

Analytical Solutions of the Schrödinger Equation with Power Potentials

Conditions for the existence of polynomial solutions of the Schrödinger equation with potentials which are linear combinations of powers of r ranging from ?2 to 2m, where m is a non‐negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.     

Algorithm for generating generalized resonance structures of single zigzag chains based on interface theory

An alternative formulation of the theory of generalized resonance structures (Clar covers) of single zigzag chains N(n), based on the novel concept of interfaces, is presented. The global structure of every Clar cover can be conveniently expressed as a unique sequence of n interfaces. The complete set of Clar covers is then robustly constructed as the complete set of walks of length \(n+1\) on the associated interface connectivity graph. The presented algorithm is readily generalizable to an arbitrary class of benzenoid structures.     

Automatized Parameterization of the Density‐functional Tight‐binding Method. II. Two‐center Integrals

We present an efficient numerical integration scheme (TWOCENT) to be used in the context of automatized parameterization of the density‐functional tight‐binding (DFTB) method. The accuracy of the integration process is assessed and its range of applicability is discussed. The functionality of the developed code is tested by reproducing the electronic portion of the existing mio parameter sets and by reproducing a series of reference DFT band structures of elemental solids.     

Intruder state avoidance multireference Møller-Plesset perturbation theory

A new perturbation approach is proposed that enhances the low‐order, perturbative convergence by modifying the zeroth‐order Hamiltonian in a manner that enlarges any small‐energy denominators that may otherwise appear in the perturbative expansion. This intruder state avoidance (ISA) method can be used in conjunction with any perturbative approach, but is most applicable to cases where small energy denominators arise from orthogonal‐space states—so‐called intruder states—that should, under normal circumstances, make a negligible contribution to the target state of interests. This ISA method is used with multireference Møller–Plesset (MRMP) perturbation theory on potential energy curves that are otherwise plagued by singularities when treated with (conventional) MRMP; calculation are performed on the 1³Σ state of O₂; and the 2¹Δ, 3¹Δ, 2³Δ, and 3³Δ states of AgH. This approach is also applied to other calculations where MRMP is influenced by intruder states; calculations are performed on the ³Π_u state of N₂, the ³Π state of CO, and the 2¹A′ state of formamide. A number of calculations are also performed to illustrate that this approach has little or no effect on MRMP when intruder states are not present in perturbative calculations; vertical excitation energies are computed for the low‐lying states of N₂, C₂, CO, formamide, and benzene; the adiabatic ¹A₁–³B₁ energy separation in CH₂, and the spectroscopic parameters of O₂ are also calculated. Vertical excitation energies are also performed on the Q and B bands states of free‐base, chlorin, and zinc–chlorin porphyrin, where somewhat larger couplings exists, and—as anticipated—a larger deviation is found between MRMP and ISA‐MRMP. © 2002 Wiley Periodicals, Inc. J Comput Chem 10: 957–965, 2002     

Micelle hydration by1H-NMR

¹H-NMR studies were carried out for solution of amphiphilic betaine ester derivatives (of the general formula (CH₃)₃N⁺CH₂COOC _n H_2n+1Cl^– (V-n), wheren=10, 12, 14, and 16) andn-dodecyltrimethylammonium chloride (I-12). The spectra were taken at concentrations above and below critical micelle concentrations and chemical shifts were analyzed. It was stated that micelles are hydrated at the depth of the two CH₂ groups in the case ofV-n and the CH₂COO group in the case ofI-12. Therefore, the CH₂COO group during the micellization behaves as if it were CH₂CH₂ group.