Biomedical subjects

Marcel Nooijen

Publications and source records attributed to Marcel Nooijen.

7 recordsLinked to original sources

PubMed2006

Dynamically screened local correlation method using enveloping localized orbitals.

In this paper we present a local coupled cluster approach based on a dynamical screening scheme, in which amplitudes are either calculated at the coupled cluster level (in this case CCSD) or at the level of perturbation theory, employing a threshold driven procedure based on MP2 energy increments. This way, controllable accuracy and smooth convergence towards the exact result are obtained in the framework of an a posteriori approximation scheme. For the representation of the occupied space a new set of local orbitals is presented with the size of a minimal basis set. This set is atom centered, is nonorthogonal, and has shapes which are fairly independent of the details of the molecular system of interest. Two slightly different versions of combined local coupled cluster and perturbation theory equations are considered. In the limit both converge to the untruncated CCSD result. Benchmark calculations for four systems (heptane, serine, water hexamer, and oxadiazole-2-oxide) are carried out, and decay of the amplitudes, truncation error, and convergence towards the exact CCSD result are analyzed.

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PubMed2005

Importance of vibronic effects on the circular dichroism spectrum of dimethyloxirane.

We present a theoretical study on the vibrational structure of a circular dichroism (CD) spectrum using time-dependent density-functional theory in combination with a Franck-Condon-type approach. This method is applied to analyze the complex CD spectrum of dimethyloxirane, which involves delicate cancellations of positive and negative CD bands. Our approach reveals that these cancellations are strongly affected by the shapes of the CD bands, and that it is vital for an accurate simulation of the spectrum to take the different envelopes of these bands into account. One crucial point in some former theoretical studies on this compound, which were restricted to vertical excitations, was the appearance of a strong negative CD band in the energy range of 7.0-7.5 eV, which is not present in the experimental spectrum. We can explain the disappearance of this 2B band by a strong vibrational progression along normal modes with C-O stretching character, so that the band extends over an energy range of almost 1.1 eV. Thus, it overlaps with many other (mostly positive) CD bands, leading to a cancellation of its intensity. The dominant vibrational features in the experimental spectrum can be assigned to the 1B, 3B, and 5B bands, which show several clear vibrational peaks and a total bandwidth of only 0.3-0.5 eV. In order to obtain close agreement between the simulated and the experimental spectrum we have to apply small shifts to the vertical excitation energies that enter the calculation. These shifts account both for possible errors in the time-dependent density-functional theory calculations and for the neglect of differential zero-point energy between ground and excited states in our gradient-based vertical Franck-Condon approach.

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PubMed2005

Vibronic coupling in the excited cationic states of ethylene: simulation of the photoelectron spectrum between 12 and 18 eV.

The effect of vibronic coupling on structure and spectroscopy is investigated in the excited cationic states of ethylene. It is found from equation of motion coupled cluster singles and doubles method for ionization potential electronic structure calculations in a triple-zeta plus double polarization basis set that ethylene in its third (B (2)A(g)) and fourth (C (2)B(2u)) ionized states does not have a stable minimum-energy geometry. The potential-energy surfaces of these states are energetically distinct and well separated at the ground-state geometry of ethylene, but in a geometry optimization as the structure of the ion relaxes, these surfaces end up in conical intersections and finally in the stable equilibrium geometry of the second ionized state (A (2)B(3g)). The topology of the potential-energy surfaces can be clearly understood using a vibronic model Hamiltonian. Furthermore, by diagonalizing this model Hamiltonian, the photoelectron spectrum of ethylene corresponding to the second, third, and fourth ionized states (12-18 eV) is simulated. Spectra from vibronic simulations including up to quartic coupling constants and using various normal-mode basis sets are compared to those from vertical Franck-Condon simulations to understand the importance of vibronic coupling and nonadiabatic effects and to examine the influence of individual normal modes on the spectrum.

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PubMed2005

Vibronic structure of the permanganate absorption spectrum from time-dependent density functional calculations.

The UV absorption spectrum of the permanganate anion is a prototype transition-metal complex spectrum. Despite this being a simple d0 Td system, for which a beautiful spectrum with detailed vibrational structure has been available since 1967, the assignment of the second and third bands is still very controversial. The issue can be resolved only by an elucidation of the intricate vibronic structure of the spectrum. We investigate the vibronic coupling by means of linear-response time-dependent density functional calculations. By means of a diabatizing scheme that employs the transition densities obtained in the TDDFT calculations in many geometries around Re, we construct a Taylor series expansion in the normal coordinates of a diabatic potential energy matrix, coupling 24 excited states. The simulated vibronic structure is in good agreement with the experimental absorption spectrum after the adjustment of some of the calculated vertical excitation energies. The peculiar blurred vibronic structure of the second band, which is a very distinctive feature of the experimental spectrum, is fully reproduced in the calculations. It is caused by the double-well shape of the adiabatic energy surface along the Jahn-Teller active e mode of the allowed 1E state arising from the second 1T2 state, which exhibits a Jahn-Teller splitting into 1B2 and 1E states. We trace the double-well shape to an avoided crossing between two diabatic states with different orbital-excitation character. The crossing can be explained at the molecular orbital level from the Jahn-Teller splitting of the set of 7t2{3d(xy), 3d(xz), 3d(yz)} orbitals (the LUMO + 1), to which the excitations characterizing the diabatic states take place. In contrast to its character in the two well regions, at Re the 2(1)T2 state is not predominantly an excitation to the LUMO + 1, but has more HOMO - 1 --> LUMO (2e = {3d(x2-y2), 3d(z2)}) character. The changing character of the 2(1)T2 - 1E state along the e mode implies that the assignment of the experimental bands to single orbital transitions is too simplistic intrinsically. This spectrum, and notably the blurring of the vibronic structure in the second band, can be understood only from the extensive configurational mixing and vibronic coupling between the excited states. This solves the long-standing assignment problem of these bands.

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PubMed2004

Combined coupled-cluster and many-body perturbation theories.

Various approximations combining coupled-cluster (CC) and many-body perturbation theories have been derived and implemented into the parallel execution programs that take into account the spin, spatial (real Abelian), and permutation symmetries and that are applicable to closed- and open-shell molecules. The implemented models range from the CCSD(T), CCSD[T], CCSD(2)(T), CCSD(2)(TQ), and CCSDT(2)(Q) methods to the completely renormalized (CR) CCSD(T) and CCSD[T] approaches, where CCSD (CCSDT) stands for the CC method with connected single and double (single, double, and triple) cluster operators, and subscripted or parenthesized 2, T, and Q indicate the perturbation order or the excitation ranks of the cluster operators included in the corrections. The derivation and computer implementation have been automated by the algebraic and symbolic manipulation program TENSOR CONTRACTION ENGINE (TCE). The TCE-synthesized subroutines generate the tensors with the highest excitation rank in a blockwise manner so that they need not be stored in their entirety, while enabling the efficient reuse of other precalculated intermediate tensors defined by prioritizing the memory optimization as well as operation minimization. Consequently, the overall storage requirements for the corrections due to connected triple and quadruple cluster operators scale as O(n(4)) and O(n(6)), respectively (n being a measure of the system size). For systems with modest multireference character of their wave functions, we found that the order of accuracy is CCSD<CR-CCSD(T) approximately CCSD(2)(T) approximately CCSD(T)<CCSDT approximately CCSD(2)(TQ)<CCSDT(2)(Q), whereas CR-CCSD(T) is more effective in cases of larger quasidegeneracy. The operation costs of the TCE-generated CCSD(2)(TQ) and CCSDT(2)(Q) codes scale as rather steep O(n(9)), while the TCE-generated CCSD(T), CCSD(2)(T), and CR-CCSD(T) codes are near operation minimum [a noniterative O(n(7))]. The perturbative correction part of the CCSD(T)/cc-pVDZ calculations for azulene exhibited a 45-fold speedup upon a 64-fold increase in the number of processors from 8 to 512.

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PubMed2004

Vibronic coupling and double excitations in linear response time-dependent density functional calculations: dipole-allowed states of N2.

The present study serves two purposes. First, we evaluate the ability of present time-dependent density functional response theory (TDDFRT) methods to deal with avoided crossings, i.e., vibronic coupling effects. In the second place, taking the vibronic coupling effects into account enables us, by comparison to the configuration analysis in a recent ab initio study [J. Chem. Phys. 115, 6438 (2001)], to identify the neglect of double excitations as the prime cause of limited accuracy of these linear response based TDDFRT calculations for specific states. The "statistical averaging of (model) orbital potentials (SAOP)" Kohn-Sham potential is used together with the standard adiabatic local-density approximation (ALDA) for the exchange-correlation kernel. We use the N2 molecule as prototype, since the TDDFRT/SAOP calculations have already been shown to be accurate for the vertical excitations, while this molecule has a well-studied, intricate vibronic structure as well as significant double excitation nature in the lowest 1Pi(u) state at elongated bond lengths. A simple diabatizing scheme is employed to obtain a diabatic potential energy matrix, from which we obtain the absorption spectrum of N2 including vibronic coupling effects. Considering the six lowest dipole allowed transitions of 1Sigma(u)+ and 1Pi(u) symmetry, we observe a good general agreement and conclude that avoided crossings and vibronic coupling can indeed be treated satisfactorily on the basis of TDDFRT excitation energies. However, there is one state for which the accuracy of TDDFRT/ALDA clearly breaks down. This is the state for which the ab initio calculations find significant double excitation character. To deal with double excitation character is an important challenge for time-dependent density functional theory.

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PubMed2004

First principles simulation of the UV absorption spectrum of ethylene using the vertical Franck-Condon approach.

A new method which we refer to as vertical Franck-Condon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the short-time picture of spectroscopy, the excited-state potential energy surface is expanded at the ground-state equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 0-0 lines. The Born-Oppenheimer approximation and the separability of the excited-state potential energy surface along the excited-state normal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full one-dimensional potential is considered along this mode. The vertical Franck-Condon approach is applicable therefore even in cases where the excited state potential energy surface is highly anharmonic and the conventional harmonic Franck-Condon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50,000 cm(-1)) and 8.7 eV (70,000 cm(-1)) is simulated, using the Similarity Transformed Equation of Motion Coupled-Cluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the pi --> 3s (Rydberg) state superimposed on top of a broad band resulting from the pi --> pi* (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, CH2 scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical Franck-Condon method is required.

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